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<MASK>
Here's why that is the case.
#### Explanation:
<MASK>
Sugar, which is the common name used for sucrose, has the chemical formula ${\text{C"_12"H"_22"O}}_{11}$. Notice that one molecule of sucrose contains
<MASK>
This of course means that two molecules of water will have a smaller mass than two molecules of sugar.
<MASK>
<UNMASK>
# One mole of sugar has a greater mass than one mole of water, how come?
Feb 24, 2016
Here's why that is the case.
#### Explanation:
First of all, it's always a good idea to start with what a mole actually means, that way you can be sure that you know what you're looking at here.
<MASK>
So, how many molecules do we need in order to have "a whole lot"? Avogadro's number, $6.022 \cdot {10}^{23}$. This is what a mole actually means, a very, very large collection of molecules.
So, in order to have a mole of sugar, for example, you need to have $6.022 \cdot {10}^{23}$ molecules of sugar. Likewise, in order to have have one mole of water, you need to have $6.022 \cdot {10}^{23}$ molecules of water.
So, why does one mole of sugar weight more than one mole of water?
Because an individual molecule of sugar weighs more than an individual molecule of water.
Sugar, which is the common name used for sucrose, has the chemical formula ${\text{C"_12"H"_22"O}}_{11}$. Notice that one molecule of sucrose contains
• $12$ atoms of carbon
• $22$ atoms of hydrogen
• $11$ atoms of oxygen
Water has the chemical formula $\text{H"_2"O}$ and it contains
<MASK>
So one molecule of water will have a smaller mass than one molecule of sugar, since it contains fewer atoms.
This of course means that two molecules of water will have a smaller mass than two molecules of sugar.
The same goes for $10$ molecules of each substance, $100$, $1000$, and $6.022 \cdot {10}^{23}$.
This is why one mole of sugar has a bigger mass than one mole of water, because one molecule of sugar has a bigger mass than one molecule of water.
|
# One mole of sugar has a greater mass than one mole of water, how come?
Feb 24, 2016
Here's why that is the case.
#### Explanation:
First of all, it's always a good idea to start with what a mole actually means, that way you can be sure that you know what you're looking at here.
<MASK>
So, how many molecules do we need in order to have "a whole lot"? Avogadro's number, $6.022 \cdot {10}^{23}$. This is what a mole actually means, a very, very large collection of molecules.
So, in order to have a mole of sugar, for example, you need to have $6.022 \cdot {10}^{23}$ molecules of sugar. Likewise, in order to have have one mole of water, you need to have $6.022 \cdot {10}^{23}$ molecules of water.
So, why does one mole of sugar weight more than one mole of water?
Because an individual molecule of sugar weighs more than an individual molecule of water.
Sugar, which is the common name used for sucrose, has the chemical formula ${\text{C"_12"H"_22"O}}_{11}$. Notice that one molecule of sucrose contains
• $12$ atoms of carbon
• $22$ atoms of hydrogen
• $11$ atoms of oxygen
Water has the chemical formula $\text{H"_2"O}$ and it contains
<MASK>
So one molecule of water will have a smaller mass than one molecule of sugar, since it contains fewer atoms.
This of course means that two molecules of water will have a smaller mass than two molecules of sugar.
The same goes for $10$ molecules of each substance, $100$, $1000$, and $6.022 \cdot {10}^{23}$.
This is why one mole of sugar has a bigger mass than one mole of water, because one molecule of sugar has a bigger mass than one molecule of water.
<UNMASK>
# One mole of sugar has a greater mass than one mole of water, how come?
Feb 24, 2016
Here's why that is the case.
#### Explanation:
First of all, it's always a good idea to start with what a mole actually means, that way you can be sure that you know what you're looking at here.
Atoms and molecules are very, very small, which of course implies that they have very, very small masses, much, much smaller than the scale we're used to in our daily lives.
In order to be able to convert this molecular scale to something that's more familiar to us, like grams, we needed to group a whole lot of these molecules together.
So, how many molecules do we need in order to have "a whole lot"? Avogadro's number, $6.022 \cdot {10}^{23}$. This is what a mole actually means, a very, very large collection of molecules.
So, in order to have a mole of sugar, for example, you need to have $6.022 \cdot {10}^{23}$ molecules of sugar. Likewise, in order to have have one mole of water, you need to have $6.022 \cdot {10}^{23}$ molecules of water.
So, why does one mole of sugar weight more than one mole of water?
Because an individual molecule of sugar weighs more than an individual molecule of water.
Sugar, which is the common name used for sucrose, has the chemical formula ${\text{C"_12"H"_22"O}}_{11}$. Notice that one molecule of sucrose contains
• $12$ atoms of carbon
• $22$ atoms of hydrogen
• $11$ atoms of oxygen
Water has the chemical formula $\text{H"_2"O}$ and it contains
• $2$ atoms of hydrogen
• $1$ atom of oxygen
So one molecule of water will have a smaller mass than one molecule of sugar, since it contains fewer atoms.
This of course means that two molecules of water will have a smaller mass than two molecules of sugar.
The same goes for $10$ molecules of each substance, $100$, $1000$, and $6.022 \cdot {10}^{23}$.
This is why one mole of sugar has a bigger mass than one mole of water, because one molecule of sugar has a bigger mass than one molecule of water.
|
<MASK>
Commented:
As clear an explanation as possible.
0
Question has a verified solution.
<MASK>
<UNMASK>
# Statistics
<MASK>
In this case, it looks like there isn't enough information to solve the problem. If you don't know how rare the disease is (the probability of a random person having it), you have no way to filter out false positive results.
0
<MASK>
Commented:
As clear an explanation as possible.
0
Question has a verified solution.
<MASK>
|
# Statistics
<MASK>
In this case, it looks like there isn't enough information to solve the problem. If you don't know how rare the disease is (the probability of a random person having it), you have no way to filter out false positive results.
0
<MASK>
Commented:
As clear an explanation as possible.
0
Question has a verified solution.
<MASK>
<UNMASK>
# Statistics
<MASK>
Commented:
"Without making some assumption about the meaning of very rare, you can not give a quantitative answer.
False positives will dominate until the disease prevalence exceeds 1% of the population. "
d-glitch is correct. I was making some "reasonable" assumptions. But there are even more difficulties. The problem is a standard one emphasizing the often overlooked difficulty of the false negatives. Here the distinction is not made clear. Is there only one test? if so we are missing 1% of the population, etc
-
False Positives and False Negatives - Math is Fun
www.mathsisfun.com/data/probability-false-negatives-positives.html
Maths Is Fun
False Positives and False Negatives. Test Says "Yes" ... or does it? When you have a test that can say "Yes" or "No" (such as a medical test), you have to think:.
0
<MASK>
If this is a homework question (and it looks like it might be), you need to say so up front and explain how far you have gotten and/or what you are having trouble with.
In this case, it looks like there isn't enough information to solve the problem. If you don't know how rare the disease is (the probability of a random person having it), you have no way to filter out false positive results.
0
Commented:
Assume the prevalence of the disease is one case per million people.
If one million people take the test, how many TRUE Positives will there be?
And how many FALSE Positives?
0
<MASK>
False positives will dominate until the disease prevalence exceeds 1% of the population.
0
Commented:
As clear an explanation as possible.
0
Question has a verified solution.
Are you are experiencing a similar issue? Get a personalized answer when you ask a related question.
Have a better answer? Share it in a comment.
|
# Statistics
<MASK>
Commented:
"Without making some assumption about the meaning of very rare, you can not give a quantitative answer.
False positives will dominate until the disease prevalence exceeds 1% of the population. "
d-glitch is correct. I was making some "reasonable" assumptions. But there are even more difficulties. The problem is a standard one emphasizing the often overlooked difficulty of the false negatives. Here the distinction is not made clear. Is there only one test? if so we are missing 1% of the population, etc
-
False Positives and False Negatives - Math is Fun
www.mathsisfun.com/data/probability-false-negatives-positives.html
Maths Is Fun
False Positives and False Negatives. Test Says "Yes" ... or does it? When you have a test that can say "Yes" or "No" (such as a medical test), you have to think:.
0
<MASK>
If this is a homework question (and it looks like it might be), you need to say so up front and explain how far you have gotten and/or what you are having trouble with.
In this case, it looks like there isn't enough information to solve the problem. If you don't know how rare the disease is (the probability of a random person having it), you have no way to filter out false positive results.
0
Commented:
Assume the prevalence of the disease is one case per million people.
If one million people take the test, how many TRUE Positives will there be?
And how many FALSE Positives?
0
<MASK>
False positives will dominate until the disease prevalence exceeds 1% of the population.
0
Commented:
As clear an explanation as possible.
0
Question has a verified solution.
Are you are experiencing a similar issue? Get a personalized answer when you ask a related question.
Have a better answer? Share it in a comment.
<UNMASK>
# Statistics
A clinic offers you a free test for a very rare, but hideous disease. The test they offer is very reliable. If you have the disease it has a 98% chance of giving a positive result, and if you don’t have the disease, it has only a 1% chance of giving a positive result. You decide to take the test, and find that you test positive. What is the probability that you have the disease?
###### Who is Participating?
Commented:
"Without making some assumption about the meaning of very rare, you can not give a quantitative answer.
False positives will dominate until the disease prevalence exceeds 1% of the population. "
d-glitch is correct. I was making some "reasonable" assumptions. But there are even more difficulties. The problem is a standard one emphasizing the often overlooked difficulty of the false negatives. Here the distinction is not made clear. Is there only one test? if so we are missing 1% of the population, etc
-
False Positives and False Negatives - Math is Fun
www.mathsisfun.com/data/probability-false-negatives-positives.html
Maths Is Fun
False Positives and False Negatives. Test Says "Yes" ... or does it? When you have a test that can say "Yes" or "No" (such as a medical test), you have to think:.
0
<MASK>
If this is a homework question (and it looks like it might be), you need to say so up front and explain how far you have gotten and/or what you are having trouble with.
In this case, it looks like there isn't enough information to solve the problem. If you don't know how rare the disease is (the probability of a random person having it), you have no way to filter out false positive results.
0
Commented:
Assume the prevalence of the disease is one case per million people.
If one million people take the test, how many TRUE Positives will there be?
And how many FALSE Positives?
0
Commented:
"In this case, it looks like there isn't enough information to solve the problem."
There is enough info to answer.
You have to combine two known probabilities.
If home work, show what you have done so far
0
Commented:
Without making some assumption about the meaning of very rare, you can not give a quantitative answer.
False positives will dominate until the disease prevalence exceeds 1% of the population.
0
Commented:
As clear an explanation as possible.
0
Question has a verified solution.
Are you are experiencing a similar issue? Get a personalized answer when you ask a related question.
Have a better answer? Share it in a comment.
|
# Statistics
A clinic offers you a free test for a very rare, but hideous disease. The test they offer is very reliable. If you have the disease it has a 98% chance of giving a positive result, and if you don’t have the disease, it has only a 1% chance of giving a positive result. You decide to take the test, and find that you test positive. What is the probability that you have the disease?
###### Who is Participating?
Commented:
"Without making some assumption about the meaning of very rare, you can not give a quantitative answer.
False positives will dominate until the disease prevalence exceeds 1% of the population. "
d-glitch is correct. I was making some "reasonable" assumptions. But there are even more difficulties. The problem is a standard one emphasizing the often overlooked difficulty of the false negatives. Here the distinction is not made clear. Is there only one test? if so we are missing 1% of the population, etc
-
False Positives and False Negatives - Math is Fun
www.mathsisfun.com/data/probability-false-negatives-positives.html
Maths Is Fun
False Positives and False Negatives. Test Says "Yes" ... or does it? When you have a test that can say "Yes" or "No" (such as a medical test), you have to think:.
0
<MASK>
If this is a homework question (and it looks like it might be), you need to say so up front and explain how far you have gotten and/or what you are having trouble with.
In this case, it looks like there isn't enough information to solve the problem. If you don't know how rare the disease is (the probability of a random person having it), you have no way to filter out false positive results.
0
Commented:
Assume the prevalence of the disease is one case per million people.
If one million people take the test, how many TRUE Positives will there be?
And how many FALSE Positives?
0
Commented:
"In this case, it looks like there isn't enough information to solve the problem."
There is enough info to answer.
You have to combine two known probabilities.
If home work, show what you have done so far
0
Commented:
Without making some assumption about the meaning of very rare, you can not give a quantitative answer.
False positives will dominate until the disease prevalence exceeds 1% of the population.
0
Commented:
As clear an explanation as possible.
0
Question has a verified solution.
Are you are experiencing a similar issue? Get a personalized answer when you ask a related question.
Have a better answer? Share it in a comment.
<UNMASK>
# Statistics
A clinic offers you a free test for a very rare, but hideous disease. The test they offer is very reliable. If you have the disease it has a 98% chance of giving a positive result, and if you don’t have the disease, it has only a 1% chance of giving a positive result. You decide to take the test, and find that you test positive. What is the probability that you have the disease?
###### Who is Participating?
Commented:
"Without making some assumption about the meaning of very rare, you can not give a quantitative answer.
False positives will dominate until the disease prevalence exceeds 1% of the population. "
d-glitch is correct. I was making some "reasonable" assumptions. But there are even more difficulties. The problem is a standard one emphasizing the often overlooked difficulty of the false negatives. Here the distinction is not made clear. Is there only one test? if so we are missing 1% of the population, etc
-
False Positives and False Negatives - Math is Fun
www.mathsisfun.com/data/probability-false-negatives-positives.html
Maths Is Fun
False Positives and False Negatives. Test Says "Yes" ... or does it? When you have a test that can say "Yes" or "No" (such as a medical test), you have to think:.
0
Commented:
Welcome to Experts Exchange. I see this is your first question.
If this is a homework question (and it looks like it might be), you need to say so up front and explain how far you have gotten and/or what you are having trouble with.
In this case, it looks like there isn't enough information to solve the problem. If you don't know how rare the disease is (the probability of a random person having it), you have no way to filter out false positive results.
0
Commented:
Assume the prevalence of the disease is one case per million people.
If one million people take the test, how many TRUE Positives will there be?
And how many FALSE Positives?
0
Commented:
"In this case, it looks like there isn't enough information to solve the problem."
There is enough info to answer.
You have to combine two known probabilities.
If home work, show what you have done so far
0
Commented:
Without making some assumption about the meaning of very rare, you can not give a quantitative answer.
False positives will dominate until the disease prevalence exceeds 1% of the population.
0
Commented:
As clear an explanation as possible.
0
Question has a verified solution.
Are you are experiencing a similar issue? Get a personalized answer when you ask a related question.
Have a better answer? Share it in a comment.
|
<MASK>
There are three ways to write down these new 4-byte AS numbers:
• Asplain
• Asdot
• Asdot+
<MASK>
Asdot represents AS numbers less than 65536 using the asplain notation and AS numbers above 65536 with the asdot+ notation.
Asdot+ breaks the AS number in two 16-bit parts, a high-order value, and a low-order value, separated by a dot. All older AS numbers can fit in the second part where the first part is set to 0. For example:
• AS 6541 becomes 0.6541
• AS 54233 becomes 0.54233
• AS 544 becomes 0.544
<MASK>
• AS 65536 becomes 1.0
• AS 65537 becomes 1.1
• AS 65538 becomes 1.2
<MASK>
Once you understand how the conversion is done, you can use the APNIC asplain to asdot calculator to convert this automatically and make your life a bit easier.
<MASK>
``````R1(config)#router bgp ?
<1-4294967295> Autonomous system number
<1.0-XX.YY> Autonomous system number``````
<MASK>
R2
<MASK>
### We're Sorry, Full Content Access is for Members Only...
<MASK>
## Forum Replies
<MASK>
You can see it in the wireshark capture:
https://www.cloudshark.org/captures/d8e5e9240959
<MASK>
In case of we adding R3 (AS3) and connect it to R2. R1 advertises one prefix (for example: 1.1.1.1/32) to R2 and R2 will forward to R3.
What will be in the AS path on R3? (22222222 1 or 23456 1)?
<MASK>
4. Hello Minh
<MASK>
<UNMASK>
<MASK>
There are three ways to write down these new 4-byte AS numbers:
• Asplain
• Asdot
• Asdot+
<MASK>
Asdot represents AS numbers less than 65536 using the asplain notation and AS numbers above 65536 with the asdot+ notation.
Asdot+ breaks the AS number in two 16-bit parts, a high-order value, and a low-order value, separated by a dot. All older AS numbers can fit in the second part where the first part is set to 0. For example:
• AS 6541 becomes 0.6541
• AS 54233 becomes 0.54233
• AS 544 becomes 0.544
<MASK>
• AS 65536 becomes 1.0
• AS 65537 becomes 1.1
• AS 65538 becomes 1.2
<MASK>
Once you understand how the conversion is done, you can use the APNIC asplain to asdot calculator to convert this automatically and make your life a bit easier.
<MASK>
### 4-byte AS support
<MASK>
``````R1(config)#router bgp ?
<1-4294967295> Autonomous system number
<1.0-XX.YY> Autonomous system number``````
<MASK>
Want to take a look for yourself? Here you will find the startup configuration of each device.
<MASK>
R2
<MASK>
### 2-byte AS support
<MASK>
### We're Sorry, Full Content Access is for Members Only...
<MASK>
## Forum Replies
<MASK>
br//zaman
<MASK>
You can see it in the wireshark capture:
https://www.cloudshark.org/captures/d8e5e9240959
Take a look at the 1st packet from R2 and the 2nd packet from R1. R1 is missing the capability.
<MASK>
In case of we adding R3 (AS3) and connect it to R2. R1 advertises one prefix (for example: 1.1.1.1/32) to R2 and R2 will forward to R3.
What will be in the AS path on R3? (22222222 1 or 23456 1)?
<MASK>
4. Hello Minh
<MASK>
|
<MASK>
There are three ways to write down these new 4-byte AS numbers:
• Asplain
• Asdot
• Asdot+
<MASK>
Asdot represents AS numbers less than 65536 using the asplain notation and AS numbers above 65536 with the asdot+ notation.
Asdot+ breaks the AS number in two 16-bit parts, a high-order value, and a low-order value, separated by a dot. All older AS numbers can fit in the second part where the first part is set to 0. For example:
• AS 6541 becomes 0.6541
• AS 54233 becomes 0.54233
• AS 544 becomes 0.544
<MASK>
• AS 65536 becomes 1.0
• AS 65537 becomes 1.1
• AS 65538 becomes 1.2
<MASK>
Once you understand how the conversion is done, you can use the APNIC asplain to asdot calculator to convert this automatically and make your life a bit easier.
<MASK>
### 4-byte AS support
<MASK>
``````R1(config)#router bgp ?
<1-4294967295> Autonomous system number
<1.0-XX.YY> Autonomous system number``````
<MASK>
Want to take a look for yourself? Here you will find the startup configuration of each device.
<MASK>
R2
<MASK>
### 2-byte AS support
<MASK>
### We're Sorry, Full Content Access is for Members Only...
<MASK>
## Forum Replies
<MASK>
br//zaman
<MASK>
You can see it in the wireshark capture:
https://www.cloudshark.org/captures/d8e5e9240959
Take a look at the 1st packet from R2 and the 2nd packet from R1. R1 is missing the capability.
<MASK>
In case of we adding R3 (AS3) and connect it to R2. R1 advertises one prefix (for example: 1.1.1.1/32) to R2 and R2 will forward to R3.
What will be in the AS path on R3? (22222222 1 or 23456 1)?
<MASK>
4. Hello Minh
<MASK>
<UNMASK>
# BGP 4-Byte AS Number
Lesson Contents
<MASK>
There are three ways to write down these new 4-byte AS numbers:
• Asplain
• Asdot
• Asdot+
<MASK>
Asdot represents AS numbers less than 65536 using the asplain notation and AS numbers above 65536 with the asdot+ notation.
Asdot+ breaks the AS number in two 16-bit parts, a high-order value, and a low-order value, separated by a dot. All older AS numbers can fit in the second part where the first part is set to 0. For example:
• AS 6541 becomes 0.6541
• AS 54233 becomes 0.54233
• AS 544 becomes 0.544
<MASK>
• AS 65536 becomes 1.0
• AS 65537 becomes 1.1
• AS 65538 becomes 1.2
<MASK>
Then, you take the asplain number and deduct (65536 * the integer) to get your low order bit value. In other words, this is the formula:
<MASK>
Once you understand how the conversion is done, you can use the APNIC asplain to asdot calculator to convert this automatically and make your life a bit easier.
<MASK>
• Two routers that both have 4-byte AS support.
• Two routers where one router only has 2-byte AS support.
### 4-byte AS support
We have two routers:
Both routers support 4-byte AS numbers. You can see this when you configure the AS number:
``````R1(config)#router bgp ?
<1-4294967295> Autonomous system number
<1.0-XX.YY> Autonomous system number``````
<MASK>
``````R1(config)#router bgp 12000012
R1(config-router)#neighbor 192.168.12.2 remote-as 12000012``````
``````R2(config)#router bgp 12000012
R2(config-router)#neighbor 192.168.12.1 remote-as 12000012``````
<MASK>
``````R1(config-router)#bgp asnotation ?
dot asdot notation``````
Let’s change it:
<MASK>
Want to take a look for yourself? Here you will find the startup configuration of each device.
R1
``````hostname R1
!
ip cef
!
interface GigabitEthernet0/1
!
router bgp 183.6924
bgp asnotation dot
neighbor 192.168.12.2 remote-as 183.6924
!
end``````
R2
<MASK>
### 2-byte AS support
<MASK>
### We're Sorry, Full Content Access is for Members Only...
<MASK>
• Learn any CCNA, CCNP and CCIE R&S Topic. Explained As Simple As Possible.
• Try for Just \$1. The Best Dollar You’ve Ever Spent on Your Cisco Career!
• Content created by Rene Molenaar (CCIE #41726)
<MASK>
## Forum Replies
1. Hi Rene,
Very Good Stuff.A quick questions for you …
How R2 know R1 only 2 byte supported before sending any open message ??
br//zaman
2. Hi Zaman,
It doesn’t. When R2 receives a reply from R1 without the “support for 4-octet AS number capability” in its OPEN message, it knows that R1 doesn’t support it.
You can see it in the wireshark capture:
https://www.cloudshark.org/captures/d8e5e9240959
Take a look at the 1st packet from R2 and the 2nd packet from R1. R1 is missing the capability.
<MASK>
3. Hi Rene,
I have question in 2-Byte & 4-Byte AS compatibility situation.
In case of we adding R3 (AS3) and connect it to R2. R1 advertises one prefix (for example: 1.1.1.1/32) to R2 and R2 will forward to R3.
What will be in the AS path on R3? (22222222 1 or 23456 1)?
Thanks,
Minh
4. Hello Minh
This is an excellent question. Essentially what you are asking (allow me to put it more generally) is how is the AS path displayed when there is a 2-byte AS compatible router in the mix?
Well, if you display the AS path on the 2-byte AS compatible router, then you will see the 23456 AS in place of the incompatible 4-byte AS number. So essentially the AS_TRANS attribute replaces the 4-byte AS number. However, the AS4 PATH number is an attribute that is received by the 2-byte AS compatible device, and is transitive. It may not understand it, but it
... Continue reading in our forum
<MASK>
|
# BGP 4-Byte AS Number
Lesson Contents
<MASK>
There are three ways to write down these new 4-byte AS numbers:
• Asplain
• Asdot
• Asdot+
<MASK>
Asdot represents AS numbers less than 65536 using the asplain notation and AS numbers above 65536 with the asdot+ notation.
Asdot+ breaks the AS number in two 16-bit parts, a high-order value, and a low-order value, separated by a dot. All older AS numbers can fit in the second part where the first part is set to 0. For example:
• AS 6541 becomes 0.6541
• AS 54233 becomes 0.54233
• AS 544 becomes 0.544
<MASK>
• AS 65536 becomes 1.0
• AS 65537 becomes 1.1
• AS 65538 becomes 1.2
<MASK>
Then, you take the asplain number and deduct (65536 * the integer) to get your low order bit value. In other words, this is the formula:
<MASK>
Once you understand how the conversion is done, you can use the APNIC asplain to asdot calculator to convert this automatically and make your life a bit easier.
<MASK>
• Two routers that both have 4-byte AS support.
• Two routers where one router only has 2-byte AS support.
### 4-byte AS support
We have two routers:
Both routers support 4-byte AS numbers. You can see this when you configure the AS number:
``````R1(config)#router bgp ?
<1-4294967295> Autonomous system number
<1.0-XX.YY> Autonomous system number``````
<MASK>
``````R1(config)#router bgp 12000012
R1(config-router)#neighbor 192.168.12.2 remote-as 12000012``````
``````R2(config)#router bgp 12000012
R2(config-router)#neighbor 192.168.12.1 remote-as 12000012``````
<MASK>
``````R1(config-router)#bgp asnotation ?
dot asdot notation``````
Let’s change it:
<MASK>
Want to take a look for yourself? Here you will find the startup configuration of each device.
R1
``````hostname R1
!
ip cef
!
interface GigabitEthernet0/1
!
router bgp 183.6924
bgp asnotation dot
neighbor 192.168.12.2 remote-as 183.6924
!
end``````
R2
<MASK>
### 2-byte AS support
<MASK>
### We're Sorry, Full Content Access is for Members Only...
<MASK>
• Learn any CCNA, CCNP and CCIE R&S Topic. Explained As Simple As Possible.
• Try for Just \$1. The Best Dollar You’ve Ever Spent on Your Cisco Career!
• Content created by Rene Molenaar (CCIE #41726)
<MASK>
## Forum Replies
1. Hi Rene,
Very Good Stuff.A quick questions for you …
How R2 know R1 only 2 byte supported before sending any open message ??
br//zaman
2. Hi Zaman,
It doesn’t. When R2 receives a reply from R1 without the “support for 4-octet AS number capability” in its OPEN message, it knows that R1 doesn’t support it.
You can see it in the wireshark capture:
https://www.cloudshark.org/captures/d8e5e9240959
Take a look at the 1st packet from R2 and the 2nd packet from R1. R1 is missing the capability.
<MASK>
3. Hi Rene,
I have question in 2-Byte & 4-Byte AS compatibility situation.
In case of we adding R3 (AS3) and connect it to R2. R1 advertises one prefix (for example: 1.1.1.1/32) to R2 and R2 will forward to R3.
What will be in the AS path on R3? (22222222 1 or 23456 1)?
Thanks,
Minh
4. Hello Minh
This is an excellent question. Essentially what you are asking (allow me to put it more generally) is how is the AS path displayed when there is a 2-byte AS compatible router in the mix?
Well, if you display the AS path on the 2-byte AS compatible router, then you will see the 23456 AS in place of the incompatible 4-byte AS number. So essentially the AS_TRANS attribute replaces the 4-byte AS number. However, the AS4 PATH number is an attribute that is received by the 2-byte AS compatible device, and is transitive. It may not understand it, but it
... Continue reading in our forum
<MASK>
<UNMASK>
# BGP 4-Byte AS Number
Lesson Contents
<MASK>
Similar to IPv4, we started running out of AS numbers so IANA increased the AS numbers by introducing 4-byte AS numbers in the range of 65536 to 4294967295.
There are three ways to write down these new 4-byte AS numbers:
• Asplain
• Asdot
• Asdot+
Asplain is the most simple to understand, these are just regular decimal numbers. For example, AS number 545435, 4294937295, 4254967294, 2294967295, etc. These numbers are simple to understand but prone to errors. It’s easy to make a configuration mistake or misread a number in the BGP table.
Asdot represents AS numbers less than 65536 using the asplain notation and AS numbers above 65536 with the asdot+ notation.
Asdot+ breaks the AS number in two 16-bit parts, a high-order value, and a low-order value, separated by a dot. All older AS numbers can fit in the second part where the first part is set to 0. For example:
• AS 6541 becomes 0.6541
• AS 54233 becomes 0.54233
• AS 544 becomes 0.544
For AS numbers above 65535, we use the next high order bit value and start counting again at 0. For example:
• AS 65536 becomes 1.0
• AS 65537 becomes 1.1
• AS 65538 becomes 1.2
These numbers are easier to read but harder to calculate than the asplain numbers, it’s also a bit trickier to create regular expressions.
If you want to convert an asplain AS number to an asdot+ AS number, you take the asplain number and see how many times you can divide it by 65536. This is the integer that we use for the high order bit value.
Then, you take the asplain number and deduct (65536 * the integer) to get your low order bit value. In other words, this is the formula:
``````integer (high order bit value) = asplain / 65536
remainder (low order bit value) = asplain - (integer * 65536)
asdot value = integer.remainder``````
Here are two examples:
``````#AS 5434995
5434995 / 65536 = 82
5434995 - (82 * 65536) = 61043
asdot = 82.61043``````
``````#AS 1499547
1499547 / 65536 = 22
1499547 - (22 * 65536) = 57755
asdot = 22.57755``````
Once you understand how the conversion is done, you can use the APNIC asplain to asdot calculator to convert this automatically and make your life a bit easier.
BGP speakers that support 4-byte AS numbers advertise this via BGP capability negotiation and there is backward compatibility. When a “new” router talks to an “old” router (one that only supports 2-byte AS numbers), it can use a reserved AS number (23456) called AS_TRANS instead of its 4-byte AS number. I’ll show you how this works in the configuration.
## Configuration
Cisco routers support the asplain and asdot representations. The configuration is pretty straightforward and I’ll show you two scenarios:
• Two routers that both have 4-byte AS support.
• Two routers where one router only has 2-byte AS support.
### 4-byte AS support
We have two routers:
Both routers support 4-byte AS numbers. You can see this when you configure the AS number:
``````R1(config)#router bgp ?
<1-4294967295> Autonomous system number
<1.0-XX.YY> Autonomous system number``````
As you can see, this IOS router supports asplain and asdot numbers. Let’s pick asplain and establish a BGP neighbor adjacency:
``````R1(config)#router bgp 12000012
R1(config-router)#neighbor 192.168.12.2 remote-as 12000012``````
``````R2(config)#router bgp 12000012
R2(config-router)#neighbor 192.168.12.1 remote-as 12000012``````
<MASK>
``````R1#show ip bgp summary
BGP router identifier 192.168.12.1, local AS number 12000012
BGP table version is 1, main routing table version 1
<MASK>
If you want, you can change the representation to the asdot format:
``````R1(config-router)#bgp asnotation ?
dot asdot notation``````
Let’s change it:
``R1(config-router)#bgp asnotation dot``
You will now see the asdot format in all show commands:
``````R1#show ip bgp summary
BGP router identifier 192.168.12.1, local AS number 183.6924
BGP table version is 1, main routing table version 1
Neighbor V AS MsgRcvd MsgSent TblVer InQ OutQ Up/Down State/PfxRcd
192.168.12.2 4 183.6924 6 6 1 0 0 00:02:38 0``````
AS 12000012 now shows up as AS 183.6924.
Configurations
Want to take a look for yourself? Here you will find the startup configuration of each device.
R1
``````hostname R1
!
ip cef
!
interface GigabitEthernet0/1
!
router bgp 183.6924
bgp asnotation dot
neighbor 192.168.12.2 remote-as 183.6924
!
end``````
R2
<MASK>
### 2-byte AS support
<MASK>
R1 has no clue what an AS number above 65535 is:
### We're Sorry, Full Content Access is for Members Only...
If you like to keep on reading, Become a Member Now! Here is why:
• Learn any CCNA, CCNP and CCIE R&S Topic. Explained As Simple As Possible.
• Try for Just \$1. The Best Dollar You’ve Ever Spent on Your Cisco Career!
• Content created by Rene Molenaar (CCIE #41726)
100% Satisfaction Guaranteed!
You may cancel your monthly membership at any time.
Tags: ,
## Forum Replies
1. Hi Rene,
Very Good Stuff.A quick questions for you …
How R2 know R1 only 2 byte supported before sending any open message ??
br//zaman
2. Hi Zaman,
It doesn’t. When R2 receives a reply from R1 without the “support for 4-octet AS number capability” in its OPEN message, it knows that R1 doesn’t support it.
You can see it in the wireshark capture:
https://www.cloudshark.org/captures/d8e5e9240959
Take a look at the 1st packet from R2 and the 2nd packet from R1. R1 is missing the capability.
<MASK>
Rene
3. Hi Rene,
I have question in 2-Byte & 4-Byte AS compatibility situation.
In case of we adding R3 (AS3) and connect it to R2. R1 advertises one prefix (for example: 1.1.1.1/32) to R2 and R2 will forward to R3.
What will be in the AS path on R3? (22222222 1 or 23456 1)?
Thanks,
Minh
4. Hello Minh
This is an excellent question. Essentially what you are asking (allow me to put it more generally) is how is the AS path displayed when there is a 2-byte AS compatible router in the mix?
Well, if you display the AS path on the 2-byte AS compatible router, then you will see the 23456 AS in place of the incompatible 4-byte AS number. So essentially the AS_TRANS attribute replaces the 4-byte AS number. However, the AS4 PATH number is an attribute that is received by the 2-byte AS compatible device, and is transitive. It may not understand it, but it
... Continue reading in our forum
5. Thanks Laz for the explanation.
|
# BGP 4-Byte AS Number
Lesson Contents
<MASK>
Similar to IPv4, we started running out of AS numbers so IANA increased the AS numbers by introducing 4-byte AS numbers in the range of 65536 to 4294967295.
There are three ways to write down these new 4-byte AS numbers:
• Asplain
• Asdot
• Asdot+
Asplain is the most simple to understand, these are just regular decimal numbers. For example, AS number 545435, 4294937295, 4254967294, 2294967295, etc. These numbers are simple to understand but prone to errors. It’s easy to make a configuration mistake or misread a number in the BGP table.
Asdot represents AS numbers less than 65536 using the asplain notation and AS numbers above 65536 with the asdot+ notation.
Asdot+ breaks the AS number in two 16-bit parts, a high-order value, and a low-order value, separated by a dot. All older AS numbers can fit in the second part where the first part is set to 0. For example:
• AS 6541 becomes 0.6541
• AS 54233 becomes 0.54233
• AS 544 becomes 0.544
For AS numbers above 65535, we use the next high order bit value and start counting again at 0. For example:
• AS 65536 becomes 1.0
• AS 65537 becomes 1.1
• AS 65538 becomes 1.2
These numbers are easier to read but harder to calculate than the asplain numbers, it’s also a bit trickier to create regular expressions.
If you want to convert an asplain AS number to an asdot+ AS number, you take the asplain number and see how many times you can divide it by 65536. This is the integer that we use for the high order bit value.
Then, you take the asplain number and deduct (65536 * the integer) to get your low order bit value. In other words, this is the formula:
``````integer (high order bit value) = asplain / 65536
remainder (low order bit value) = asplain - (integer * 65536)
asdot value = integer.remainder``````
Here are two examples:
``````#AS 5434995
5434995 / 65536 = 82
5434995 - (82 * 65536) = 61043
asdot = 82.61043``````
``````#AS 1499547
1499547 / 65536 = 22
1499547 - (22 * 65536) = 57755
asdot = 22.57755``````
Once you understand how the conversion is done, you can use the APNIC asplain to asdot calculator to convert this automatically and make your life a bit easier.
BGP speakers that support 4-byte AS numbers advertise this via BGP capability negotiation and there is backward compatibility. When a “new” router talks to an “old” router (one that only supports 2-byte AS numbers), it can use a reserved AS number (23456) called AS_TRANS instead of its 4-byte AS number. I’ll show you how this works in the configuration.
## Configuration
Cisco routers support the asplain and asdot representations. The configuration is pretty straightforward and I’ll show you two scenarios:
• Two routers that both have 4-byte AS support.
• Two routers where one router only has 2-byte AS support.
### 4-byte AS support
We have two routers:
Both routers support 4-byte AS numbers. You can see this when you configure the AS number:
``````R1(config)#router bgp ?
<1-4294967295> Autonomous system number
<1.0-XX.YY> Autonomous system number``````
As you can see, this IOS router supports asplain and asdot numbers. Let’s pick asplain and establish a BGP neighbor adjacency:
``````R1(config)#router bgp 12000012
R1(config-router)#neighbor 192.168.12.2 remote-as 12000012``````
``````R2(config)#router bgp 12000012
R2(config-router)#neighbor 192.168.12.1 remote-as 12000012``````
<MASK>
``````R1#show ip bgp summary
BGP router identifier 192.168.12.1, local AS number 12000012
BGP table version is 1, main routing table version 1
<MASK>
If you want, you can change the representation to the asdot format:
``````R1(config-router)#bgp asnotation ?
dot asdot notation``````
Let’s change it:
``R1(config-router)#bgp asnotation dot``
You will now see the asdot format in all show commands:
``````R1#show ip bgp summary
BGP router identifier 192.168.12.1, local AS number 183.6924
BGP table version is 1, main routing table version 1
Neighbor V AS MsgRcvd MsgSent TblVer InQ OutQ Up/Down State/PfxRcd
192.168.12.2 4 183.6924 6 6 1 0 0 00:02:38 0``````
AS 12000012 now shows up as AS 183.6924.
Configurations
Want to take a look for yourself? Here you will find the startup configuration of each device.
R1
``````hostname R1
!
ip cef
!
interface GigabitEthernet0/1
!
router bgp 183.6924
bgp asnotation dot
neighbor 192.168.12.2 remote-as 183.6924
!
end``````
R2
<MASK>
### 2-byte AS support
<MASK>
R1 has no clue what an AS number above 65535 is:
### We're Sorry, Full Content Access is for Members Only...
If you like to keep on reading, Become a Member Now! Here is why:
• Learn any CCNA, CCNP and CCIE R&S Topic. Explained As Simple As Possible.
• Try for Just \$1. The Best Dollar You’ve Ever Spent on Your Cisco Career!
• Content created by Rene Molenaar (CCIE #41726)
100% Satisfaction Guaranteed!
You may cancel your monthly membership at any time.
Tags: ,
## Forum Replies
1. Hi Rene,
Very Good Stuff.A quick questions for you …
How R2 know R1 only 2 byte supported before sending any open message ??
br//zaman
2. Hi Zaman,
It doesn’t. When R2 receives a reply from R1 without the “support for 4-octet AS number capability” in its OPEN message, it knows that R1 doesn’t support it.
You can see it in the wireshark capture:
https://www.cloudshark.org/captures/d8e5e9240959
Take a look at the 1st packet from R2 and the 2nd packet from R1. R1 is missing the capability.
<MASK>
Rene
3. Hi Rene,
I have question in 2-Byte & 4-Byte AS compatibility situation.
In case of we adding R3 (AS3) and connect it to R2. R1 advertises one prefix (for example: 1.1.1.1/32) to R2 and R2 will forward to R3.
What will be in the AS path on R3? (22222222 1 or 23456 1)?
Thanks,
Minh
4. Hello Minh
This is an excellent question. Essentially what you are asking (allow me to put it more generally) is how is the AS path displayed when there is a 2-byte AS compatible router in the mix?
Well, if you display the AS path on the 2-byte AS compatible router, then you will see the 23456 AS in place of the incompatible 4-byte AS number. So essentially the AS_TRANS attribute replaces the 4-byte AS number. However, the AS4 PATH number is an attribute that is received by the 2-byte AS compatible device, and is transitive. It may not understand it, but it
... Continue reading in our forum
5. Thanks Laz for the explanation.
<UNMASK>
# BGP 4-Byte AS Number
Lesson Contents
Before January 2009, we only had 2 byte AS numbers in the range of 1-65535. 1024 of those (64512-65534) are reserved for private AS numbers.
Similar to IPv4, we started running out of AS numbers so IANA increased the AS numbers by introducing 4-byte AS numbers in the range of 65536 to 4294967295.
There are three ways to write down these new 4-byte AS numbers:
• Asplain
• Asdot
• Asdot+
Asplain is the most simple to understand, these are just regular decimal numbers. For example, AS number 545435, 4294937295, 4254967294, 2294967295, etc. These numbers are simple to understand but prone to errors. It’s easy to make a configuration mistake or misread a number in the BGP table.
Asdot represents AS numbers less than 65536 using the asplain notation and AS numbers above 65536 with the asdot+ notation.
Asdot+ breaks the AS number in two 16-bit parts, a high-order value, and a low-order value, separated by a dot. All older AS numbers can fit in the second part where the first part is set to 0. For example:
• AS 6541 becomes 0.6541
• AS 54233 becomes 0.54233
• AS 544 becomes 0.544
For AS numbers above 65535, we use the next high order bit value and start counting again at 0. For example:
• AS 65536 becomes 1.0
• AS 65537 becomes 1.1
• AS 65538 becomes 1.2
These numbers are easier to read but harder to calculate than the asplain numbers, it’s also a bit trickier to create regular expressions.
If you want to convert an asplain AS number to an asdot+ AS number, you take the asplain number and see how many times you can divide it by 65536. This is the integer that we use for the high order bit value.
Then, you take the asplain number and deduct (65536 * the integer) to get your low order bit value. In other words, this is the formula:
``````integer (high order bit value) = asplain / 65536
remainder (low order bit value) = asplain - (integer * 65536)
asdot value = integer.remainder``````
Here are two examples:
``````#AS 5434995
5434995 / 65536 = 82
5434995 - (82 * 65536) = 61043
asdot = 82.61043``````
``````#AS 1499547
1499547 / 65536 = 22
1499547 - (22 * 65536) = 57755
asdot = 22.57755``````
Once you understand how the conversion is done, you can use the APNIC asplain to asdot calculator to convert this automatically and make your life a bit easier.
BGP speakers that support 4-byte AS numbers advertise this via BGP capability negotiation and there is backward compatibility. When a “new” router talks to an “old” router (one that only supports 2-byte AS numbers), it can use a reserved AS number (23456) called AS_TRANS instead of its 4-byte AS number. I’ll show you how this works in the configuration.
## Configuration
Cisco routers support the asplain and asdot representations. The configuration is pretty straightforward and I’ll show you two scenarios:
• Two routers that both have 4-byte AS support.
• Two routers where one router only has 2-byte AS support.
### 4-byte AS support
We have two routers:
Both routers support 4-byte AS numbers. You can see this when you configure the AS number:
``````R1(config)#router bgp ?
<1-4294967295> Autonomous system number
<1.0-XX.YY> Autonomous system number``````
As you can see, this IOS router supports asplain and asdot numbers. Let’s pick asplain and establish a BGP neighbor adjacency:
``````R1(config)#router bgp 12000012
R1(config-router)#neighbor 192.168.12.2 remote-as 12000012``````
``````R2(config)#router bgp 12000012
R2(config-router)#neighbor 192.168.12.1 remote-as 12000012``````
You can see the asplain AS numbers in all bgp show commands:
``````R1#show ip bgp summary
BGP router identifier 192.168.12.1, local AS number 12000012
BGP table version is 1, main routing table version 1
Neighbor V AS MsgRcvd MsgSent TblVer InQ OutQ Up/Down State/PfxRcd
192.168.12.2 4 12000012 5 5 1 0 0 00:01:02 0``````
If you want, you can change the representation to the asdot format:
``````R1(config-router)#bgp asnotation ?
dot asdot notation``````
Let’s change it:
``R1(config-router)#bgp asnotation dot``
You will now see the asdot format in all show commands:
``````R1#show ip bgp summary
BGP router identifier 192.168.12.1, local AS number 183.6924
BGP table version is 1, main routing table version 1
Neighbor V AS MsgRcvd MsgSent TblVer InQ OutQ Up/Down State/PfxRcd
192.168.12.2 4 183.6924 6 6 1 0 0 00:02:38 0``````
AS 12000012 now shows up as AS 183.6924.
Configurations
Want to take a look for yourself? Here you will find the startup configuration of each device.
R1
``````hostname R1
!
ip cef
!
interface GigabitEthernet0/1
!
router bgp 183.6924
bgp asnotation dot
neighbor 192.168.12.2 remote-as 183.6924
!
end``````
R2
``````hostname R2
!
ip cef
!
interface GigabitEthernet0/1
!
router bgp 12000012
neighbor 192.168.12.1 remote-as 12000012
!
end``````
### 2-byte AS support
Let’s use two routers. R1 only supports 2-byte AS numbers, R2 supports 4-byte AS numbers:
R1 has no clue what an AS number above 65535 is:
### We're Sorry, Full Content Access is for Members Only...
If you like to keep on reading, Become a Member Now! Here is why:
• Learn any CCNA, CCNP and CCIE R&S Topic. Explained As Simple As Possible.
• Try for Just \$1. The Best Dollar You’ve Ever Spent on Your Cisco Career!
• Content created by Rene Molenaar (CCIE #41726)
100% Satisfaction Guaranteed!
You may cancel your monthly membership at any time.
Tags: ,
## Forum Replies
1. Hi Rene,
Very Good Stuff.A quick questions for you …
How R2 know R1 only 2 byte supported before sending any open message ??
br//zaman
2. Hi Zaman,
It doesn’t. When R2 receives a reply from R1 without the “support for 4-octet AS number capability” in its OPEN message, it knows that R1 doesn’t support it.
You can see it in the wireshark capture:
https://www.cloudshark.org/captures/d8e5e9240959
Take a look at the 1st packet from R2 and the 2nd packet from R1. R1 is missing the capability.
Hope this helps!
Rene
3. Hi Rene,
I have question in 2-Byte & 4-Byte AS compatibility situation.
In case of we adding R3 (AS3) and connect it to R2. R1 advertises one prefix (for example: 1.1.1.1/32) to R2 and R2 will forward to R3.
What will be in the AS path on R3? (22222222 1 or 23456 1)?
Thanks,
Minh
4. Hello Minh
This is an excellent question. Essentially what you are asking (allow me to put it more generally) is how is the AS path displayed when there is a 2-byte AS compatible router in the mix?
Well, if you display the AS path on the 2-byte AS compatible router, then you will see the 23456 AS in place of the incompatible 4-byte AS number. So essentially the AS_TRANS attribute replaces the 4-byte AS number. However, the AS4 PATH number is an attribute that is received by the 2-byte AS compatible device, and is transitive. It may not understand it, but it
... Continue reading in our forum
5. Thanks Laz for the explanation.
|
<MASK>
## Patterns
<MASK>
In each set, which number is greater?
<MASK>
Less than <, greater >, or equal to =?
65 _____ 100 13 _____ 71 4 _____ 4
Can you fill in the missing numbers?
<MASK>
## Simple Word Problems
Subtraction
Timothy and Brie went to the corner store for some treats. Their mother gave money them to buy six treats for everyone at home to enjoy. Brie brought four popsicles to the counter to buy. How many popsicles does Timothy need to bring to the counter?
<MASK>
Saturday ____
<MASK>
Wednesday _____
<MASK>
Which coin is the quarter?
<MASK>
______ .10
<MASK>
Which length would be a hairpin?
<MASK>
How many cups are in a pint?
<MASK>
2_____
10____
<MASK>
4 _____
12_____
<MASK>
How tall is a telephone pole?
<MASK>
3 yards _____
<UNMASK>
<MASK>
## Patterns
<MASK>
In each set, which number is greater?
7 ________2
1 ________ 3
16 _______ 15
0 ________6
Less than <, greater >, or equal to =?
65 _____ 100 13 _____ 71 4 _____ 4
Can you fill in the missing numbers?
_____, ______, _____, _____, 89, ______, ______ , 92
Are there more triangles or squares?
## Simple Word Problems
Subtraction
Timothy and Brie went to the corner store for some treats. Their mother gave money them to buy six treats for everyone at home to enjoy. Brie brought four popsicles to the counter to buy. How many popsicles does Timothy need to bring to the counter?
Today is the fourth day of the week and my sister said that church is 3 days away. What day will you be going to church?
Fractions
<MASK>
Place a check next to the cone.
____________
___________
<MASK>
Monday _____
Saturday ____
Thursday _____
Wednesday _____
## Money
Which coin is the quarter?
<MASK>
______ .10
<MASK>
## Measurment
Which length would be a hairpin?
_______11 inches
<MASK>
How many cups are in a pint?
<MASK>
2_____
10____
<MASK>
56_____
<MASK>
4 _____
12_____
1______
How tall is a telephone pole?
30 feet _____
20 inches _____
3 yards _____
|
<MASK>
## Patterns
<MASK>
In each set, which number is greater?
7 ________2
1 ________ 3
16 _______ 15
0 ________6
Less than <, greater >, or equal to =?
65 _____ 100 13 _____ 71 4 _____ 4
Can you fill in the missing numbers?
_____, ______, _____, _____, 89, ______, ______ , 92
Are there more triangles or squares?
## Simple Word Problems
Subtraction
Timothy and Brie went to the corner store for some treats. Their mother gave money them to buy six treats for everyone at home to enjoy. Brie brought four popsicles to the counter to buy. How many popsicles does Timothy need to bring to the counter?
Today is the fourth day of the week and my sister said that church is 3 days away. What day will you be going to church?
Fractions
<MASK>
Place a check next to the cone.
____________
___________
<MASK>
Monday _____
Saturday ____
Thursday _____
Wednesday _____
## Money
Which coin is the quarter?
<MASK>
______ .10
<MASK>
## Measurment
Which length would be a hairpin?
_______11 inches
<MASK>
How many cups are in a pint?
<MASK>
2_____
10____
<MASK>
56_____
<MASK>
4 _____
12_____
1______
How tall is a telephone pole?
30 feet _____
20 inches _____
3 yards _____
<UNMASK>
<MASK>
## Patterns
Fill in the blanks counting by 5 to 50.
________ _________ _________ _________ _______ 30 ________ ________ ______ _______
<MASK>
In each set, which number is greater?
7 ________2
1 ________ 3
16 _______ 15
0 ________6
Less than <, greater >, or equal to =?
65 _____ 100 13 _____ 71 4 _____ 4
Can you fill in the missing numbers?
_____, ______, _____, _____, 89, ______, ______ , 92
Are there more triangles or squares?
## Simple Word Problems
Subtraction
Timothy and Brie went to the corner store for some treats. Their mother gave money them to buy six treats for everyone at home to enjoy. Brie brought four popsicles to the counter to buy. How many popsicles does Timothy need to bring to the counter?
Today is the fourth day of the week and my sister said that church is 3 days away. What day will you be going to church?
Fractions
My aunt and I bought 5 new movies last night. 4 of those movies are mine. How many movies belong to my aunt? Write your answer as a fraction.
<MASK>
Place a check next to the cone.
____________
___________
<MASK>
Monday _____
Saturday ____
Thursday _____
Wednesday _____
## Money
Which coin is the quarter?
<MASK>
______ .10
<MASK>
______ .25
How many dimes and how many nickels do you need to make 1 quarter? (use real money for manipulation)
## Measurment
Which length would be a hairpin?
_______11 inches
<MASK>
How many cups are in a pint?
<MASK>
2_____
10____
<MASK>
56_____
<MASK>
4 _____
12_____
1______
How tall is a telephone pole?
30 feet _____
20 inches _____
3 yards _____
|
<MASK>
## Patterns
Fill in the blanks counting by 5 to 50.
________ _________ _________ _________ _______ 30 ________ ________ ______ _______
<MASK>
In each set, which number is greater?
7 ________2
1 ________ 3
16 _______ 15
0 ________6
Less than <, greater >, or equal to =?
65 _____ 100 13 _____ 71 4 _____ 4
Can you fill in the missing numbers?
_____, ______, _____, _____, 89, ______, ______ , 92
Are there more triangles or squares?
## Simple Word Problems
Subtraction
Timothy and Brie went to the corner store for some treats. Their mother gave money them to buy six treats for everyone at home to enjoy. Brie brought four popsicles to the counter to buy. How many popsicles does Timothy need to bring to the counter?
Today is the fourth day of the week and my sister said that church is 3 days away. What day will you be going to church?
Fractions
My aunt and I bought 5 new movies last night. 4 of those movies are mine. How many movies belong to my aunt? Write your answer as a fraction.
<MASK>
Place a check next to the cone.
____________
___________
<MASK>
Monday _____
Saturday ____
Thursday _____
Wednesday _____
## Money
Which coin is the quarter?
<MASK>
______ .10
<MASK>
______ .25
How many dimes and how many nickels do you need to make 1 quarter? (use real money for manipulation)
## Measurment
Which length would be a hairpin?
_______11 inches
<MASK>
How many cups are in a pint?
<MASK>
2_____
10____
<MASK>
56_____
<MASK>
4 _____
12_____
1______
How tall is a telephone pole?
30 feet _____
20 inches _____
3 yards _____
<UNMASK>
<MASK>
## Patterns
Fill in the blanks counting by 5 to 50.
________ _________ _________ _________ _______ 30 ________ ________ ______ _______
<MASK>
## Comparing Numbers
In each set, which number is greater?
7 ________2
1 ________ 3
16 _______ 15
0 ________6
Less than <, greater >, or equal to =?
65 _____ 100 13 _____ 71 4 _____ 4
Can you fill in the missing numbers?
_____, ______, _____, _____, 89, ______, ______ , 92
Are there more triangles or squares?
## Simple Word Problems
Subtraction
Timothy and Brie went to the corner store for some treats. Their mother gave money them to buy six treats for everyone at home to enjoy. Brie brought four popsicles to the counter to buy. How many popsicles does Timothy need to bring to the counter?
Today is the fourth day of the week and my sister said that church is 3 days away. What day will you be going to church?
Fractions
My aunt and I bought 5 new movies last night. 4 of those movies are mine. How many movies belong to my aunt? Write your answer as a fraction.
<MASK>
Place a check next to the cone.
____________
___________
___________
<MASK>
Monday _____
Saturday ____
Thursday _____
Wednesday _____
## Money
Which coin is the quarter?
<MASK>
______ .10
<MASK>
______ .25
How many dimes and how many nickels do you need to make 1 quarter? (use real money for manipulation)
## Measurment
Which length would be a hairpin?
_______11 inches
_______ 2 inch
How many cups are in a pint?
<MASK>
2_____
10____
<MASK>
56_____
<MASK>
4 _____
12_____
1______
How tall is a telephone pole?
30 feet _____
20 inches _____
3 yards _____
|
<MASK>
## Patterns
Fill in the blanks counting by 5 to 50.
________ _________ _________ _________ _______ 30 ________ ________ ______ _______
<MASK>
## Comparing Numbers
In each set, which number is greater?
7 ________2
1 ________ 3
16 _______ 15
0 ________6
Less than <, greater >, or equal to =?
65 _____ 100 13 _____ 71 4 _____ 4
Can you fill in the missing numbers?
_____, ______, _____, _____, 89, ______, ______ , 92
Are there more triangles or squares?
## Simple Word Problems
Subtraction
Timothy and Brie went to the corner store for some treats. Their mother gave money them to buy six treats for everyone at home to enjoy. Brie brought four popsicles to the counter to buy. How many popsicles does Timothy need to bring to the counter?
Today is the fourth day of the week and my sister said that church is 3 days away. What day will you be going to church?
Fractions
My aunt and I bought 5 new movies last night. 4 of those movies are mine. How many movies belong to my aunt? Write your answer as a fraction.
<MASK>
Place a check next to the cone.
____________
___________
___________
<MASK>
Monday _____
Saturday ____
Thursday _____
Wednesday _____
## Money
Which coin is the quarter?
<MASK>
______ .10
<MASK>
______ .25
How many dimes and how many nickels do you need to make 1 quarter? (use real money for manipulation)
## Measurment
Which length would be a hairpin?
_______11 inches
_______ 2 inch
How many cups are in a pint?
<MASK>
2_____
10____
<MASK>
56_____
<MASK>
4 _____
12_____
1______
How tall is a telephone pole?
30 feet _____
20 inches _____
3 yards _____
<UNMASK>
# Build a Better Student With First-Grade Math Activities
## Taking Advantage of Teachable Moments
You may not have realized it but just about any activity that a child performs on a daily basis is usable for meaningful teaching. First-grade math activities get kids into the habit of solving everyday problems, which is a task that will go on for the rest of their lives, becoming more complex as they do more and see more. It makes sense to get them started early on in their educational career, at home and at school. Copy or paste these activities into another document to edit or download for printing.
## Patterns
Fill in the blanks counting by 5 to 50.
________ _________ _________ _________ _______ 30 ________ ________ ______ _______
Four friends decide at the start of the school year to see how many flips they can do each month at recess. Who had the most flips?
## Comparing Numbers
In each set, which number is greater?
7 ________2
1 ________ 3
16 _______ 15
0 ________6
Less than <, greater >, or equal to =?
65 _____ 100 13 _____ 71 4 _____ 4
Can you fill in the missing numbers?
_____, ______, _____, _____, 89, ______, ______ , 92
Are there more triangles or squares?
## Simple Word Problems
Subtraction
Timothy and Brie went to the corner store for some treats. Their mother gave money them to buy six treats for everyone at home to enjoy. Brie brought four popsicles to the counter to buy. How many popsicles does Timothy need to bring to the counter?
Today is the fourth day of the week and my sister said that church is 3 days away. What day will you be going to church?
Fractions
My aunt and I bought 5 new movies last night. 4 of those movies are mine. How many movies belong to my aunt? Write your answer as a fraction.
## Identifying Shapes
Place a check next to the cone.
____________
___________
___________
## Days of the Week (Telling Time)
Place an X next to the day before Friday.
Monday _____
Saturday ____
Thursday _____
Wednesday _____
## Money
Which coin is the quarter?
How much is a dime worth?
______ .10
______ .01
______ .25
How many dimes and how many nickels do you need to make 1 quarter? (use real money for manipulation)
## Measurment
Which length would be a hairpin?
_______11 inches
_______ 2 inch
How many cups are in a pint?
8_____
2_____
10____
How many inches are in a foot?
56_____
7______
12_____
How many 1/4 inches are in a whole inch?
4 _____
12_____
1______
How tall is a telephone pole?
30 feet _____
20 inches _____
3 yards _____
|
<MASK>
<UNMASK>
This site is supported by donations to The OEIS Foundation.
<MASK>
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This site is supported by donations to The OEIS Foundation.
<MASK>
<UNMASK>
This site is supported by donations to The OEIS Foundation.
Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate
<MASK>
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<MASK>
<UNMASK>
This site is supported by donations to The OEIS Foundation.
Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate
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This site is supported by donations to The OEIS Foundation.
Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate
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This site is supported by donations to The OEIS Foundation.
Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate
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A223078 Positive integers with the property that if the base-4 representation is reversed the result is three times the original number. 2
75, 315, 1275, 5115, 19275, 20475, 76875, 81915, 307275, 322875, 327675, 1228875, 1290555, 1310715, 4915275, 4934475, 5161275, 5223675, 5242875, 19660875, 19741515, 20644155, 20890875, 20971515, 78643275, 78720075, 78969675, 82575675, 82652475, 83559675 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,1 COMMENTS From Robert Israel, Apr 23 2019: (Start) All terms are divisible by 15. If x is a term and x < 4^k, then x*(4^k+1) is a term. In particular the sequence is infinite. (End) LINKS Robert Israel, Table of n, a(n) for n = 1..985 MAPLE rev4:= proc(n) local L, i; L:= convert(n, base, 4); add(L[-i]*4^(i-1), i=1..nops(L)) end proc: Res:= NULL: for d from 2 to 15 do d1:= ceil(d/2); d2:= d-d1; for a from 4^(d1-1) to 4^d1/3 do b:= rev4(a)/3 mod 4^d2; x:= 4^d2*a+b; if rev4(x) = 3*x then Res:= Res, x; fi od od: Res; # Robert Israel, Apr 23 2019 MATHEMATICA Select[Range[84*10^6], 3#==FromDigits[Reverse[IntegerDigits[#, 4]], 4]&] (* Harvey P. Dale, Mar 03 2018 *) CROSSREFS Cf. A173951, A223077, A223079, A214927. Sequence in context: A292313 A158765 A226741 * A055561 A193252 A223452 Adjacent sequences: A223075 A223076 A223077 * A223079 A223080 A223081 KEYWORD nonn,base AUTHOR N. J. A. Sloane, Mar 14 2013 EXTENSIONS More terms from Alois P. Heinz, Mar 14 2013 STATUS approved
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Last modified December 15 00:30 EST 2019. Contains 329988 sequences. (Running on oeis4.)
|
<MASK>
<UNMASK>
<MASK>
by Kaldanis
Tags: circuit, current, series
P: 106 This isn't a specific homework question, it's just something I'm having trouble understanding or visualising. Take this L.E.D. circuit for example, which works according to our textbook: The current flows from the - to the +, so clockwise in this circuit. To me, it looks like the current would leave the battery and 12V would flow straight to the LED light and melt it before it gets a chance to reach the resistor. So based on that, I'd think that this circuit wouldn't work... but I also know that current is equal at all points in a series circuit, so the resistor must have affected the current before it reaches the LED? If I worked it out right then the resistor has 10.5V and 52.5Ω. I don't understand how it can take 10.5V and lower the current if the LED is before it in the circuit, can someone please explain this? I'm sure I'm just thinking about it the wrong way! 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution
HW Helper Thanks P: 10,768 First: the current flows out from the positive terminal of the battery and in at the negative one, so it is anti-clockwise in the circuit shown. Do not visualize the current as a car, reaching at different points of the circuit at different times. It is more similar to a long train all round the loop. When the engine starts, it pulls the first carriage, but as soon it starts to move, it pulls the next one and so on... practically, the whole train starts to move at the same time. When you switch on a battery, the electrons near the negative pole of the battery are pushed away and get closer to the electrons farther away and push them, those will push the electrons in front of them and so on, round the loop to the positive pole where the excess electrons are absorbed by the battery. Meanwhile new electrons enter at the negative pole, so the electron density does not change in time , only "the push" travels along the circuit: The potential difference between the terminals sets up an electric field in the loop almost without time delay: it is the electromagnetic field that travels, not the electrons, they are set into motion by the electric field.The current is the same at every point of a series circuit. In the LED, there is mechanism at the pn junction which allows a certain current and voltage to set up. Do not worry about it, just use the given data. ehild
P: 106
Quote by ehild First: the current flows out from the positive terminal of the battery and in at the negative one, so it is anti-clockwise in the circuit shown. Do not visualize the current as a car, reaching at different points of the circuit at different times. It is more similar to a long train all round the loop. When the engine starts, it pulls the first carriage, but as soon it starts to move, it pulls the next one and so on... practically, the whole train starts to move at the same time. When you switch on a battery, the electrons near the negative pole of the battery are pushed away and get closer to the electrons farther away and push them, those will push the electrons in front of them and so on, round the loop to the positive pole where the excess electrons are absorbed by the battery. Meanwhile new electrons enter at the negative pole, so the electron density does not change in time , only "the push" travels along the circuit: The potential difference between the terminals sets up an electric field in the loop almost without time delay: it is the electromagnetic field that travels, not the electrons, they are set into motion by the electric field.The current is the same at every point of a series circuit. In the LED, there is mechanism at the pn junction which allows a certain current and voltage to set up. Do not worry about it, just use the given data. ehild
|
<MASK>
by Kaldanis
Tags: circuit, current, series
P: 106 This isn't a specific homework question, it's just something I'm having trouble understanding or visualising. Take this L.E.D. circuit for example, which works according to our textbook: The current flows from the - to the +, so clockwise in this circuit. To me, it looks like the current would leave the battery and 12V would flow straight to the LED light and melt it before it gets a chance to reach the resistor. So based on that, I'd think that this circuit wouldn't work... but I also know that current is equal at all points in a series circuit, so the resistor must have affected the current before it reaches the LED? If I worked it out right then the resistor has 10.5V and 52.5Ω. I don't understand how it can take 10.5V and lower the current if the LED is before it in the circuit, can someone please explain this? I'm sure I'm just thinking about it the wrong way! 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution
HW Helper Thanks P: 10,768 First: the current flows out from the positive terminal of the battery and in at the negative one, so it is anti-clockwise in the circuit shown. Do not visualize the current as a car, reaching at different points of the circuit at different times. It is more similar to a long train all round the loop. When the engine starts, it pulls the first carriage, but as soon it starts to move, it pulls the next one and so on... practically, the whole train starts to move at the same time. When you switch on a battery, the electrons near the negative pole of the battery are pushed away and get closer to the electrons farther away and push them, those will push the electrons in front of them and so on, round the loop to the positive pole where the excess electrons are absorbed by the battery. Meanwhile new electrons enter at the negative pole, so the electron density does not change in time , only "the push" travels along the circuit: The potential difference between the terminals sets up an electric field in the loop almost without time delay: it is the electromagnetic field that travels, not the electrons, they are set into motion by the electric field.The current is the same at every point of a series circuit. In the LED, there is mechanism at the pn junction which allows a certain current and voltage to set up. Do not worry about it, just use the given data. ehild
P: 106
Quote by ehild First: the current flows out from the positive terminal of the battery and in at the negative one, so it is anti-clockwise in the circuit shown. Do not visualize the current as a car, reaching at different points of the circuit at different times. It is more similar to a long train all round the loop. When the engine starts, it pulls the first carriage, but as soon it starts to move, it pulls the next one and so on... practically, the whole train starts to move at the same time. When you switch on a battery, the electrons near the negative pole of the battery are pushed away and get closer to the electrons farther away and push them, those will push the electrons in front of them and so on, round the loop to the positive pole where the excess electrons are absorbed by the battery. Meanwhile new electrons enter at the negative pole, so the electron density does not change in time , only "the push" travels along the circuit: The potential difference between the terminals sets up an electric field in the loop almost without time delay: it is the electromagnetic field that travels, not the electrons, they are set into motion by the electric field.The current is the same at every point of a series circuit. In the LED, there is mechanism at the pn junction which allows a certain current and voltage to set up. Do not worry about it, just use the given data. ehild
<UNMASK>
# Help understanding current through series circuit
by Kaldanis
Tags: circuit, current, series
P: 106 This isn't a specific homework question, it's just something I'm having trouble understanding or visualising. Take this L.E.D. circuit for example, which works according to our textbook: The current flows from the - to the +, so clockwise in this circuit. To me, it looks like the current would leave the battery and 12V would flow straight to the LED light and melt it before it gets a chance to reach the resistor. So based on that, I'd think that this circuit wouldn't work... but I also know that current is equal at all points in a series circuit, so the resistor must have affected the current before it reaches the LED? If I worked it out right then the resistor has 10.5V and 52.5Ω. I don't understand how it can take 10.5V and lower the current if the LED is before it in the circuit, can someone please explain this? I'm sure I'm just thinking about it the wrong way! 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution
HW Helper Thanks P: 10,768 First: the current flows out from the positive terminal of the battery and in at the negative one, so it is anti-clockwise in the circuit shown. Do not visualize the current as a car, reaching at different points of the circuit at different times. It is more similar to a long train all round the loop. When the engine starts, it pulls the first carriage, but as soon it starts to move, it pulls the next one and so on... practically, the whole train starts to move at the same time. When you switch on a battery, the electrons near the negative pole of the battery are pushed away and get closer to the electrons farther away and push them, those will push the electrons in front of them and so on, round the loop to the positive pole where the excess electrons are absorbed by the battery. Meanwhile new electrons enter at the negative pole, so the electron density does not change in time , only "the push" travels along the circuit: The potential difference between the terminals sets up an electric field in the loop almost without time delay: it is the electromagnetic field that travels, not the electrons, they are set into motion by the electric field.The current is the same at every point of a series circuit. In the LED, there is mechanism at the pn junction which allows a certain current and voltage to set up. Do not worry about it, just use the given data. ehild
P: 106
Quote by ehild First: the current flows out from the positive terminal of the battery and in at the negative one, so it is anti-clockwise in the circuit shown. Do not visualize the current as a car, reaching at different points of the circuit at different times. It is more similar to a long train all round the loop. When the engine starts, it pulls the first carriage, but as soon it starts to move, it pulls the next one and so on... practically, the whole train starts to move at the same time. When you switch on a battery, the electrons near the negative pole of the battery are pushed away and get closer to the electrons farther away and push them, those will push the electrons in front of them and so on, round the loop to the positive pole where the excess electrons are absorbed by the battery. Meanwhile new electrons enter at the negative pole, so the electron density does not change in time , only "the push" travels along the circuit: The potential difference between the terminals sets up an electric field in the loop almost without time delay: it is the electromagnetic field that travels, not the electrons, they are set into motion by the electric field.The current is the same at every point of a series circuit. In the LED, there is mechanism at the pn junction which allows a certain current and voltage to set up. Do not worry about it, just use the given data. ehild
|
<MASK>
Solve the simultaneous equations
<MASK>
This tells us that y has to be either 3 or 1. If $y=3$, then $x=5-2\times 3=-1$ (from the second equation rearranged) and if $y=1$ then $x=5-2\times 1=3$.
We obtain the solutions $(x_1,y_1)=(-1,3)$ and $(x_2,y_2)=(3,1)$.
<MASK>
$y=x-4$
<MASK>
Sketch the graphs of $x^2+y^2=10$ and $x+2y=5$ on the same plot. Determine the coordinates of the intersection points.
Click here to find Questions by Topic all scroll down to all past SIMULTANEOUS EQUATIONS questions to practice some more questions.
<MASK>
<UNMASK>
<MASK>
Solve the simultaneous equations
<MASK>
Divide both by sides by 5: $y^2-4y+3=0$
<MASK>
This tells us that y has to be either 3 or 1. If $y=3$, then $x=5-2\times 3=-1$ (from the second equation rearranged) and if $y=1$ then $x=5-2\times 1=3$.
We obtain the solutions $(x_1,y_1)=(-1,3)$ and $(x_2,y_2)=(3,1)$.
<MASK>
Solve the simultaneous equations:
$y=x-4$
<MASK>
Sketch the graphs of $x^2+y^2=10$ and $x+2y=5$ on the same plot. Determine the coordinates of the intersection points.
Click here to find Questions by Topic all scroll down to all past SIMULTANEOUS EQUATIONS questions to practice some more questions.
Are you ready to test your Pure Maths knowledge? If so, visit our Practice Papers page and take StudyWell’s own Pure Maths tests. Alternatively, try the
|
<MASK>
Solve the simultaneous equations
<MASK>
Divide both by sides by 5: $y^2-4y+3=0$
<MASK>
This tells us that y has to be either 3 or 1. If $y=3$, then $x=5-2\times 3=-1$ (from the second equation rearranged) and if $y=1$ then $x=5-2\times 1=3$.
We obtain the solutions $(x_1,y_1)=(-1,3)$ and $(x_2,y_2)=(3,1)$.
<MASK>
Solve the simultaneous equations:
$y=x-4$
<MASK>
Sketch the graphs of $x^2+y^2=10$ and $x+2y=5$ on the same plot. Determine the coordinates of the intersection points.
Click here to find Questions by Topic all scroll down to all past SIMULTANEOUS EQUATIONS questions to practice some more questions.
Are you ready to test your Pure Maths knowledge? If so, visit our Practice Papers page and take StudyWell’s own Pure Maths tests. Alternatively, try the
<UNMASK>
Simultaneous equations can be thought of as being two equations in two unknowns, say x and y. Note that the word simultaneous means ‘at the same time’. It follows that for the values of x and y found both equations must be true at the same time. Sometimes it is easy to inspect the equations and guess the answers. However, when one of the equations is quadratic this becomes less likely. The answers could be surds, in which case, this is very difficult to guess.
<MASK>
There are three methods for solving simultaneous equations:
<MASK>
Solve the simultaneous equations
<MASK>
$x+2y=5$.
This example requires solution via substitution, i.e. make either x or y the subject of one equation and insert it into the other. The obvious choice would be to make x the subject of the second equation – it is the quickest, least complicated choice. The second equation tells us that $x=5-2y$. We can insert this into the first equation: $(5-2y)^2+y^2=10$. By multiplying out the brackets and simplifying we see that this is a quadratic equation in y:
$(5-2y)^2+y^2=10$
<MASK>
Simplify: $5y^2-20y+15=0$
Divide both by sides by 5: $y^2-4y+3=0$
<MASK>
This tells us that y has to be either 3 or 1. If $y=3$, then $x=5-2\times 3=-1$ (from the second equation rearranged) and if $y=1$ then $x=5-2\times 1=3$.
We obtain the solutions $(x_1,y_1)=(-1,3)$ and $(x_2,y_2)=(3,1)$.
<MASK>
Solve the simultaneous equations:
$y=x-4$
<MASK>
Sketch the graphs of $x^2+y^2=10$ and $x+2y=5$ on the same plot. Determine the coordinates of the intersection points.
Click here to find Questions by Topic all scroll down to all past SIMULTANEOUS EQUATIONS questions to practice some more questions.
Are you ready to test your Pure Maths knowledge? If so, visit our Practice Papers page and take StudyWell’s own Pure Maths tests. Alternatively, try the
|
Simultaneous equations can be thought of as being two equations in two unknowns, say x and y. Note that the word simultaneous means ‘at the same time’. It follows that for the values of x and y found both equations must be true at the same time. Sometimes it is easy to inspect the equations and guess the answers. However, when one of the equations is quadratic this becomes less likely. The answers could be surds, in which case, this is very difficult to guess.
<MASK>
There are three methods for solving simultaneous equations:
<MASK>
Solve the simultaneous equations
<MASK>
$x+2y=5$.
This example requires solution via substitution, i.e. make either x or y the subject of one equation and insert it into the other. The obvious choice would be to make x the subject of the second equation – it is the quickest, least complicated choice. The second equation tells us that $x=5-2y$. We can insert this into the first equation: $(5-2y)^2+y^2=10$. By multiplying out the brackets and simplifying we see that this is a quadratic equation in y:
$(5-2y)^2+y^2=10$
<MASK>
Simplify: $5y^2-20y+15=0$
Divide both by sides by 5: $y^2-4y+3=0$
<MASK>
This tells us that y has to be either 3 or 1. If $y=3$, then $x=5-2\times 3=-1$ (from the second equation rearranged) and if $y=1$ then $x=5-2\times 1=3$.
We obtain the solutions $(x_1,y_1)=(-1,3)$ and $(x_2,y_2)=(3,1)$.
<MASK>
Solve the simultaneous equations:
$y=x-4$
<MASK>
Sketch the graphs of $x^2+y^2=10$ and $x+2y=5$ on the same plot. Determine the coordinates of the intersection points.
Click here to find Questions by Topic all scroll down to all past SIMULTANEOUS EQUATIONS questions to practice some more questions.
Are you ready to test your Pure Maths knowledge? If so, visit our Practice Papers page and take StudyWell’s own Pure Maths tests. Alternatively, try the
<UNMASK>
Simultaneous equations can be thought of as being two equations in two unknowns, say x and y. Note that the word simultaneous means ‘at the same time’. It follows that for the values of x and y found both equations must be true at the same time. Sometimes it is easy to inspect the equations and guess the answers. However, when one of the equations is quadratic this becomes less likely. The answers could be surds, in which case, this is very difficult to guess.
Note that a question may ask you to solve simultaneous equations explicitly. In others, it will be implied and you must deduce that it is simultaneous equations to solve. For example, you could be asked to find out which points two curves have in common. See Example 2 below.
<MASK>
There are three methods for solving simultaneous equations:
<MASK>
Solve the simultaneous equations
$x^2+y^2=10$
<MASK>
$x+2y=5$.
This example requires solution via substitution, i.e. make either x or y the subject of one equation and insert it into the other. The obvious choice would be to make x the subject of the second equation – it is the quickest, least complicated choice. The second equation tells us that $x=5-2y$. We can insert this into the first equation: $(5-2y)^2+y^2=10$. By multiplying out the brackets and simplifying we see that this is a quadratic equation in y:
$(5-2y)^2+y^2=10$
<MASK>
Simplify: $5y^2-20y+15=0$
Divide both by sides by 5: $y^2-4y+3=0$
<MASK>
This tells us that y has to be either 3 or 1. If $y=3$, then $x=5-2\times 3=-1$ (from the second equation rearranged) and if $y=1$ then $x=5-2\times 1=3$.
We obtain the solutions $(x_1,y_1)=(-1,3)$ and $(x_2,y_2)=(3,1)$.
<MASK>
Solve the simultaneous equations:
$y=x-4$
<MASK>
Sketch the graphs of $x^2+y^2=10$ and $x+2y=5$ on the same plot. Determine the coordinates of the intersection points.
Click here to find Questions by Topic all scroll down to all past SIMULTANEOUS EQUATIONS questions to practice some more questions.
Are you ready to test your Pure Maths knowledge? If so, visit our Practice Papers page and take StudyWell’s own Pure Maths tests. Alternatively, try the
|
Simultaneous equations can be thought of as being two equations in two unknowns, say x and y. Note that the word simultaneous means ‘at the same time’. It follows that for the values of x and y found both equations must be true at the same time. Sometimes it is easy to inspect the equations and guess the answers. However, when one of the equations is quadratic this becomes less likely. The answers could be surds, in which case, this is very difficult to guess.
Note that a question may ask you to solve simultaneous equations explicitly. In others, it will be implied and you must deduce that it is simultaneous equations to solve. For example, you could be asked to find out which points two curves have in common. See Example 2 below.
<MASK>
There are three methods for solving simultaneous equations:
<MASK>
Solve the simultaneous equations
$x^2+y^2=10$
<MASK>
$x+2y=5$.
This example requires solution via substitution, i.e. make either x or y the subject of one equation and insert it into the other. The obvious choice would be to make x the subject of the second equation – it is the quickest, least complicated choice. The second equation tells us that $x=5-2y$. We can insert this into the first equation: $(5-2y)^2+y^2=10$. By multiplying out the brackets and simplifying we see that this is a quadratic equation in y:
$(5-2y)^2+y^2=10$
<MASK>
Simplify: $5y^2-20y+15=0$
Divide both by sides by 5: $y^2-4y+3=0$
<MASK>
This tells us that y has to be either 3 or 1. If $y=3$, then $x=5-2\times 3=-1$ (from the second equation rearranged) and if $y=1$ then $x=5-2\times 1=3$.
We obtain the solutions $(x_1,y_1)=(-1,3)$ and $(x_2,y_2)=(3,1)$.
<MASK>
Solve the simultaneous equations:
$y=x-4$
<MASK>
Sketch the graphs of $x^2+y^2=10$ and $x+2y=5$ on the same plot. Determine the coordinates of the intersection points.
Click here to find Questions by Topic all scroll down to all past SIMULTANEOUS EQUATIONS questions to practice some more questions.
Are you ready to test your Pure Maths knowledge? If so, visit our Practice Papers page and take StudyWell’s own Pure Maths tests. Alternatively, try the
<UNMASK>
Simultaneous equations can be thought of as being two equations in two unknowns, say x and y. Note that the word simultaneous means ‘at the same time’. It follows that for the values of x and y found both equations must be true at the same time. Sometimes it is easy to inspect the equations and guess the answers. However, when one of the equations is quadratic this becomes less likely. The answers could be surds, in which case, this is very difficult to guess.
Note that a question may ask you to solve simultaneous equations explicitly. In others, it will be implied and you must deduce that it is simultaneous equations to solve. For example, you could be asked to find out which points two curves have in common. See Example 2 below.
## Methods for solving Simultaneous Equations
There are three methods for solving simultaneous equations:
1. Elimination – this is where you multiply both equations through by different coefficient in order to eliminate one of the unknowns. This page will focus on substitution since it works for more complicated simultaneous equations. For example, when one of the equations is a quadratic. Click here to see an example using elimination.
2. Substitution – one of the equations can be quadratic, in which case, substitution is the method to use. You will need to know how to solve quadratics. By making x or y the subject of one of the equations, it can be substituted into the other. See the Worked Example and Example 1 below.
3. Graphical method – the solution of simultaneous equations can be interpreted as the intersection of their graphs. This plot shows the graphs of $y=2x-3$ in red and $4x+5y=6$ in blue. Their intersection lies on the x-axis and has coordinates (1.5,0). This is the solution when solving simultaneously. Also see Example 2 below.
## Simultaneous Equations Worked Example
Solve the simultaneous equations
$x^2+y^2=10$
and
$x+2y=5$.
This example requires solution via substitution, i.e. make either x or y the subject of one equation and insert it into the other. The obvious choice would be to make x the subject of the second equation – it is the quickest, least complicated choice. The second equation tells us that $x=5-2y$. We can insert this into the first equation: $(5-2y)^2+y^2=10$. By multiplying out the brackets and simplifying we see that this is a quadratic equation in y:
$(5-2y)^2+y^2=10$
Write out the brackets: $(5-2y)(5-2y)+y^2=10$
Expand the brackets: $25-10y-10y+4y^2+y^2=10$
Simplify: $5y^2-20y+15=0$
Divide both by sides by 5: $y^2-4y+3=0$
Factorise: $(y-3)(y-1)=0$
This tells us that y has to be either 3 or 1. If $y=3$, then $x=5-2\times 3=-1$ (from the second equation rearranged) and if $y=1$ then $x=5-2\times 1=3$.
We obtain the solutions $(x_1,y_1)=(-1,3)$ and $(x_2,y_2)=(3,1)$.
### Example 1
Solve the simultaneous equations:
$y=x-4$
$2x^2-xy=8$
### Example 2
Sketch the graphs of $x^2+y^2=10$ and $x+2y=5$ on the same plot. Determine the coordinates of the intersection points.
Click here to find Questions by Topic all scroll down to all past SIMULTANEOUS EQUATIONS questions to practice some more questions.
Are you ready to test your Pure Maths knowledge? If so, visit our Practice Papers page and take StudyWell’s own Pure Maths tests. Alternatively, try the
|
<MASK>
Point elasticity is the measure of responsiveness or sensitivity of quantity demanded to changes in price. However, arc elasticity is the measure of elasticity between two points on the demand curve. At the two points move closer together on the demand curve, it approaches point elasticity.
<MASK>
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1707 words - 7 pages
<MASK>
Point elasticity is the measure of responsiveness or sensitivity of quantity demanded to changes in price. However, arc elasticity is the measure of elasticity between two points on the demand curve. At the two points move closer together on the demand curve, it approaches point elasticity.
<MASK>
The price elasticity of illegal drugs is less than one, which is inelastic. This is because drug addicts are will to pay anything to get their hit that they crave. If the person is craving the drug very badly, they will be willing to pay a lot of money, as they don't care f or substitutes and need the drug as soon as possible. Even if the price increases, the addicts still need the drug.
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<MASK>
# Microneconomics Essay
1707 words - 7 pages
<MASK>
The law of demand states the relationship between quantity demanded and price, showing that the lower the price, the higher the demand and vice versa. If we do not have scarce resources, there will still be a law of demand, because all humans are greedy. This means that we will always want more of what is there and demand always initially exceeds supply, but supply will then catch up, and over time will fall behind again, although this bottlenecking' is always temporary. This can be seen in fibre optic cables, as they catapulted the amount of information able to be ...view middle of the document...
<MASK>
Point elasticity is the measure of responsiveness or sensitivity of quantity demanded to changes in price. However, arc elasticity is the measure of elasticity between two points on the demand curve. At the two points move closer together on the demand curve, it approaches point elasticity.
Point elasticity is calculated by the percentage change in quantity demanded divided by the percentage change in price, which is shown in formula by: ∆Q% P1
∆P% x Q1
<MASK>
b. Construct on the same graph two straight-line demand curves with the same intercept on the vertical axis, with one curve flatter than the other. Can you make a general statement about which one is the more elastic curve? If so, what is it?
This demand curve shows two straight lines. Line A is steeper and represents a less elastic curve while Line B is flatter and represents a more elastic curve. Point elasticity is the measure of responsiveness or sensitivity of quantity demanded to changes in price. If the elasticity is higher (more than 1), it means that there will be a larger response in demand with price, which is illustrated by curve B. One reason for lower elasticity is brand loyalty, with consumers sticking to one brand all the time. A reason for higher elasticity is the number of substitute products, because as soon as one product reduces its price, it will gain more sales than its substitutes.
<MASK>
a. Would you expect that the price elasticity of demand for illegal drugs to be greater than, or less than one?
The price elasticity of illegal drugs is less than one, which is inelastic. This is because drug addicts are will to pay anything to get their hit that they crave. If the person is craving the drug very badly, they will be willing to pay a lot of money, as they don't care f or substitutes and need the drug as soon as possible. Even if the price increases, the addicts still need the drug.
b. Given your answer to a, what happens to total expenditure on illegal drugs when their price increases? What do you think would happen to the amount of drug related crime?
Because drug addicts need the drugs, they are going to pay for the drugs regardless of the price, which means that total expenditure of the users will increase. This could result in the users having to leave more essential expenses to pay for drugs, as the drug opportunity cost far outweighs other...
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<MASK>
# Microneconomics Essay
1707 words - 7 pages
<MASK>
The law of demand states the relationship between quantity demanded and price, showing that the lower the price, the higher the demand and vice versa. If we do not have scarce resources, there will still be a law of demand, because all humans are greedy. This means that we will always want more of what is there and demand always initially exceeds supply, but supply will then catch up, and over time will fall behind again, although this bottlenecking' is always temporary. This can be seen in fibre optic cables, as they catapulted the amount of information able to be ...view middle of the document...
<MASK>
Point elasticity is the measure of responsiveness or sensitivity of quantity demanded to changes in price. However, arc elasticity is the measure of elasticity between two points on the demand curve. At the two points move closer together on the demand curve, it approaches point elasticity.
Point elasticity is calculated by the percentage change in quantity demanded divided by the percentage change in price, which is shown in formula by: ∆Q% P1
∆P% x Q1
<MASK>
b. Construct on the same graph two straight-line demand curves with the same intercept on the vertical axis, with one curve flatter than the other. Can you make a general statement about which one is the more elastic curve? If so, what is it?
This demand curve shows two straight lines. Line A is steeper and represents a less elastic curve while Line B is flatter and represents a more elastic curve. Point elasticity is the measure of responsiveness or sensitivity of quantity demanded to changes in price. If the elasticity is higher (more than 1), it means that there will be a larger response in demand with price, which is illustrated by curve B. One reason for lower elasticity is brand loyalty, with consumers sticking to one brand all the time. A reason for higher elasticity is the number of substitute products, because as soon as one product reduces its price, it will gain more sales than its substitutes.
<MASK>
a. Would you expect that the price elasticity of demand for illegal drugs to be greater than, or less than one?
The price elasticity of illegal drugs is less than one, which is inelastic. This is because drug addicts are will to pay anything to get their hit that they crave. If the person is craving the drug very badly, they will be willing to pay a lot of money, as they don't care f or substitutes and need the drug as soon as possible. Even if the price increases, the addicts still need the drug.
b. Given your answer to a, what happens to total expenditure on illegal drugs when their price increases? What do you think would happen to the amount of drug related crime?
Because drug addicts need the drugs, they are going to pay for the drugs regardless of the price, which means that total expenditure of the users will increase. This could result in the users having to leave more essential expenses to pay for drugs, as the drug opportunity cost far outweighs other...
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<UNMASK>
<MASK>
# Microneconomics Essay
1707 words - 7 pages
<MASK>
The law of demand states the relationship between quantity demanded and price, showing that the lower the price, the higher the demand and vice versa. If we do not have scarce resources, there will still be a law of demand, because all humans are greedy. This means that we will always want more of what is there and demand always initially exceeds supply, but supply will then catch up, and over time will fall behind again, although this bottlenecking' is always temporary. This can be seen in fibre optic cables, as they catapulted the amount of information able to be ...view middle of the document...
2) a. Explain the difference between point elasticity of demand and arc elasticity of demand.
Point elasticity is the measure of responsiveness or sensitivity of quantity demanded to changes in price. However, arc elasticity is the measure of elasticity between two points on the demand curve. At the two points move closer together on the demand curve, it approaches point elasticity.
Point elasticity is calculated by the percentage change in quantity demanded divided by the percentage change in price, which is shown in formula by: ∆Q% P1
∆P% x Q1
Arc elasticity is calculated the same as point elasticity, although instead of the percentage change, it is calculated by the actual difference between the points. This is shown in formula by: Q2-Q1 P1+P2
P2-P1 x Q2+Q1
This formula is used when there is the change in Price and the Quantity, which allows arc elasticity to be more accurate than point elasticity.
b. Construct on the same graph two straight-line demand curves with the same intercept on the vertical axis, with one curve flatter than the other. Can you make a general statement about which one is the more elastic curve? If so, what is it?
This demand curve shows two straight lines. Line A is steeper and represents a less elastic curve while Line B is flatter and represents a more elastic curve. Point elasticity is the measure of responsiveness or sensitivity of quantity demanded to changes in price. If the elasticity is higher (more than 1), it means that there will be a larger response in demand with price, which is illustrated by curve B. One reason for lower elasticity is brand loyalty, with consumers sticking to one brand all the time. A reason for higher elasticity is the number of substitute products, because as soon as one product reduces its price, it will gain more sales than its substitutes.
3) It has been argued that in order to fight drug abuse sensibly, policy makers must understand the demand for drugs
a. Would you expect that the price elasticity of demand for illegal drugs to be greater than, or less than one?
The price elasticity of illegal drugs is less than one, which is inelastic. This is because drug addicts are will to pay anything to get their hit that they crave. If the person is craving the drug very badly, they will be willing to pay a lot of money, as they don't care f or substitutes and need the drug as soon as possible. Even if the price increases, the addicts still need the drug.
b. Given your answer to a, what happens to total expenditure on illegal drugs when their price increases? What do you think would happen to the amount of drug related crime?
Because drug addicts need the drugs, they are going to pay for the drugs regardless of the price, which means that total expenditure of the users will increase. This could result in the users having to leave more essential expenses to pay for drugs, as the drug opportunity cost far outweighs other...
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<MASK>
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<MASK>
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|
<MASK>
# Microneconomics Essay
1707 words - 7 pages
<MASK>
The law of demand states the relationship between quantity demanded and price, showing that the lower the price, the higher the demand and vice versa. If we do not have scarce resources, there will still be a law of demand, because all humans are greedy. This means that we will always want more of what is there and demand always initially exceeds supply, but supply will then catch up, and over time will fall behind again, although this bottlenecking' is always temporary. This can be seen in fibre optic cables, as they catapulted the amount of information able to be ...view middle of the document...
2) a. Explain the difference between point elasticity of demand and arc elasticity of demand.
Point elasticity is the measure of responsiveness or sensitivity of quantity demanded to changes in price. However, arc elasticity is the measure of elasticity between two points on the demand curve. At the two points move closer together on the demand curve, it approaches point elasticity.
Point elasticity is calculated by the percentage change in quantity demanded divided by the percentage change in price, which is shown in formula by: ∆Q% P1
∆P% x Q1
Arc elasticity is calculated the same as point elasticity, although instead of the percentage change, it is calculated by the actual difference between the points. This is shown in formula by: Q2-Q1 P1+P2
P2-P1 x Q2+Q1
This formula is used when there is the change in Price and the Quantity, which allows arc elasticity to be more accurate than point elasticity.
b. Construct on the same graph two straight-line demand curves with the same intercept on the vertical axis, with one curve flatter than the other. Can you make a general statement about which one is the more elastic curve? If so, what is it?
This demand curve shows two straight lines. Line A is steeper and represents a less elastic curve while Line B is flatter and represents a more elastic curve. Point elasticity is the measure of responsiveness or sensitivity of quantity demanded to changes in price. If the elasticity is higher (more than 1), it means that there will be a larger response in demand with price, which is illustrated by curve B. One reason for lower elasticity is brand loyalty, with consumers sticking to one brand all the time. A reason for higher elasticity is the number of substitute products, because as soon as one product reduces its price, it will gain more sales than its substitutes.
3) It has been argued that in order to fight drug abuse sensibly, policy makers must understand the demand for drugs
a. Would you expect that the price elasticity of demand for illegal drugs to be greater than, or less than one?
The price elasticity of illegal drugs is less than one, which is inelastic. This is because drug addicts are will to pay anything to get their hit that they crave. If the person is craving the drug very badly, they will be willing to pay a lot of money, as they don't care f or substitutes and need the drug as soon as possible. Even if the price increases, the addicts still need the drug.
b. Given your answer to a, what happens to total expenditure on illegal drugs when their price increases? What do you think would happen to the amount of drug related crime?
Because drug addicts need the drugs, they are going to pay for the drugs regardless of the price, which means that total expenditure of the users will increase. This could result in the users having to leave more essential expenses to pay for drugs, as the drug opportunity cost far outweighs other...
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<UNMASK>
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# Microneconomics Essay
1707 words - 7 pages
1) a. If we do not have scarce resources, will we have a law of demand? Will we observe price rationing for goods?
The law of demand states the relationship between quantity demanded and price, showing that the lower the price, the higher the demand and vice versa. If we do not have scarce resources, there will still be a law of demand, because all humans are greedy. This means that we will always want more of what is there and demand always initially exceeds supply, but supply will then catch up, and over time will fall behind again, although this bottlenecking' is always temporary. This can be seen in fibre optic cables, as they catapulted the amount of information able to be ...view middle of the document...
2) a. Explain the difference between point elasticity of demand and arc elasticity of demand.
Point elasticity is the measure of responsiveness or sensitivity of quantity demanded to changes in price. However, arc elasticity is the measure of elasticity between two points on the demand curve. At the two points move closer together on the demand curve, it approaches point elasticity.
Point elasticity is calculated by the percentage change in quantity demanded divided by the percentage change in price, which is shown in formula by: ∆Q% P1
∆P% x Q1
Arc elasticity is calculated the same as point elasticity, although instead of the percentage change, it is calculated by the actual difference between the points. This is shown in formula by: Q2-Q1 P1+P2
P2-P1 x Q2+Q1
This formula is used when there is the change in Price and the Quantity, which allows arc elasticity to be more accurate than point elasticity.
b. Construct on the same graph two straight-line demand curves with the same intercept on the vertical axis, with one curve flatter than the other. Can you make a general statement about which one is the more elastic curve? If so, what is it?
This demand curve shows two straight lines. Line A is steeper and represents a less elastic curve while Line B is flatter and represents a more elastic curve. Point elasticity is the measure of responsiveness or sensitivity of quantity demanded to changes in price. If the elasticity is higher (more than 1), it means that there will be a larger response in demand with price, which is illustrated by curve B. One reason for lower elasticity is brand loyalty, with consumers sticking to one brand all the time. A reason for higher elasticity is the number of substitute products, because as soon as one product reduces its price, it will gain more sales than its substitutes.
3) It has been argued that in order to fight drug abuse sensibly, policy makers must understand the demand for drugs
a. Would you expect that the price elasticity of demand for illegal drugs to be greater than, or less than one?
The price elasticity of illegal drugs is less than one, which is inelastic. This is because drug addicts are will to pay anything to get their hit that they crave. If the person is craving the drug very badly, they will be willing to pay a lot of money, as they don't care f or substitutes and need the drug as soon as possible. Even if the price increases, the addicts still need the drug.
b. Given your answer to a, what happens to total expenditure on illegal drugs when their price increases? What do you think would happen to the amount of drug related crime?
Because drug addicts need the drugs, they are going to pay for the drugs regardless of the price, which means that total expenditure of the users will increase. This could result in the users having to leave more essential expenses to pay for drugs, as the drug opportunity cost far outweighs other...
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|
This is the solution to Homework 2: Problems - Variables, Values, and Types.
<MASK>
Due Date: Monday Oct 2, 2017 9:00 AM. This homework aims at giving you some experience with MATLAB variables.
1. Type the following in the command window and submit the results. Briefy explain what each assignment does.
>> a = 1
>> b = 'x'
>> c = true
>> whos a b c
>> a == c
>> a + c
>> d = [1 2 3 4]
>> e = ['a' 'b' 'c' 'd']
>> f = ['abcd']
>> g = {‘a’ ‘b’ ‘c’ ‘d’}
>> h = { a b c d}
>> whos d e f g h
<MASK>
7. Use MATLAB help to find out how you can create a new directory named mynewdir from MATLAB command line. Then change the working directory the newly created directory. Then create a MATLAB script in this directory named myscript.m with the following code in it,
<MASK>
<UNMASK>
This is the solution to Homework 2: Problems - Variables, Values, and Types.
<MASK>
Due Date: Monday Oct 2, 2017 9:00 AM. This homework aims at giving you some experience with MATLAB variables.
1. Type the following in the command window and submit the results. Briefy explain what each assignment does.
>> a = 1
>> b = 'x'
>> c = true
>> whos a b c
>> a == c
>> a + c
>> d = [1 2 3 4]
>> e = ['a' 'b' 'c' 'd']
>> f = ['abcd']
>> g = {‘a’ ‘b’ ‘c’ ‘d’}
>> h = { a b c d}
>> whos d e f g h
<MASK>
>> d = [1 2 3 4]
d =
1 2 3 4
>> e = ['a' 'b' 'c' 'd']
e =
abcd
>> f = ['abcd']
f =
abcd
>> g = {'a' 'b' 'c' 'd'}
g =
1×4 cell array
'a' 'b' 'c' 'd'
>> h = { a b c d}
h =
1×4 cell array
[1] 'x' [1] [1×4 double]
>> whos d e f g h
Name Size Bytes Class Attributes
d 1x4 32 double
e 1x4 8 char
f 1x4 8 char
g 1x4 456 cell
h 1x4 491 cell
<MASK>
>> 1\2
>> 1/2
>> int8(1/2)
>> int8(1/3)
>> -5^2
>> (-5) ^ 2
>> 10-6/2
>> 5*4/2*3
<MASK>
>> a = zeros(3,3);
>> a(1,1) = 2;
>> a(2,2) = 2;
>> a(3,3) = 2;
>> a
a =
2 0 0
0 2 0
0 0 2
<MASK>
7. Use MATLAB help to find out how you can create a new directory named mynewdir from MATLAB command line. Then change the working directory the newly created directory. Then create a MATLAB script in this directory named myscript.m with the following code in it,
<MASK>
The script myscript generates a plot of $y$ versus $x$ where $y = |sin(x)|$. In doing so, MATLAB opens a new window called plot window that contains the plot of y as a function of x. Here is the resulting figure:
<MASK>
You get an error message like the following,
<MASK>
|
This is the solution to Homework 2: Problems - Variables, Values, and Types.
<MASK>
Due Date: Monday Oct 2, 2017 9:00 AM. This homework aims at giving you some experience with MATLAB variables.
1. Type the following in the command window and submit the results. Briefy explain what each assignment does.
>> a = 1
>> b = 'x'
>> c = true
>> whos a b c
>> a == c
>> a + c
>> d = [1 2 3 4]
>> e = ['a' 'b' 'c' 'd']
>> f = ['abcd']
>> g = {‘a’ ‘b’ ‘c’ ‘d’}
>> h = { a b c d}
>> whos d e f g h
<MASK>
>> d = [1 2 3 4]
d =
1 2 3 4
>> e = ['a' 'b' 'c' 'd']
e =
abcd
>> f = ['abcd']
f =
abcd
>> g = {'a' 'b' 'c' 'd'}
g =
1×4 cell array
'a' 'b' 'c' 'd'
>> h = { a b c d}
h =
1×4 cell array
[1] 'x' [1] [1×4 double]
>> whos d e f g h
Name Size Bytes Class Attributes
d 1x4 32 double
e 1x4 8 char
f 1x4 8 char
g 1x4 456 cell
h 1x4 491 cell
<MASK>
>> 1\2
>> 1/2
>> int8(1/2)
>> int8(1/3)
>> -5^2
>> (-5) ^ 2
>> 10-6/2
>> 5*4/2*3
<MASK>
>> a = zeros(3,3);
>> a(1,1) = 2;
>> a(2,2) = 2;
>> a(3,3) = 2;
>> a
a =
2 0 0
0 2 0
0 0 2
<MASK>
7. Use MATLAB help to find out how you can create a new directory named mynewdir from MATLAB command line. Then change the working directory the newly created directory. Then create a MATLAB script in this directory named myscript.m with the following code in it,
<MASK>
The script myscript generates a plot of $y$ versus $x$ where $y = |sin(x)|$. In doing so, MATLAB opens a new window called plot window that contains the plot of y as a function of x. Here is the resulting figure:
<MASK>
You get an error message like the following,
<MASK>
<UNMASK>
This is the solution to Homework 2: Problems - Variables, Values, and Types.
The following figure illustrates the grade distribution for this homework.
Due Date: Monday Oct 2, 2017 9:00 AM. This homework aims at giving you some experience with MATLAB variables.
1. Type the following in the command window and submit the results. Briefy explain what each assignment does.
>> a = 1
>> b = 'x'
>> c = true
>> whos a b c
>> a == c
>> a + c
>> d = [1 2 3 4]
>> e = ['a' 'b' 'c' 'd']
>> f = ['abcd']
>> g = {‘a’ ‘b’ ‘c’ ‘d’}
>> h = { a b c d}
>> whos d e f g h
<MASK>
>> d = [1 2 3 4]
d =
1 2 3 4
>> e = ['a' 'b' 'c' 'd']
e =
abcd
>> f = ['abcd']
f =
abcd
>> g = {'a' 'b' 'c' 'd'}
g =
1×4 cell array
'a' 'b' 'c' 'd'
>> h = { a b c d}
h =
1×4 cell array
[1] 'x' [1] [1×4 double]
>> whos d e f g h
Name Size Bytes Class Attributes
d 1x4 32 double
e 1x4 8 char
f 1x4 8 char
g 1x4 456 cell
h 1x4 491 cell
<MASK>
2. What would happen if you go beyond the range for a particular type? For example, the largest integer that can be stored in int8 is 127, and the smallest integer is -128, so what would happen if we type cast a larger integer to the type int8? Smaller integer? Use the built-in functions intmin and intmax to find the largest and smallest integers that can be stored in int16 and int32.
<MASK>
3. Think about what the results would be for the following expressions, and then type them in to the terminal to verify your answers. Briefly explain the results for each one.
>> 1\2
>> 1/2
>> int8(1/2)
>> int8(1/3)
>> -5^2
>> (-5) ^ 2
>> 10-6/2
>> 5*4/2*3
>> 1\2
ans =
2
>> 1/2
ans =
0.5000
>> int8(1/2)
ans =
int8
1
>> int8(1/3)
ans =
int8
0
>> -5^2
ans =
-25
>> (-5)^2
ans =
25
>> 10-6/2
ans =
7
>> 5*4/2*3
ans =
30
<MASK>
>> a
a =
1 0
2 1
>> b
b =
-1 2
0 1
>> c
c =
3
2
>> d
d =
5
<MASK>
4.(b) What is the result of each of the following expressions? Briefly explain what MATLAB is doing for each operation.
1. a + b
2. a .* b
3. a * b
4. a * c
5. a + c
6. a + d
7. a .* d
8. a * d
>> a + b
ans =
0 2
2 2
>> a .* b
ans =
-1 0
0 1
>> a * b
ans =
-1 2
-2 5
>> a * c
ans =
3
8
>> a + c
ans =
4 3
4 3
>> a + d
ans =
6 5
7 6
>> a .* d
ans =
5 0
10 5
>> a * d
ans =
5 0
10 5
<MASK>
>> a
a =
2 0 0
0 2 0
0 0 2
>> a = eye(3,3) * 2
a =
2 0 0
0 2 0
0 0 2
>> d = [2 2 2]
d =
2 2 2
>> a = diag(d)
a =
2 0 0
0 2 0
0 0 2
>> a = zeros(3,3);
>> a(1,1) = 2;
>> a(2,2) = 2;
>> a(3,3) = 2;
>> a
a =
2 0 0
0 2 0
0 0 2
6. Download this code. This code is full syntax errors. Fix the errors and submit the corrected code with name script_full_of_errors_fixed.m in your folder for this HW. Explain in front of each corrected MATLAB statement, why the error occurred. Modify the last two variables so that they display,
>> Persian
Persian =
Persian is a human language
>> Spanish
Spanish =
'Spanish ' 'is ' ' another' 'language'
Modify the last line such that for the last line the code displays,
<MASK>
The corrected script can be found here
7. Use MATLAB help to find out how you can create a new directory named mynewdir from MATLAB command line. Then change the working directory the newly created directory. Then create a MATLAB script in this directory named myscript.m with the following code in it,
% First create an array from -2*pi to 2:pi
x = -2*pi:pi/20:2*pi;
<MASK>
>> mkdir mynewdir
>> cd mynewdir
The script myscript generates a plot of $y$ versus $x$ where $y = |sin(x)|$. In doing so, MATLAB opens a new window called plot window that contains the plot of y as a function of x. Here is the resulting figure:
<MASK>
You get an error message like the following,
<MASK>
And this happens because the script we are trying to run is neither in MATLAB’s working directory, nor in any of MATLAB’s search paths. Therefore, MATLAB gives an error, as it cannot find the requested file.
|
This is the solution to Homework 2: Problems - Variables, Values, and Types.
The following figure illustrates the grade distribution for this homework.
Due Date: Monday Oct 2, 2017 9:00 AM. This homework aims at giving you some experience with MATLAB variables.
1. Type the following in the command window and submit the results. Briefy explain what each assignment does.
>> a = 1
>> b = 'x'
>> c = true
>> whos a b c
>> a == c
>> a + c
>> d = [1 2 3 4]
>> e = ['a' 'b' 'c' 'd']
>> f = ['abcd']
>> g = {‘a’ ‘b’ ‘c’ ‘d’}
>> h = { a b c d}
>> whos d e f g h
<MASK>
>> d = [1 2 3 4]
d =
1 2 3 4
>> e = ['a' 'b' 'c' 'd']
e =
abcd
>> f = ['abcd']
f =
abcd
>> g = {'a' 'b' 'c' 'd'}
g =
1×4 cell array
'a' 'b' 'c' 'd'
>> h = { a b c d}
h =
1×4 cell array
[1] 'x' [1] [1×4 double]
>> whos d e f g h
Name Size Bytes Class Attributes
d 1x4 32 double
e 1x4 8 char
f 1x4 8 char
g 1x4 456 cell
h 1x4 491 cell
<MASK>
2. What would happen if you go beyond the range for a particular type? For example, the largest integer that can be stored in int8 is 127, and the smallest integer is -128, so what would happen if we type cast a larger integer to the type int8? Smaller integer? Use the built-in functions intmin and intmax to find the largest and smallest integers that can be stored in int16 and int32.
<MASK>
3. Think about what the results would be for the following expressions, and then type them in to the terminal to verify your answers. Briefly explain the results for each one.
>> 1\2
>> 1/2
>> int8(1/2)
>> int8(1/3)
>> -5^2
>> (-5) ^ 2
>> 10-6/2
>> 5*4/2*3
>> 1\2
ans =
2
>> 1/2
ans =
0.5000
>> int8(1/2)
ans =
int8
1
>> int8(1/3)
ans =
int8
0
>> -5^2
ans =
-25
>> (-5)^2
ans =
25
>> 10-6/2
ans =
7
>> 5*4/2*3
ans =
30
<MASK>
>> a
a =
1 0
2 1
>> b
b =
-1 2
0 1
>> c
c =
3
2
>> d
d =
5
<MASK>
4.(b) What is the result of each of the following expressions? Briefly explain what MATLAB is doing for each operation.
1. a + b
2. a .* b
3. a * b
4. a * c
5. a + c
6. a + d
7. a .* d
8. a * d
>> a + b
ans =
0 2
2 2
>> a .* b
ans =
-1 0
0 1
>> a * b
ans =
-1 2
-2 5
>> a * c
ans =
3
8
>> a + c
ans =
4 3
4 3
>> a + d
ans =
6 5
7 6
>> a .* d
ans =
5 0
10 5
>> a * d
ans =
5 0
10 5
<MASK>
>> a
a =
2 0 0
0 2 0
0 0 2
>> a = eye(3,3) * 2
a =
2 0 0
0 2 0
0 0 2
>> d = [2 2 2]
d =
2 2 2
>> a = diag(d)
a =
2 0 0
0 2 0
0 0 2
>> a = zeros(3,3);
>> a(1,1) = 2;
>> a(2,2) = 2;
>> a(3,3) = 2;
>> a
a =
2 0 0
0 2 0
0 0 2
6. Download this code. This code is full syntax errors. Fix the errors and submit the corrected code with name script_full_of_errors_fixed.m in your folder for this HW. Explain in front of each corrected MATLAB statement, why the error occurred. Modify the last two variables so that they display,
>> Persian
Persian =
Persian is a human language
>> Spanish
Spanish =
'Spanish ' 'is ' ' another' 'language'
Modify the last line such that for the last line the code displays,
<MASK>
The corrected script can be found here
7. Use MATLAB help to find out how you can create a new directory named mynewdir from MATLAB command line. Then change the working directory the newly created directory. Then create a MATLAB script in this directory named myscript.m with the following code in it,
% First create an array from -2*pi to 2:pi
x = -2*pi:pi/20:2*pi;
<MASK>
>> mkdir mynewdir
>> cd mynewdir
The script myscript generates a plot of $y$ versus $x$ where $y = |sin(x)|$. In doing so, MATLAB opens a new window called plot window that contains the plot of y as a function of x. Here is the resulting figure:
<MASK>
You get an error message like the following,
<MASK>
And this happens because the script we are trying to run is neither in MATLAB’s working directory, nor in any of MATLAB’s search paths. Therefore, MATLAB gives an error, as it cannot find the requested file.
<UNMASK>
This is the solution to Homework 2: Problems - Variables, Values, and Types.
The following figure illustrates the grade distribution for this homework.
Due Date: Monday Oct 2, 2017 9:00 AM. This homework aims at giving you some experience with MATLAB variables.
1. Type the following in the command window and submit the results. Briefy explain what each assignment does.
>> a = 1
>> b = 'x'
>> c = true
>> whos a b c
>> a == c
>> a + c
>> d = [1 2 3 4]
>> e = ['a' 'b' 'c' 'd']
>> f = ['abcd']
>> g = {‘a’ ‘b’ ‘c’ ‘d’}
>> h = { a b c d}
>> whos d e f g h
<MASK>
>> d = [1 2 3 4]
d =
1 2 3 4
>> e = ['a' 'b' 'c' 'd']
e =
abcd
>> f = ['abcd']
f =
abcd
>> g = {'a' 'b' 'c' 'd'}
g =
1×4 cell array
'a' 'b' 'c' 'd'
>> h = { a b c d}
h =
1×4 cell array
[1] 'x' [1] [1×4 double]
>> whos d e f g h
Name Size Bytes Class Attributes
d 1x4 32 double
e 1x4 8 char
f 1x4 8 char
g 1x4 456 cell
h 1x4 491 cell
<MASK>
2. What would happen if you go beyond the range for a particular type? For example, the largest integer that can be stored in int8 is 127, and the smallest integer is -128, so what would happen if we type cast a larger integer to the type int8? Smaller integer? Use the built-in functions intmin and intmax to find the largest and smallest integers that can be stored in int16 and int32.
<MASK>
3. Think about what the results would be for the following expressions, and then type them in to the terminal to verify your answers. Briefly explain the results for each one.
>> 1\2
>> 1/2
>> int8(1/2)
>> int8(1/3)
>> -5^2
>> (-5) ^ 2
>> 10-6/2
>> 5*4/2*3
>> 1\2
ans =
2
>> 1/2
ans =
0.5000
>> int8(1/2)
ans =
int8
1
>> int8(1/3)
ans =
int8
0
>> -5^2
ans =
-25
>> (-5)^2
ans =
25
>> 10-6/2
ans =
7
>> 5*4/2*3
ans =
30
4.(a) Define the following variables:
>> a
a =
1 0
2 1
>> b
b =
-1 2
0 1
>> c
c =
3
2
>> d
d =
5
<MASK>
4.(b) What is the result of each of the following expressions? Briefly explain what MATLAB is doing for each operation.
1. a + b
2. a .* b
3. a * b
4. a * c
5. a + c
6. a + d
7. a .* d
8. a * d
>> a + b
ans =
0 2
2 2
>> a .* b
ans =
-1 0
0 1
>> a * b
ans =
-1 2
-2 5
>> a * c
ans =
3
8
>> a + c
ans =
4 3
4 3
>> a + d
ans =
6 5
7 6
>> a .* d
ans =
5 0
10 5
>> a * d
ans =
5 0
10 5
<MASK>
>> a
a =
2 0 0
0 2 0
0 0 2
>> a = eye(3,3) * 2
a =
2 0 0
0 2 0
0 0 2
>> d = [2 2 2]
d =
2 2 2
>> a = diag(d)
a =
2 0 0
0 2 0
0 0 2
>> a = zeros(3,3);
>> a(1,1) = 2;
>> a(2,2) = 2;
>> a(3,3) = 2;
>> a
a =
2 0 0
0 2 0
0 0 2
6. Download this code. This code is full syntax errors. Fix the errors and submit the corrected code with name script_full_of_errors_fixed.m in your folder for this HW. Explain in front of each corrected MATLAB statement, why the error occurred. Modify the last two variables so that they display,
>> Persian
Persian =
Persian is a human language
>> Spanish
Spanish =
'Spanish ' 'is ' ' another' 'language'
Modify the last line such that for the last line the code displays,
Persian is not the same as Spanish
<MASK>
The corrected script can be found here
7. Use MATLAB help to find out how you can create a new directory named mynewdir from MATLAB command line. Then change the working directory the newly created directory. Then create a MATLAB script in this directory named myscript.m with the following code in it,
% First create an array from -2*pi to 2:pi
x = -2*pi:pi/20:2*pi;
<MASK>
You can create a new directory and switch the current directory to it using the following commands,
>> mkdir mynewdir
>> cd mynewdir
The script myscript generates a plot of $y$ versus $x$ where $y = |sin(x)|$. In doing so, MATLAB opens a new window called plot window that contains the plot of y as a function of x. Here is the resulting figure:
<MASK>
You get an error message like the following,
<MASK>
And this happens because the script we are trying to run is neither in MATLAB’s working directory, nor in any of MATLAB’s search paths. Therefore, MATLAB gives an error, as it cannot find the requested file.
|
This is the solution to Homework 2: Problems - Variables, Values, and Types.
The following figure illustrates the grade distribution for this homework.
Due Date: Monday Oct 2, 2017 9:00 AM. This homework aims at giving you some experience with MATLAB variables.
1. Type the following in the command window and submit the results. Briefy explain what each assignment does.
>> a = 1
>> b = 'x'
>> c = true
>> whos a b c
>> a == c
>> a + c
>> d = [1 2 3 4]
>> e = ['a' 'b' 'c' 'd']
>> f = ['abcd']
>> g = {‘a’ ‘b’ ‘c’ ‘d’}
>> h = { a b c d}
>> whos d e f g h
<MASK>
>> d = [1 2 3 4]
d =
1 2 3 4
>> e = ['a' 'b' 'c' 'd']
e =
abcd
>> f = ['abcd']
f =
abcd
>> g = {'a' 'b' 'c' 'd'}
g =
1×4 cell array
'a' 'b' 'c' 'd'
>> h = { a b c d}
h =
1×4 cell array
[1] 'x' [1] [1×4 double]
>> whos d e f g h
Name Size Bytes Class Attributes
d 1x4 32 double
e 1x4 8 char
f 1x4 8 char
g 1x4 456 cell
h 1x4 491 cell
<MASK>
2. What would happen if you go beyond the range for a particular type? For example, the largest integer that can be stored in int8 is 127, and the smallest integer is -128, so what would happen if we type cast a larger integer to the type int8? Smaller integer? Use the built-in functions intmin and intmax to find the largest and smallest integers that can be stored in int16 and int32.
<MASK>
3. Think about what the results would be for the following expressions, and then type them in to the terminal to verify your answers. Briefly explain the results for each one.
>> 1\2
>> 1/2
>> int8(1/2)
>> int8(1/3)
>> -5^2
>> (-5) ^ 2
>> 10-6/2
>> 5*4/2*3
>> 1\2
ans =
2
>> 1/2
ans =
0.5000
>> int8(1/2)
ans =
int8
1
>> int8(1/3)
ans =
int8
0
>> -5^2
ans =
-25
>> (-5)^2
ans =
25
>> 10-6/2
ans =
7
>> 5*4/2*3
ans =
30
4.(a) Define the following variables:
>> a
a =
1 0
2 1
>> b
b =
-1 2
0 1
>> c
c =
3
2
>> d
d =
5
<MASK>
4.(b) What is the result of each of the following expressions? Briefly explain what MATLAB is doing for each operation.
1. a + b
2. a .* b
3. a * b
4. a * c
5. a + c
6. a + d
7. a .* d
8. a * d
>> a + b
ans =
0 2
2 2
>> a .* b
ans =
-1 0
0 1
>> a * b
ans =
-1 2
-2 5
>> a * c
ans =
3
8
>> a + c
ans =
4 3
4 3
>> a + d
ans =
6 5
7 6
>> a .* d
ans =
5 0
10 5
>> a * d
ans =
5 0
10 5
<MASK>
>> a
a =
2 0 0
0 2 0
0 0 2
>> a = eye(3,3) * 2
a =
2 0 0
0 2 0
0 0 2
>> d = [2 2 2]
d =
2 2 2
>> a = diag(d)
a =
2 0 0
0 2 0
0 0 2
>> a = zeros(3,3);
>> a(1,1) = 2;
>> a(2,2) = 2;
>> a(3,3) = 2;
>> a
a =
2 0 0
0 2 0
0 0 2
6. Download this code. This code is full syntax errors. Fix the errors and submit the corrected code with name script_full_of_errors_fixed.m in your folder for this HW. Explain in front of each corrected MATLAB statement, why the error occurred. Modify the last two variables so that they display,
>> Persian
Persian =
Persian is a human language
>> Spanish
Spanish =
'Spanish ' 'is ' ' another' 'language'
Modify the last line such that for the last line the code displays,
Persian is not the same as Spanish
<MASK>
The corrected script can be found here
7. Use MATLAB help to find out how you can create a new directory named mynewdir from MATLAB command line. Then change the working directory the newly created directory. Then create a MATLAB script in this directory named myscript.m with the following code in it,
% First create an array from -2*pi to 2:pi
x = -2*pi:pi/20:2*pi;
<MASK>
You can create a new directory and switch the current directory to it using the following commands,
>> mkdir mynewdir
>> cd mynewdir
The script myscript generates a plot of $y$ versus $x$ where $y = |sin(x)|$. In doing so, MATLAB opens a new window called plot window that contains the plot of y as a function of x. Here is the resulting figure:
<MASK>
You get an error message like the following,
<MASK>
And this happens because the script we are trying to run is neither in MATLAB’s working directory, nor in any of MATLAB’s search paths. Therefore, MATLAB gives an error, as it cannot find the requested file.
<UNMASK>
This is the solution to Homework 2: Problems - Variables, Values, and Types.
The following figure illustrates the grade distribution for this homework.
Due Date: Monday Oct 2, 2017 9:00 AM. This homework aims at giving you some experience with MATLAB variables.
1. Type the following in the command window and submit the results. Briefy explain what each assignment does.
>> a = 1
>> b = 'x'
>> c = true
>> whos a b c
>> a == c
>> a + c
>> d = [1 2 3 4]
>> e = ['a' 'b' 'c' 'd']
>> f = ['abcd']
>> g = {‘a’ ‘b’ ‘c’ ‘d’}
>> h = { a b c d}
>> whos d e f g h
>> a = 1
a =
1
>> b = 'x'
b =
x
>> c = true
c =
logical
1
>> whos abc
>> whos a b c
Name Size Bytes Class Attributes
a 1x1 8 double
b 1x1 2 char
c 1x1 1 logical
>> a == c
ans =
logical
1
>> a + c
ans =
2
a == c because, although they are different types, a logical type of true is also represented by the integer 1, so a and c are equivalent, and can be added together.
>> d = [1 2 3 4]
d =
1 2 3 4
>> e = ['a' 'b' 'c' 'd']
e =
abcd
>> f = ['abcd']
f =
abcd
>> g = {'a' 'b' 'c' 'd'}
g =
1×4 cell array
'a' 'b' 'c' 'd'
>> h = { a b c d}
h =
1×4 cell array
[1] 'x' [1] [1×4 double]
>> whos d e f g h
Name Size Bytes Class Attributes
d 1x4 32 double
e 1x4 8 char
f 1x4 8 char
g 1x4 456 cell
h 1x4 491 cell
e and f are equivalent, because they are both just character arrays, e just concatenated all the individual single characters into one array, while f was already concatenated together. g is a cell array of characters ‘a’, ‘b’, ‘c’, and ‘d’, and h is a cell array of the variables a, b, c, and d.
2. What would happen if you go beyond the range for a particular type? For example, the largest integer that can be stored in int8 is 127, and the smallest integer is -128, so what would happen if we type cast a larger integer to the type int8? Smaller integer? Use the built-in functions intmin and intmax to find the largest and smallest integers that can be stored in int16 and int32.
>> int8(200)
ans =
int8
127
>> int8(-150)
ans =
int8
-128
>> intmax('int16')
ans =
int16
32767
>> intmin('int16')
ans =
int16
-32768
>> intmax('int32')
ans =
int32
2147483647
>> intmin('int32')
ans =
int32
-2147483648
3. Think about what the results would be for the following expressions, and then type them in to the terminal to verify your answers. Briefly explain the results for each one.
>> 1\2
>> 1/2
>> int8(1/2)
>> int8(1/3)
>> -5^2
>> (-5) ^ 2
>> 10-6/2
>> 5*4/2*3
>> 1\2
ans =
2
>> 1/2
ans =
0.5000
>> int8(1/2)
ans =
int8
1
>> int8(1/3)
ans =
int8
0
>> -5^2
ans =
-25
>> (-5)^2
ans =
25
>> 10-6/2
ans =
7
>> 5*4/2*3
ans =
30
4.(a) Define the following variables:
>> a
a =
1 0
2 1
>> b
b =
-1 2
0 1
>> c
c =
3
2
>> d
d =
5
>> a = [1 0; 2 1]
a =
1 0
2 1
>> b = [-1 2; 0 1]
b =
-1 2
0 1
>> c = [3; 2]
c =
3
2
>> d = 5
d =
5
4.(b) What is the result of each of the following expressions? Briefly explain what MATLAB is doing for each operation.
1. a + b
2. a .* b
3. a * b
4. a * c
5. a + c
6. a + d
7. a .* d
8. a * d
>> a + b
ans =
0 2
2 2
>> a .* b
ans =
-1 0
0 1
>> a * b
ans =
-1 2
-2 5
>> a * c
ans =
3
8
>> a + c
ans =
4 3
4 3
>> a + d
ans =
6 5
7 6
>> a .* d
ans =
5 0
10 5
>> a * d
ans =
5 0
10 5
5. Provide three different methods of generating the matrix a, one method should use the diag() function, one should use the eye function, and one should use the zeros function.
>> a
a =
2 0 0
0 2 0
0 0 2
>> a = eye(3,3) * 2
a =
2 0 0
0 2 0
0 0 2
>> d = [2 2 2]
d =
2 2 2
>> a = diag(d)
a =
2 0 0
0 2 0
0 0 2
>> a = zeros(3,3);
>> a(1,1) = 2;
>> a(2,2) = 2;
>> a(3,3) = 2;
>> a
a =
2 0 0
0 2 0
0 0 2
6. Download this code. This code is full syntax errors. Fix the errors and submit the corrected code with name script_full_of_errors_fixed.m in your folder for this HW. Explain in front of each corrected MATLAB statement, why the error occurred. Modify the last two variables so that they display,
>> Persian
Persian =
Persian is a human language
>> Spanish
Spanish =
'Spanish ' 'is ' ' another' 'language'
Modify the last line such that for the last line the code displays,
Persian is not the same as Spanish
Explain these results.
The corrected script can be found here
7. Use MATLAB help to find out how you can create a new directory named mynewdir from MATLAB command line. Then change the working directory the newly created directory. Then create a MATLAB script in this directory named myscript.m with the following code in it,
% First create an array from -2*pi to 2:pi
x = -2*pi:pi/20:2*pi;
% Calculate |sin(x)|
y = abs(sin(x));
plot(x,y);
Now on MATLAB command line, run the script by calling its name. What do you get? Save the output as a figure and submit it with your homework.
You can create a new directory and switch the current directory to it using the following commands,
>> mkdir mynewdir
>> cd mynewdir
The script myscript generates a plot of $y$ versus $x$ where $y = |sin(x)|$. In doing so, MATLAB opens a new window called plot window that contains the plot of y as a function of x. Here is the resulting figure:
8. Now change your working directory to the original directory before you created mynewdir directory. Try to run the script myscript you had created again, from MATLAB command line. What do you get? and why?
You get an error message like the following,
>> cd mynewdir\
>> myscript
>> cd ..
>> myscript
Undefined function or variable 'myscript'.
And this happens because the script we are trying to run is neither in MATLAB’s working directory, nor in any of MATLAB’s search paths. Therefore, MATLAB gives an error, as it cannot find the requested file.
|
<MASK>
EXAMPLE 50
The velocity of a particle moving along a line is given by v(t) = 4t3 − 3t2 at time t. If the particle is initially at x = 3 on the line, find its position when t = 2.
<MASK>
Suppose that a(t), the acceleration of a particle at time t, is given by a(t) = 4t − 3, that v(1) = 6, and that f (2) = 5, where f (t) is the position function.
<MASK>
<UNMASK>
<MASK>
CHAPTER 5 Antidifferentiation
E. APPLICATIONS OF ANTIDERIVATIVES; DIFFERENTIAL EQUATIONS
<MASK>
Since f (1) = 6, 13 + C must equal 6; so C must equal 6 − 1 or 5, and f (x) = x3 + 5.
<MASK>
Find a curve whose slope at each point (x, y) equals the reciprocal of the x-value if the curve contains the point (e, −3).
<MASK>
Thus, y = ln x + C. We now use the given condition, by substituting the point (e, −3), to determine C. Since −3 = ln e + C, we have −3 = 1 + C, and C = −4. Then, the solution of the given equation subject to the given condition is
y = ln x − 4.
<MASK>
An equation involving a derivative is called a differential equation. In Examples 48 and 49, we solved two simple differential equations. In each one we were given the derivative of a function and the value of the function at a particular point. The problem of finding the function is called aninitial-value problem and the given condition is called the initial condition.
<MASK>
EXAMPLE 50
The velocity of a particle moving along a line is given by v(t) = 4t3 − 3t2 at time t. If the particle is initially at x = 3 on the line, find its position when t = 2.
SOLUTION: Since
<MASK>
Suppose that a(t), the acceleration of a particle at time t, is given by a(t) = 4t − 3, that v(1) = 6, and that f (2) = 5, where f (t) is the position function.
(a) Find v(t) and f (t).
<MASK>
SOLUTIONS:
<MASK>
For more examples of motion along a line, see Chapter 8, Further Applications of Integration, and Chapter 9, Differential Equations.
Chapter Summary
<MASK>
<MASK>
|
<MASK>
CHAPTER 5 Antidifferentiation
E. APPLICATIONS OF ANTIDERIVATIVES; DIFFERENTIAL EQUATIONS
<MASK>
Since f (1) = 6, 13 + C must equal 6; so C must equal 6 − 1 or 5, and f (x) = x3 + 5.
<MASK>
Find a curve whose slope at each point (x, y) equals the reciprocal of the x-value if the curve contains the point (e, −3).
<MASK>
Thus, y = ln x + C. We now use the given condition, by substituting the point (e, −3), to determine C. Since −3 = ln e + C, we have −3 = 1 + C, and C = −4. Then, the solution of the given equation subject to the given condition is
y = ln x − 4.
<MASK>
An equation involving a derivative is called a differential equation. In Examples 48 and 49, we solved two simple differential equations. In each one we were given the derivative of a function and the value of the function at a particular point. The problem of finding the function is called aninitial-value problem and the given condition is called the initial condition.
<MASK>
EXAMPLE 50
The velocity of a particle moving along a line is given by v(t) = 4t3 − 3t2 at time t. If the particle is initially at x = 3 on the line, find its position when t = 2.
SOLUTION: Since
<MASK>
Suppose that a(t), the acceleration of a particle at time t, is given by a(t) = 4t − 3, that v(1) = 6, and that f (2) = 5, where f (t) is the position function.
(a) Find v(t) and f (t).
<MASK>
SOLUTIONS:
<MASK>
For more examples of motion along a line, see Chapter 8, Further Applications of Integration, and Chapter 9, Differential Equations.
Chapter Summary
<MASK>
<MASK>
<UNMASK>
<MASK>
CHAPTER 5 Antidifferentiation
E. APPLICATIONS OF ANTIDERIVATIVES; DIFFERENTIAL EQUATIONS
<MASK>
Since f (1) = 6, 13 + C must equal 6; so C must equal 6 − 1 or 5, and f (x) = x3 + 5.
<MASK>
Find a curve whose slope at each point (x, y) equals the reciprocal of the x-value if the curve contains the point (e, −3).
<MASK>
Thus, y = ln x + C. We now use the given condition, by substituting the point (e, −3), to determine C. Since −3 = ln e + C, we have −3 = 1 + C, and C = −4. Then, the solution of the given equation subject to the given condition is
y = ln x − 4.
<MASK>
An equation involving a derivative is called a differential equation. In Examples 48 and 49, we solved two simple differential equations. In each one we were given the derivative of a function and the value of the function at a particular point. The problem of finding the function is called aninitial-value problem and the given condition is called the initial condition.
<MASK>
EXAMPLE 50
The velocity of a particle moving along a line is given by v(t) = 4t3 − 3t2 at time t. If the particle is initially at x = 3 on the line, find its position when t = 2.
SOLUTION: Since
Since x(0) = 04 − 03 + C = 3, we see that C = 3, and that the position function is x(t) = t4 t3 + 3. When t = 2, we see that
<MASK>
Suppose that a(t), the acceleration of a particle at time t, is given by a(t) = 4t − 3, that v(1) = 6, and that f (2) = 5, where f (t) is the position function.
(a) Find v(t) and f (t).
<MASK>
SOLUTIONS:
Using v(1) = 6, we get 6 = 2(1)2 − 3(1) + C1, and C1 = 7, from which it follows that v(t) = 2t2 − 3t + 7. Since
<MASK>
For more examples of motion along a line, see Chapter 8, Further Applications of Integration, and Chapter 9, Differential Equations.
Chapter Summary
<MASK>
|
<MASK>
CHAPTER 5 Antidifferentiation
E. APPLICATIONS OF ANTIDERIVATIVES; DIFFERENTIAL EQUATIONS
<MASK>
Since f (1) = 6, 13 + C must equal 6; so C must equal 6 − 1 or 5, and f (x) = x3 + 5.
<MASK>
Find a curve whose slope at each point (x, y) equals the reciprocal of the x-value if the curve contains the point (e, −3).
<MASK>
Thus, y = ln x + C. We now use the given condition, by substituting the point (e, −3), to determine C. Since −3 = ln e + C, we have −3 = 1 + C, and C = −4. Then, the solution of the given equation subject to the given condition is
y = ln x − 4.
<MASK>
An equation involving a derivative is called a differential equation. In Examples 48 and 49, we solved two simple differential equations. In each one we were given the derivative of a function and the value of the function at a particular point. The problem of finding the function is called aninitial-value problem and the given condition is called the initial condition.
<MASK>
EXAMPLE 50
The velocity of a particle moving along a line is given by v(t) = 4t3 − 3t2 at time t. If the particle is initially at x = 3 on the line, find its position when t = 2.
SOLUTION: Since
Since x(0) = 04 − 03 + C = 3, we see that C = 3, and that the position function is x(t) = t4 t3 + 3. When t = 2, we see that
<MASK>
Suppose that a(t), the acceleration of a particle at time t, is given by a(t) = 4t − 3, that v(1) = 6, and that f (2) = 5, where f (t) is the position function.
(a) Find v(t) and f (t).
<MASK>
SOLUTIONS:
Using v(1) = 6, we get 6 = 2(1)2 − 3(1) + C1, and C1 = 7, from which it follows that v(t) = 2t2 − 3t + 7. Since
<MASK>
For more examples of motion along a line, see Chapter 8, Further Applications of Integration, and Chapter 9, Differential Equations.
Chapter Summary
<MASK>
<UNMASK>
<MASK>
CHAPTER 5 Antidifferentiation
E. APPLICATIONS OF ANTIDERIVATIVES; DIFFERENTIAL EQUATIONS
<MASK>
SOLUTION:
Since f (1) = 6, 13 + C must equal 6; so C must equal 6 − 1 or 5, and f (x) = x3 + 5.
<MASK>
Find a curve whose slope at each point (x, y) equals the reciprocal of the x-value if the curve contains the point (e, −3).
<MASK>
Thus, y = ln x + C. We now use the given condition, by substituting the point (e, −3), to determine C. Since −3 = ln e + C, we have −3 = 1 + C, and C = −4. Then, the solution of the given equation subject to the given condition is
y = ln x − 4.
<MASK>
An equation involving a derivative is called a differential equation. In Examples 48 and 49, we solved two simple differential equations. In each one we were given the derivative of a function and the value of the function at a particular point. The problem of finding the function is called aninitial-value problem and the given condition is called the initial condition.
<MASK>
EXAMPLE 50
The velocity of a particle moving along a line is given by v(t) = 4t3 − 3t2 at time t. If the particle is initially at x = 3 on the line, find its position when t = 2.
SOLUTION: Since
Since x(0) = 04 − 03 + C = 3, we see that C = 3, and that the position function is x(t) = t4 t3 + 3. When t = 2, we see that
<MASK>
Suppose that a(t), the acceleration of a particle at time t, is given by a(t) = 4t − 3, that v(1) = 6, and that f (2) = 5, where f (t) is the position function.
(a) Find v(t) and f (t).
<MASK>
SOLUTIONS:
Using v(1) = 6, we get 6 = 2(1)2 − 3(1) + C1, and C1 = 7, from which it follows that v(t) = 2t2 − 3t + 7. Since
<MASK>
For more examples of motion along a line, see Chapter 8, Further Applications of Integration, and Chapter 9, Differential Equations.
Chapter Summary
<MASK>
|
<MASK>
CHAPTER 5 Antidifferentiation
E. APPLICATIONS OF ANTIDERIVATIVES; DIFFERENTIAL EQUATIONS
<MASK>
SOLUTION:
Since f (1) = 6, 13 + C must equal 6; so C must equal 6 − 1 or 5, and f (x) = x3 + 5.
<MASK>
Find a curve whose slope at each point (x, y) equals the reciprocal of the x-value if the curve contains the point (e, −3).
<MASK>
Thus, y = ln x + C. We now use the given condition, by substituting the point (e, −3), to determine C. Since −3 = ln e + C, we have −3 = 1 + C, and C = −4. Then, the solution of the given equation subject to the given condition is
y = ln x − 4.
<MASK>
An equation involving a derivative is called a differential equation. In Examples 48 and 49, we solved two simple differential equations. In each one we were given the derivative of a function and the value of the function at a particular point. The problem of finding the function is called aninitial-value problem and the given condition is called the initial condition.
<MASK>
EXAMPLE 50
The velocity of a particle moving along a line is given by v(t) = 4t3 − 3t2 at time t. If the particle is initially at x = 3 on the line, find its position when t = 2.
SOLUTION: Since
Since x(0) = 04 − 03 + C = 3, we see that C = 3, and that the position function is x(t) = t4 t3 + 3. When t = 2, we see that
<MASK>
Suppose that a(t), the acceleration of a particle at time t, is given by a(t) = 4t − 3, that v(1) = 6, and that f (2) = 5, where f (t) is the position function.
(a) Find v(t) and f (t).
<MASK>
SOLUTIONS:
Using v(1) = 6, we get 6 = 2(1)2 − 3(1) + C1, and C1 = 7, from which it follows that v(t) = 2t2 − 3t + 7. Since
<MASK>
For more examples of motion along a line, see Chapter 8, Further Applications of Integration, and Chapter 9, Differential Equations.
Chapter Summary
<MASK>
<UNMASK>
APPLICATIONS OF ANTIDERIVATIVES; DIFFERENTIAL EQUATIONS - Antidifferentiation - Calculus AB and Calculus BC
CHAPTER 5 Antidifferentiation
E. APPLICATIONS OF ANTIDERIVATIVES; DIFFERENTIAL EQUATIONS
The following examples show how we use given conditions to determine constants of integration.
EXAMPLE 48
Find f (x) if f (x) = 3x2 and f (1) = 6.
SOLUTION:
Since f (1) = 6, 13 + C must equal 6; so C must equal 6 − 1 or 5, and f (x) = x3 + 5.
EXAMPLE 49
Find a curve whose slope at each point (x, y) equals the reciprocal of the x-value if the curve contains the point (e, −3).
SOLUTION: We are given that and that y = −3 when x = e. This equation is also solved by integration. Since
Thus, y = ln x + C. We now use the given condition, by substituting the point (e, −3), to determine C. Since −3 = ln e + C, we have −3 = 1 + C, and C = −4. Then, the solution of the given equation subject to the given condition is
y = ln x − 4.
DIFFERENTIAL EQUATIONS: MOTION PROBLEMS.
An equation involving a derivative is called a differential equation. In Examples 48 and 49, we solved two simple differential equations. In each one we were given the derivative of a function and the value of the function at a particular point. The problem of finding the function is called aninitial-value problem and the given condition is called the initial condition.
In Examples 50 and 51, we use the velocity (or the acceleration) of a particle moving on a line to find the position of the particle. Note especially how the initial conditions are used to evaluate constants of integration.
EXAMPLE 50
The velocity of a particle moving along a line is given by v(t) = 4t3 − 3t2 at time t. If the particle is initially at x = 3 on the line, find its position when t = 2.
SOLUTION: Since
Since x(0) = 04 − 03 + C = 3, we see that C = 3, and that the position function is x(t) = t4 t3 + 3. When t = 2, we see that
x(2) = 24 − 23 + 3 = 16 − 8 + 3 = 11.
EXAMPLE 51
Suppose that a(t), the acceleration of a particle at time t, is given by a(t) = 4t − 3, that v(1) = 6, and that f (2) = 5, where f (t) is the position function.
(a) Find v(t) and f (t).
(b) Find the position of the particle when t = 1.
SOLUTIONS:
Using v(1) = 6, we get 6 = 2(1)2 − 3(1) + C1, and C1 = 7, from which it follows that v(t) = 2t2 − 3t + 7. Since
Using f (2) = 5, we get + 14 + C2, so Thus,
For more examples of motion along a line, see Chapter 8, Further Applications of Integration, and Chapter 9, Differential Equations.
Chapter Summary
In this chapter, we have reviewed basic skills for finding indefinite integrals. We’ve looked at the antiderivative formulas for all of the basic functions and reviewed techniques for finding antiderivatives of other functions.
We’ve also reviewed the more advanced techniques of integration by partial fractions and integration by parts, both topics only for the BC Calculus course.
|
Question
<MASK>
<UNMASK>
Question
<MASK>
The example given above is great and BMI is a great tool for those who are overweight and looking to lose weight and be healthier. However once you get in good shape I would encourage you to start to go more toward body fat testing once you are in a healthy range in your BMI.
• The body mass index (BMI) calculation is the easiest way to get an idea of a healthy weight for your height. The calculation is:
[weight in pounds ÷ inches squared] × 703 = BMI
A healthy BMI score is between 19 and 24.9.
We can reverse the calculation in order to calculate a healthy weight range:
o First square your height in inches. Then multiply be 0.027 (this number comes from a BMI of 19 divided by 703). This is the lower end of your healthy weight range.
o Then take your height in inches squared and multiply by 0.0354 (calculated using a BMI of 24.9 divided by 703). This will give you the high end of your healthy weight range.
Example for a 5’6” person (66 inches):
66 x 66 = 4356.
4356 x 0.027 = 117.7
4356 x 0.0354 = 154.2
o The healthy weight range for this person is 117.7 – 154.2 pounds.
|
Question
<MASK>
The example given above is great and BMI is a great tool for those who are overweight and looking to lose weight and be healthier. However once you get in good shape I would encourage you to start to go more toward body fat testing once you are in a healthy range in your BMI.
• The body mass index (BMI) calculation is the easiest way to get an idea of a healthy weight for your height. The calculation is:
[weight in pounds ÷ inches squared] × 703 = BMI
A healthy BMI score is between 19 and 24.9.
We can reverse the calculation in order to calculate a healthy weight range:
o First square your height in inches. Then multiply be 0.027 (this number comes from a BMI of 19 divided by 703). This is the lower end of your healthy weight range.
o Then take your height in inches squared and multiply by 0.0354 (calculated using a BMI of 24.9 divided by 703). This will give you the high end of your healthy weight range.
Example for a 5’6” person (66 inches):
66 x 66 = 4356.
4356 x 0.027 = 117.7
4356 x 0.0354 = 154.2
o The healthy weight range for this person is 117.7 – 154.2 pounds.
<UNMASK>
Question
<MASK>
# What is a healthy weight for my height?
• BMI is a great tool for measuring healthy weight to height in most people but I wanted to add another thing.
<MASK>
Lets say we have two females, each are 68 in tall. One weighs 120 lbs and has a body fat of 30% and the other is 125 lbs and has a body fat of 20%. Doing the math we will find that the first has about 36 lbs of fat and lean mass of 84 lbs. The second person although heavier has only 25 lbs of fat and lean mass of 100 lbs. The second person believe it or not will be smaller and fit into smaller clothes because they are more dense and compact and toned and tight.
The example given above is great and BMI is a great tool for those who are overweight and looking to lose weight and be healthier. However once you get in good shape I would encourage you to start to go more toward body fat testing once you are in a healthy range in your BMI.
• The body mass index (BMI) calculation is the easiest way to get an idea of a healthy weight for your height. The calculation is:
[weight in pounds ÷ inches squared] × 703 = BMI
A healthy BMI score is between 19 and 24.9.
We can reverse the calculation in order to calculate a healthy weight range:
o First square your height in inches. Then multiply be 0.027 (this number comes from a BMI of 19 divided by 703). This is the lower end of your healthy weight range.
o Then take your height in inches squared and multiply by 0.0354 (calculated using a BMI of 24.9 divided by 703). This will give you the high end of your healthy weight range.
Example for a 5’6” person (66 inches):
66 x 66 = 4356.
4356 x 0.027 = 117.7
4356 x 0.0354 = 154.2
o The healthy weight range for this person is 117.7 – 154.2 pounds.
|
Question
<MASK>
# What is a healthy weight for my height?
• BMI is a great tool for measuring healthy weight to height in most people but I wanted to add another thing.
<MASK>
Lets say we have two females, each are 68 in tall. One weighs 120 lbs and has a body fat of 30% and the other is 125 lbs and has a body fat of 20%. Doing the math we will find that the first has about 36 lbs of fat and lean mass of 84 lbs. The second person although heavier has only 25 lbs of fat and lean mass of 100 lbs. The second person believe it or not will be smaller and fit into smaller clothes because they are more dense and compact and toned and tight.
The example given above is great and BMI is a great tool for those who are overweight and looking to lose weight and be healthier. However once you get in good shape I would encourage you to start to go more toward body fat testing once you are in a healthy range in your BMI.
• The body mass index (BMI) calculation is the easiest way to get an idea of a healthy weight for your height. The calculation is:
[weight in pounds ÷ inches squared] × 703 = BMI
A healthy BMI score is between 19 and 24.9.
We can reverse the calculation in order to calculate a healthy weight range:
o First square your height in inches. Then multiply be 0.027 (this number comes from a BMI of 19 divided by 703). This is the lower end of your healthy weight range.
o Then take your height in inches squared and multiply by 0.0354 (calculated using a BMI of 24.9 divided by 703). This will give you the high end of your healthy weight range.
Example for a 5’6” person (66 inches):
66 x 66 = 4356.
4356 x 0.027 = 117.7
4356 x 0.0354 = 154.2
o The healthy weight range for this person is 117.7 – 154.2 pounds.
<UNMASK>
Question
Evaluating & Measuring Fitness
# What is a healthy weight for my height?
• BMI is a great tool for measuring healthy weight to height in most people but I wanted to add another thing.
<MASK>
Lets say we have two females, each are 68 in tall. One weighs 120 lbs and has a body fat of 30% and the other is 125 lbs and has a body fat of 20%. Doing the math we will find that the first has about 36 lbs of fat and lean mass of 84 lbs. The second person although heavier has only 25 lbs of fat and lean mass of 100 lbs. The second person believe it or not will be smaller and fit into smaller clothes because they are more dense and compact and toned and tight.
The example given above is great and BMI is a great tool for those who are overweight and looking to lose weight and be healthier. However once you get in good shape I would encourage you to start to go more toward body fat testing once you are in a healthy range in your BMI.
• The body mass index (BMI) calculation is the easiest way to get an idea of a healthy weight for your height. The calculation is:
[weight in pounds ÷ inches squared] × 703 = BMI
A healthy BMI score is between 19 and 24.9.
We can reverse the calculation in order to calculate a healthy weight range:
o First square your height in inches. Then multiply be 0.027 (this number comes from a BMI of 19 divided by 703). This is the lower end of your healthy weight range.
o Then take your height in inches squared and multiply by 0.0354 (calculated using a BMI of 24.9 divided by 703). This will give you the high end of your healthy weight range.
Example for a 5’6” person (66 inches):
66 x 66 = 4356.
4356 x 0.027 = 117.7
4356 x 0.0354 = 154.2
o The healthy weight range for this person is 117.7 – 154.2 pounds.
|
Question
Evaluating & Measuring Fitness
# What is a healthy weight for my height?
• BMI is a great tool for measuring healthy weight to height in most people but I wanted to add another thing.
<MASK>
Lets say we have two females, each are 68 in tall. One weighs 120 lbs and has a body fat of 30% and the other is 125 lbs and has a body fat of 20%. Doing the math we will find that the first has about 36 lbs of fat and lean mass of 84 lbs. The second person although heavier has only 25 lbs of fat and lean mass of 100 lbs. The second person believe it or not will be smaller and fit into smaller clothes because they are more dense and compact and toned and tight.
The example given above is great and BMI is a great tool for those who are overweight and looking to lose weight and be healthier. However once you get in good shape I would encourage you to start to go more toward body fat testing once you are in a healthy range in your BMI.
• The body mass index (BMI) calculation is the easiest way to get an idea of a healthy weight for your height. The calculation is:
[weight in pounds ÷ inches squared] × 703 = BMI
A healthy BMI score is between 19 and 24.9.
We can reverse the calculation in order to calculate a healthy weight range:
o First square your height in inches. Then multiply be 0.027 (this number comes from a BMI of 19 divided by 703). This is the lower end of your healthy weight range.
o Then take your height in inches squared and multiply by 0.0354 (calculated using a BMI of 24.9 divided by 703). This will give you the high end of your healthy weight range.
Example for a 5’6” person (66 inches):
66 x 66 = 4356.
4356 x 0.027 = 117.7
4356 x 0.0354 = 154.2
o The healthy weight range for this person is 117.7 – 154.2 pounds.
<UNMASK>
Question
Evaluating & Measuring Fitness
# What is a healthy weight for my height?
• BMI is a great tool for measuring healthy weight to height in most people but I wanted to add another thing.
The better in shape you get and the closer you get to your weight goal I would advice finding a reputable fitness professional that can accurately test your body fat percentage. For many fitness enthusiasts that get in great shape they will have a phenomenal fat to muscle ratio and because they are in shape their weight may not be extremely low because they carry a higher percentage of muscle.
Lets say we have two females, each are 68 in tall. One weighs 120 lbs and has a body fat of 30% and the other is 125 lbs and has a body fat of 20%. Doing the math we will find that the first has about 36 lbs of fat and lean mass of 84 lbs. The second person although heavier has only 25 lbs of fat and lean mass of 100 lbs. The second person believe it or not will be smaller and fit into smaller clothes because they are more dense and compact and toned and tight.
The example given above is great and BMI is a great tool for those who are overweight and looking to lose weight and be healthier. However once you get in good shape I would encourage you to start to go more toward body fat testing once you are in a healthy range in your BMI.
• The body mass index (BMI) calculation is the easiest way to get an idea of a healthy weight for your height. The calculation is:
[weight in pounds ÷ inches squared] × 703 = BMI
A healthy BMI score is between 19 and 24.9.
We can reverse the calculation in order to calculate a healthy weight range:
o First square your height in inches. Then multiply be 0.027 (this number comes from a BMI of 19 divided by 703). This is the lower end of your healthy weight range.
o Then take your height in inches squared and multiply by 0.0354 (calculated using a BMI of 24.9 divided by 703). This will give you the high end of your healthy weight range.
Example for a 5’6” person (66 inches):
66 x 66 = 4356.
4356 x 0.027 = 117.7
4356 x 0.0354 = 154.2
o The healthy weight range for this person is 117.7 – 154.2 pounds.
|
<MASK>
Given that sin x + sin y = a and cos x + cos y =a, where a not equal to 0, express sin x + cos x in terms of a. attemp: sin x = a - sin y cos x = a - cos y sin x + cos x = 2A - (sin y + cos y)
<MASK>
<UNMASK>
<MASK>
express 3 cos x -2 sin x in th eform R cos (x + a) and hence write down the maximum and minimum values of 3 cos x - 2 sin x.
<MASK>
but sin^2a + cos^2a = 1
4/R^2 + 9/R^2 = 1
R^2 = 13
R = √13
<MASK>
check by taking any angle x
let x = 26°
LS =1.8196...
RS = √13 cos(5969) = 1.8196
<MASK>
Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 …
9. ### Trig
<MASK>
Given that sin x + sin y = a and cos x + cos y =a, where a not equal to 0, express sin x + cos x in terms of a. attemp: sin x = a - sin y cos x = a - cos y sin x + cos x = 2A - (sin y + cos y)
<MASK>
|
<MASK>
express 3 cos x -2 sin x in th eform R cos (x + a) and hence write down the maximum and minimum values of 3 cos x - 2 sin x.
<MASK>
but sin^2a + cos^2a = 1
4/R^2 + 9/R^2 = 1
R^2 = 13
R = √13
<MASK>
check by taking any angle x
let x = 26°
LS =1.8196...
RS = √13 cos(5969) = 1.8196
<MASK>
Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 …
9. ### Trig
<MASK>
Given that sin x + sin y = a and cos x + cos y =a, where a not equal to 0, express sin x + cos x in terms of a. attemp: sin x = a - sin y cos x = a - cos y sin x + cos x = 2A - (sin y + cos y)
<MASK>
<UNMASK>
<MASK>
express 3 cos x -2 sin x in th eform R cos (x + a) and hence write down the maximum and minimum values of 3 cos x - 2 sin x.
<MASK>
Rcos(x+a) = R(cosxcosa - sinxsina)
= Rcosxcosa - Rsinxsina
<MASK>
let x = 0
then
Rcos0cosa - Rsin0sins = 3cos0 - 2sin0
Rcosa = 3
cosa = 3/R
<MASK>
but sin^2a + cos^2a = 1
4/R^2 + 9/R^2 = 1
R^2 = 13
R = √13
also : sina/cosa = (2/R) / (3/R) = 23
tana = 2/3
a = arctan (2/3) = 33.69°
thus 3cosx - 2sinx = √13cos(x + 33.69°)
check by taking any angle x
let x = 26°
LS =1.8196...
RS = √13 cos(5969) = 1.8196
## Similar Questions
<MASK>
Reduce the following to the sine or cosine of one angle: (i) sin145*cos75 - cos145*sin75 (ii) cos35*cos15 - sin35*sin15 Use the formulae: sin(a+b)= sin(a) cos(b) + cos(a)sin(b) and cos(a+b)= cos(a)cos(b) - sin(a)sin)(b) (1)The quantity …
2. ### tigonometry
<MASK>
Prove that for all real values of a, b, t (theta): (a * cos t + b * sin t)^2 <= a^2 + b^2 I will be happy to critique your work. Start on the left, square it, (a * cos t + b * sin t)^2 = a^2 (1 - sin^2t) + 2ab sin t cost+ b^2 (1 …
4. ### Trig
Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < 2pi Find: sin (v + u) cos (v - u) tan (v + u) First compute or list the cosine and sine of both u and v. Then use the combination rules sin (v + u) = sin u cos …
<MASK>
Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 …
9. ### Trig
Find sin(s+t) and (s-t) if cos(s)= 1/5 and sin(t) = 3/5 and s and t are in quadrant 1. =Sin(s)cos(t) + Cos(s)Sin(t) =Sin(1/5)Cos(3/5) + Cos(-1/5)Sin(3/5) = 0.389418 Sin(s-t) =sin(s)cos(t) - cos(s)sin(t) =sin(-3/5)cos(1/5) - cos(1/5)sin(3/5) …
10. ### math
Given that sin x + sin y = a and cos x + cos y =a, where a not equal to 0, express sin x + cos x in terms of a. attemp: sin x = a - sin y cos x = a - cos y sin x + cos x = 2A - (sin y + cos y)
More Similar Questions
|
<MASK>
express 3 cos x -2 sin x in th eform R cos (x + a) and hence write down the maximum and minimum values of 3 cos x - 2 sin x.
<MASK>
Rcos(x+a) = R(cosxcosa - sinxsina)
= Rcosxcosa - Rsinxsina
<MASK>
let x = 0
then
Rcos0cosa - Rsin0sins = 3cos0 - 2sin0
Rcosa = 3
cosa = 3/R
<MASK>
but sin^2a + cos^2a = 1
4/R^2 + 9/R^2 = 1
R^2 = 13
R = √13
also : sina/cosa = (2/R) / (3/R) = 23
tana = 2/3
a = arctan (2/3) = 33.69°
thus 3cosx - 2sinx = √13cos(x + 33.69°)
check by taking any angle x
let x = 26°
LS =1.8196...
RS = √13 cos(5969) = 1.8196
## Similar Questions
<MASK>
Reduce the following to the sine or cosine of one angle: (i) sin145*cos75 - cos145*sin75 (ii) cos35*cos15 - sin35*sin15 Use the formulae: sin(a+b)= sin(a) cos(b) + cos(a)sin(b) and cos(a+b)= cos(a)cos(b) - sin(a)sin)(b) (1)The quantity …
2. ### tigonometry
<MASK>
Prove that for all real values of a, b, t (theta): (a * cos t + b * sin t)^2 <= a^2 + b^2 I will be happy to critique your work. Start on the left, square it, (a * cos t + b * sin t)^2 = a^2 (1 - sin^2t) + 2ab sin t cost+ b^2 (1 …
4. ### Trig
Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < 2pi Find: sin (v + u) cos (v - u) tan (v + u) First compute or list the cosine and sine of both u and v. Then use the combination rules sin (v + u) = sin u cos …
<MASK>
Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 …
9. ### Trig
Find sin(s+t) and (s-t) if cos(s)= 1/5 and sin(t) = 3/5 and s and t are in quadrant 1. =Sin(s)cos(t) + Cos(s)Sin(t) =Sin(1/5)Cos(3/5) + Cos(-1/5)Sin(3/5) = 0.389418 Sin(s-t) =sin(s)cos(t) - cos(s)sin(t) =sin(-3/5)cos(1/5) - cos(1/5)sin(3/5) …
10. ### math
Given that sin x + sin y = a and cos x + cos y =a, where a not equal to 0, express sin x + cos x in terms of a. attemp: sin x = a - sin y cos x = a - cos y sin x + cos x = 2A - (sin y + cos y)
More Similar Questions
<UNMASK>
# trigonometry
posted by .
express 3 cos x -2 sin x in th eform R cos (x + a) and hence write down the maximum and minimum values of 3 cos x - 2 sin x.
• trigonometry -
let 3cosx - 2sinx = Rcos(x+a)
Rcos(x+a) = R(cosxcosa - sinxsina)
= Rcosxcosa - Rsinxsina
so we have the identity
Rcosxcosa - Rsinxsina = 3cosx-2sinx
this must be valid for any x
so let's pick x's that simplify this
let x = 0
then
Rcos0cosa - Rsin0sins = 3cos0 - 2sin0
Rcosa = 3
cosa = 3/R
let x = 90°
Rcos90cosa - Rsin90sina = 3cos90 - 2sin90
-Rsina = -2
sina = 2/R
but sin^2a + cos^2a = 1
4/R^2 + 9/R^2 = 1
R^2 = 13
R = √13
also : sina/cosa = (2/R) / (3/R) = 23
tana = 2/3
a = arctan (2/3) = 33.69°
thus 3cosx - 2sinx = √13cos(x + 33.69°)
check by taking any angle x
let x = 26°
LS =1.8196...
RS = √13 cos(5969) = 1.8196
## Similar Questions
1. ### trig
Reduce the following to the sine or cosine of one angle: (i) sin145*cos75 - cos145*sin75 (ii) cos35*cos15 - sin35*sin15 Use the formulae: sin(a+b)= sin(a) cos(b) + cos(a)sin(b) and cos(a+b)= cos(a)cos(b) - sin(a)sin)(b) (1)The quantity …
2. ### tigonometry
expres the following as sums and differences of sines or cosines cos8t * sin2t sin(a+b) = sin(a)cos(b) + cos(a)sin(b) replacing by by -b and using that cos(-b)= cos(b) sin(-b)= -sin(b) gives: sin(a-b) = sin(a)cos(b) - cos(a)sin(b) …
3. ### math
Prove that for all real values of a, b, t (theta): (a * cos t + b * sin t)^2 <= a^2 + b^2 I will be happy to critique your work. Start on the left, square it, (a * cos t + b * sin t)^2 = a^2 (1 - sin^2t) + 2ab sin t cost+ b^2 (1 …
4. ### Trig
Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < 2pi Find: sin (v + u) cos (v - u) tan (v + u) First compute or list the cosine and sine of both u and v. Then use the combination rules sin (v + u) = sin u cos …
6. ### pre-cal
Simplify the given expression........? (2sin2x)(cos6x) sin 2x and cos 6x can be expressed as a series of terms that involve sin x or cos x only, but the end result is not a simplification. sin 2x = 2 sinx cosx cos 6x = 32 cos^6 x -48
7. ### Mathematics - Trigonometric Identities
<MASK>
Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 …
9. ### Trig
Find sin(s+t) and (s-t) if cos(s)= 1/5 and sin(t) = 3/5 and s and t are in quadrant 1. =Sin(s)cos(t) + Cos(s)Sin(t) =Sin(1/5)Cos(3/5) + Cos(-1/5)Sin(3/5) = 0.389418 Sin(s-t) =sin(s)cos(t) - cos(s)sin(t) =sin(-3/5)cos(1/5) - cos(1/5)sin(3/5) …
10. ### math
Given that sin x + sin y = a and cos x + cos y =a, where a not equal to 0, express sin x + cos x in terms of a. attemp: sin x = a - sin y cos x = a - cos y sin x + cos x = 2A - (sin y + cos y)
More Similar Questions
|
# trigonometry
posted by .
express 3 cos x -2 sin x in th eform R cos (x + a) and hence write down the maximum and minimum values of 3 cos x - 2 sin x.
• trigonometry -
let 3cosx - 2sinx = Rcos(x+a)
Rcos(x+a) = R(cosxcosa - sinxsina)
= Rcosxcosa - Rsinxsina
so we have the identity
Rcosxcosa - Rsinxsina = 3cosx-2sinx
this must be valid for any x
so let's pick x's that simplify this
let x = 0
then
Rcos0cosa - Rsin0sins = 3cos0 - 2sin0
Rcosa = 3
cosa = 3/R
let x = 90°
Rcos90cosa - Rsin90sina = 3cos90 - 2sin90
-Rsina = -2
sina = 2/R
but sin^2a + cos^2a = 1
4/R^2 + 9/R^2 = 1
R^2 = 13
R = √13
also : sina/cosa = (2/R) / (3/R) = 23
tana = 2/3
a = arctan (2/3) = 33.69°
thus 3cosx - 2sinx = √13cos(x + 33.69°)
check by taking any angle x
let x = 26°
LS =1.8196...
RS = √13 cos(5969) = 1.8196
## Similar Questions
1. ### trig
Reduce the following to the sine or cosine of one angle: (i) sin145*cos75 - cos145*sin75 (ii) cos35*cos15 - sin35*sin15 Use the formulae: sin(a+b)= sin(a) cos(b) + cos(a)sin(b) and cos(a+b)= cos(a)cos(b) - sin(a)sin)(b) (1)The quantity …
2. ### tigonometry
expres the following as sums and differences of sines or cosines cos8t * sin2t sin(a+b) = sin(a)cos(b) + cos(a)sin(b) replacing by by -b and using that cos(-b)= cos(b) sin(-b)= -sin(b) gives: sin(a-b) = sin(a)cos(b) - cos(a)sin(b) …
3. ### math
Prove that for all real values of a, b, t (theta): (a * cos t + b * sin t)^2 <= a^2 + b^2 I will be happy to critique your work. Start on the left, square it, (a * cos t + b * sin t)^2 = a^2 (1 - sin^2t) + 2ab sin t cost+ b^2 (1 …
4. ### Trig
Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < 2pi Find: sin (v + u) cos (v - u) tan (v + u) First compute or list the cosine and sine of both u and v. Then use the combination rules sin (v + u) = sin u cos …
6. ### pre-cal
Simplify the given expression........? (2sin2x)(cos6x) sin 2x and cos 6x can be expressed as a series of terms that involve sin x or cos x only, but the end result is not a simplification. sin 2x = 2 sinx cosx cos 6x = 32 cos^6 x -48
7. ### Mathematics - Trigonometric Identities
<MASK>
Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 …
9. ### Trig
Find sin(s+t) and (s-t) if cos(s)= 1/5 and sin(t) = 3/5 and s and t are in quadrant 1. =Sin(s)cos(t) + Cos(s)Sin(t) =Sin(1/5)Cos(3/5) + Cos(-1/5)Sin(3/5) = 0.389418 Sin(s-t) =sin(s)cos(t) - cos(s)sin(t) =sin(-3/5)cos(1/5) - cos(1/5)sin(3/5) …
10. ### math
Given that sin x + sin y = a and cos x + cos y =a, where a not equal to 0, express sin x + cos x in terms of a. attemp: sin x = a - sin y cos x = a - cos y sin x + cos x = 2A - (sin y + cos y)
More Similar Questions
<UNMASK>
# trigonometry
posted by .
express 3 cos x -2 sin x in th eform R cos (x + a) and hence write down the maximum and minimum values of 3 cos x - 2 sin x.
• trigonometry -
let 3cosx - 2sinx = Rcos(x+a)
Rcos(x+a) = R(cosxcosa - sinxsina)
= Rcosxcosa - Rsinxsina
so we have the identity
Rcosxcosa - Rsinxsina = 3cosx-2sinx
this must be valid for any x
so let's pick x's that simplify this
let x = 0
then
Rcos0cosa - Rsin0sins = 3cos0 - 2sin0
Rcosa = 3
cosa = 3/R
let x = 90°
Rcos90cosa - Rsin90sina = 3cos90 - 2sin90
-Rsina = -2
sina = 2/R
but sin^2a + cos^2a = 1
4/R^2 + 9/R^2 = 1
R^2 = 13
R = √13
also : sina/cosa = (2/R) / (3/R) = 23
tana = 2/3
a = arctan (2/3) = 33.69°
thus 3cosx - 2sinx = √13cos(x + 33.69°)
check by taking any angle x
let x = 26°
LS =1.8196...
RS = √13 cos(5969) = 1.8196
## Similar Questions
1. ### trig
Reduce the following to the sine or cosine of one angle: (i) sin145*cos75 - cos145*sin75 (ii) cos35*cos15 - sin35*sin15 Use the formulae: sin(a+b)= sin(a) cos(b) + cos(a)sin(b) and cos(a+b)= cos(a)cos(b) - sin(a)sin)(b) (1)The quantity …
2. ### tigonometry
expres the following as sums and differences of sines or cosines cos8t * sin2t sin(a+b) = sin(a)cos(b) + cos(a)sin(b) replacing by by -b and using that cos(-b)= cos(b) sin(-b)= -sin(b) gives: sin(a-b) = sin(a)cos(b) - cos(a)sin(b) …
3. ### math
Prove that for all real values of a, b, t (theta): (a * cos t + b * sin t)^2 <= a^2 + b^2 I will be happy to critique your work. Start on the left, square it, (a * cos t + b * sin t)^2 = a^2 (1 - sin^2t) + 2ab sin t cost+ b^2 (1 …
4. ### Trig
Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < 2pi Find: sin (v + u) cos (v - u) tan (v + u) First compute or list the cosine and sine of both u and v. Then use the combination rules sin (v + u) = sin u cos …
6. ### pre-cal
Simplify the given expression........? (2sin2x)(cos6x) sin 2x and cos 6x can be expressed as a series of terms that involve sin x or cos x only, but the end result is not a simplification. sin 2x = 2 sinx cosx cos 6x = 32 cos^6 x -48
7. ### Mathematics - Trigonometric Identities
Let y represent theta Prove: 1 + 1/tan^2y = 1/sin^2y My Answer: LS: = 1 + 1/tan^2y = (sin^2y + cos^2y) + 1 /(sin^2y/cos^2y) = (sin^2y + cos^2y) + 1 x (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y) (cos^2y/sin^2y) = (sin^2y …
8. ### TRIG!
Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 …
9. ### Trig
Find sin(s+t) and (s-t) if cos(s)= 1/5 and sin(t) = 3/5 and s and t are in quadrant 1. =Sin(s)cos(t) + Cos(s)Sin(t) =Sin(1/5)Cos(3/5) + Cos(-1/5)Sin(3/5) = 0.389418 Sin(s-t) =sin(s)cos(t) - cos(s)sin(t) =sin(-3/5)cos(1/5) - cos(1/5)sin(3/5) …
10. ### math
Given that sin x + sin y = a and cos x + cos y =a, where a not equal to 0, express sin x + cos x in terms of a. attemp: sin x = a - sin y cos x = a - cos y sin x + cos x = 2A - (sin y + cos y)
More Similar Questions
|
<MASK>
12% = 12 percent = 12 parts out the 100 =
<MASK>
B) 11%
<MASK>
A) 3%
Incorrect. Three complete columns that 10 squares space shaded, plus an additional 8 squares indigenous the next column. So, there space 30 + 8, or 38, squares shaded the end of the 100 squares in the large square. The exactly answer is 38%.
<MASK>
Incorrect. Three complete columns of 10 squares room shaded, plus another 8 squares native the following column. So, there space 30 + 8, or 38, squares shaded the end of the 100 squares in the big square. The correct answer is 38%.
C) 38%
<MASK>
Rewriting Percents, Decimals, and also Fractions
<MASK>
Percents can be composed as fractions and also decimals in very few steps.
<MASK>
Notice that in the vault example, rewriting a percent together a decimal takes just a shift of the decimal point. You have the right to use fractions to recognize why this is the case. Any type of percentage x can be represented as the portion , and any fraction can be created as a decimal by moving the decimal suggest in x two places to the left. For example, 81% can be composed as
, and dividing 81 by 100 results in 0.81. People often skip end the intermediary portion step and just convert a percent come a decimal by relocating the decimal suggest two places to the left.
<MASK>
In this example, the percent is not a entirety number. You can handle this in the exact same way, yet it’s usually less complicated to convert the percent come a decimal and also then transform the decimal to a fraction.
<MASK>
Example Problem Write as a decimal and as a percent. Write together a decimal. Find one equivalent portion with 10, 100, 1,000, or various other power that 10 in the denominator. Due to the fact that 100 is a lot of of 4, you deserve to multiply 4 through 25 to obtain 100. Multiply both the numerator and also the denominator by 25. = 0.75 Write the fraction as a decimal through the 5 in the percentage percent place. Write as a percent. 0.75 = 75% To create the decimal together a percent, move the decimal suggest two locations to the right. Answer = 0.75 = 75%
<MASK>
Example Problem Write as a decimal and also as a percent. Write as a decimal. Divide the molecule by the denominator. 3 ÷ 8 = 0.375. Write as a percent. 0.375 = 37.5% To create the decimal together a percent, relocate the decimal allude two areas to the right. Answer = 0.375 = 37.5%
<MASK>
A) 80.0 and 0.8%
<MASK>
D) 0.8 and also 8%
A) 80.0 and also 0.8%
<MASK>
Incorrect. It is true the = 0.8, however this does not equal 8%. To create 0.8 as a percent, relocate the decimal allude two locations to the right: 0.8 = 0.80 = 80%. The correct answer is 0.8 and also 80%.
<MASK>
In the diagram below, 115% is shaded. Every grid is taken into consideration a whole, and also you require two grids for 115%.
<MASK>
<UNMASK>
<MASK>
Notice the 12 that the 100 squares in the grid below have to be shaded green. This to represent 12 percent (12 per 100).
12% = 12 percent = 12 parts out the 100 =
<MASK>
What percent that this network is shaded?
<MASK>
B) 11%
<MASK>
A) 3%
Incorrect. Three complete columns that 10 squares space shaded, plus an additional 8 squares indigenous the next column. So, there space 30 + 8, or 38, squares shaded the end of the 100 squares in the large square. The exactly answer is 38%.
<MASK>
Incorrect. Three complete columns of 10 squares room shaded, plus another 8 squares native the following column. So, there space 30 + 8, or 38, squares shaded the end of the 100 squares in the big square. The correct answer is 38%.
C) 38%
<MASK>
Rewriting Percents, Decimals, and also Fractions
<MASK>
Percents can be composed as fractions and also decimals in very few steps.
<MASK>
Notice that in the vault example, rewriting a percent together a decimal takes just a shift of the decimal point. You have the right to use fractions to recognize why this is the case. Any type of percentage x can be represented as the portion , and any fraction can be created as a decimal by moving the decimal suggest in x two places to the left. For example, 81% can be composed as
, and dividing 81 by 100 results in 0.81. People often skip end the intermediary portion step and just convert a percent come a decimal by relocating the decimal suggest two places to the left.
<MASK>
In this example, the percent is not a entirety number. You can handle this in the exact same way, yet it’s usually less complicated to convert the percent come a decimal and also then transform the decimal to a fraction.
<MASK>
Example Problem Write as a decimal and as a percent. Write together a decimal. Find one equivalent portion with 10, 100, 1,000, or various other power that 10 in the denominator. Due to the fact that 100 is a lot of of 4, you deserve to multiply 4 through 25 to obtain 100. Multiply both the numerator and also the denominator by 25. = 0.75 Write the fraction as a decimal through the 5 in the percentage percent place. Write as a percent. 0.75 = 75% To create the decimal together a percent, move the decimal suggest two locations to the right. Answer = 0.75 = 75%
<MASK>
Example Problem Write as a decimal and also as a percent. Write as a decimal. Divide the molecule by the denominator. 3 ÷ 8 = 0.375. Write as a percent. 0.375 = 37.5% To create the decimal together a percent, relocate the decimal allude two areas to the right. Answer = 0.375 = 37.5%
<MASK>
A) 80.0 and 0.8%
B) 0.4 and 4%
<MASK>
D) 0.8 and also 8%
A) 80.0 and also 0.8%
<MASK>
Incorrect. To uncover a decimal indistinguishable for , an initial convert the portion to tenths. Multiply the numerator and denominator by 2 to acquire . The tantamount decimal is 0.8. So, and 0.4 space not indistinguishable quantities. The correct answer is 0.8 and 80%.
C) 0.8 and also 80%
Correct. The price is = 0.8 = 80%.
<MASK>
Incorrect. It is true the = 0.8, however this does not equal 8%. To create 0.8 as a percent, relocate the decimal allude two locations to the right: 0.8 = 0.80 = 80%. The correct answer is 0.8 and also 80%.
<MASK>
In the diagram below, 115% is shaded. Every grid is taken into consideration a whole, and also you require two grids for 115%.
<MASK>
Write 4.12 as a percent and also as a simplified fraction. A) 0.0412% and B) 412% and also C) 412% and also D) 4.12% and also Show/Hide Answer A) 0.0412% and Incorrect. To convert 4.12 to a percent, move the decimal suggest two locations to the right, not the left. The exactly answer is 412% and also . B) 412% and also Correct. 4.12 amounts to 412%, and also the simplified kind of is . C) 412% and Incorrect. 4.12 does equal 412%, yet it is also equivalent to , no . The correct answer is 412% and also . D) 4.12% and also Incorrect. To transform 4.12 come a percent, relocate the decimal allude two places to the right. The exactly answer is 412% and .See more: How To Build An Indoor Pitching Mound Plans: Step By Step Instructions Summary Percents space a common means to stand for fractional amounts, simply as decimals and fractions are. Any number that deserve to be composed as a decimal, fraction, or percent can also be written utilizing the various other two representations. .tags a { color: #fff; background: #909295; padding: 3px 10px; border-radius: 10px; font-size: 13px; line-height: 30px; white-space: nowrap; } .tags a:hover { background: #818182; } Home Contact - Advertising Copyright © 2022 dearteassociazione.org #footer {font-size: 14px;background: #ffffff;padding: 10px;text-align: center;} #footer a {color: #2c2b2b;margin-right: 10px;}
|
<MASK>
Notice the 12 that the 100 squares in the grid below have to be shaded green. This to represent 12 percent (12 per 100).
12% = 12 percent = 12 parts out the 100 =
<MASK>
What percent that this network is shaded?
<MASK>
B) 11%
<MASK>
A) 3%
Incorrect. Three complete columns that 10 squares space shaded, plus an additional 8 squares indigenous the next column. So, there space 30 + 8, or 38, squares shaded the end of the 100 squares in the large square. The exactly answer is 38%.
<MASK>
Incorrect. Three complete columns of 10 squares room shaded, plus another 8 squares native the following column. So, there space 30 + 8, or 38, squares shaded the end of the 100 squares in the big square. The correct answer is 38%.
C) 38%
<MASK>
Rewriting Percents, Decimals, and also Fractions
<MASK>
Percents can be composed as fractions and also decimals in very few steps.
<MASK>
Notice that in the vault example, rewriting a percent together a decimal takes just a shift of the decimal point. You have the right to use fractions to recognize why this is the case. Any type of percentage x can be represented as the portion , and any fraction can be created as a decimal by moving the decimal suggest in x two places to the left. For example, 81% can be composed as
, and dividing 81 by 100 results in 0.81. People often skip end the intermediary portion step and just convert a percent come a decimal by relocating the decimal suggest two places to the left.
<MASK>
In this example, the percent is not a entirety number. You can handle this in the exact same way, yet it’s usually less complicated to convert the percent come a decimal and also then transform the decimal to a fraction.
<MASK>
Example Problem Write as a decimal and as a percent. Write together a decimal. Find one equivalent portion with 10, 100, 1,000, or various other power that 10 in the denominator. Due to the fact that 100 is a lot of of 4, you deserve to multiply 4 through 25 to obtain 100. Multiply both the numerator and also the denominator by 25. = 0.75 Write the fraction as a decimal through the 5 in the percentage percent place. Write as a percent. 0.75 = 75% To create the decimal together a percent, move the decimal suggest two locations to the right. Answer = 0.75 = 75%
<MASK>
Example Problem Write as a decimal and also as a percent. Write as a decimal. Divide the molecule by the denominator. 3 ÷ 8 = 0.375. Write as a percent. 0.375 = 37.5% To create the decimal together a percent, relocate the decimal allude two areas to the right. Answer = 0.375 = 37.5%
<MASK>
A) 80.0 and 0.8%
B) 0.4 and 4%
<MASK>
D) 0.8 and also 8%
A) 80.0 and also 0.8%
<MASK>
Incorrect. To uncover a decimal indistinguishable for , an initial convert the portion to tenths. Multiply the numerator and denominator by 2 to acquire . The tantamount decimal is 0.8. So, and 0.4 space not indistinguishable quantities. The correct answer is 0.8 and 80%.
C) 0.8 and also 80%
Correct. The price is = 0.8 = 80%.
<MASK>
Incorrect. It is true the = 0.8, however this does not equal 8%. To create 0.8 as a percent, relocate the decimal allude two locations to the right: 0.8 = 0.80 = 80%. The correct answer is 0.8 and also 80%.
<MASK>
In the diagram below, 115% is shaded. Every grid is taken into consideration a whole, and also you require two grids for 115%.
<MASK>
Write 4.12 as a percent and also as a simplified fraction. A) 0.0412% and B) 412% and also C) 412% and also D) 4.12% and also Show/Hide Answer A) 0.0412% and Incorrect. To convert 4.12 to a percent, move the decimal suggest two locations to the right, not the left. The exactly answer is 412% and also . B) 412% and also Correct. 4.12 amounts to 412%, and also the simplified kind of is . C) 412% and Incorrect. 4.12 does equal 412%, yet it is also equivalent to , no . The correct answer is 412% and also . D) 4.12% and also Incorrect. To transform 4.12 come a percent, relocate the decimal allude two places to the right. The exactly answer is 412% and .See more: How To Build An Indoor Pitching Mound Plans: Step By Step Instructions Summary Percents space a common means to stand for fractional amounts, simply as decimals and fractions are. Any number that deserve to be composed as a decimal, fraction, or percent can also be written utilizing the various other two representations. .tags a { color: #fff; background: #909295; padding: 3px 10px; border-radius: 10px; font-size: 13px; line-height: 30px; white-space: nowrap; } .tags a:hover { background: #818182; } Home Contact - Advertising Copyright © 2022 dearteassociazione.org #footer {font-size: 14px;background: #ffffff;padding: 10px;text-align: center;} #footer a {color: #2c2b2b;margin-right: 10px;}
<UNMASK>
<MASK>
Notice the 12 that the 100 squares in the grid below have to be shaded green. This to represent 12 percent (12 per 100).
12% = 12 percent = 12 parts out the 100 =
How countless of the squares in the grid over are unshaded? due to the fact that 12 space shaded and there room a full of 100 squares, 88 space unshaded. The unshaded section of the totality grid is 88 components out of 100, or 88% of the grid. Notice that the shaded and also unshaded portions together make 100% of the network (100 out of 100 squares).
<MASK>
What percent that this network is shaded?
<MASK>
B) 11%
<MASK>
A) 3%
Incorrect. Three complete columns that 10 squares space shaded, plus an additional 8 squares indigenous the next column. So, there space 30 + 8, or 38, squares shaded the end of the 100 squares in the large square. The exactly answer is 38%.
<MASK>
Incorrect. Three complete columns of 10 squares room shaded, plus another 8 squares native the following column. So, there space 30 + 8, or 38, squares shaded the end of the 100 squares in the big square. The correct answer is 38%.
C) 38%
<MASK>
D) 62%
<MASK>
Rewriting Percents, Decimals, and also Fractions
It is often helpful to readjust the layout of a number. Because that example, girlfriend may find it less complicated to add decimals 보다 to include fractions. If you have the right to write the fractions together decimals, girlfriend can add them as decimals. Then you can rewrite your decimal amount as a fraction, if necessary.
Percents can be composed as fractions and also decimals in very few steps.
<MASK>
Notice that in the vault example, rewriting a percent together a decimal takes just a shift of the decimal point. You have the right to use fractions to recognize why this is the case. Any type of percentage x can be represented as the portion , and any fraction can be created as a decimal by moving the decimal suggest in x two places to the left. For example, 81% can be composed as
, and dividing 81 by 100 results in 0.81. People often skip end the intermediary portion step and just convert a percent come a decimal by relocating the decimal suggest two places to the left.
<MASK>
In this example, the percent is not a entirety number. You can handle this in the exact same way, yet it’s usually less complicated to convert the percent come a decimal and also then transform the decimal to a fraction.
<MASK>
Example Problem Write as a decimal and as a percent. Write together a decimal. Find one equivalent portion with 10, 100, 1,000, or various other power that 10 in the denominator. Due to the fact that 100 is a lot of of 4, you deserve to multiply 4 through 25 to obtain 100. Multiply both the numerator and also the denominator by 25. = 0.75 Write the fraction as a decimal through the 5 in the percentage percent place. Write as a percent. 0.75 = 75% To create the decimal together a percent, move the decimal suggest two locations to the right. Answer = 0.75 = 75%
<MASK>
Example Problem Write as a decimal and also as a percent. Write as a decimal. Divide the molecule by the denominator. 3 ÷ 8 = 0.375. Write as a percent. 0.375 = 37.5% To create the decimal together a percent, relocate the decimal allude two areas to the right. Answer = 0.375 = 37.5%
<MASK>
A) 80.0 and 0.8%
B) 0.4 and 4%
<MASK>
D) 0.8 and also 8%
A) 80.0 and also 0.8%
<MASK>
Incorrect. To uncover a decimal indistinguishable for , an initial convert the portion to tenths. Multiply the numerator and denominator by 2 to acquire . The tantamount decimal is 0.8. So, and 0.4 space not indistinguishable quantities. The correct answer is 0.8 and 80%.
C) 0.8 and also 80%
Correct. The price is = 0.8 = 80%.
<MASK>
Incorrect. It is true the = 0.8, however this does not equal 8%. To create 0.8 as a percent, relocate the decimal allude two locations to the right: 0.8 = 0.80 = 80%. The correct answer is 0.8 and also 80%.
<MASK>
In the diagram below, 115% is shaded. Every grid is taken into consideration a whole, and also you require two grids for 115%.
<MASK>
Write 4.12 as a percent and also as a simplified fraction. A) 0.0412% and B) 412% and also C) 412% and also D) 4.12% and also Show/Hide Answer A) 0.0412% and Incorrect. To convert 4.12 to a percent, move the decimal suggest two locations to the right, not the left. The exactly answer is 412% and also . B) 412% and also Correct. 4.12 amounts to 412%, and also the simplified kind of is . C) 412% and Incorrect. 4.12 does equal 412%, yet it is also equivalent to , no . The correct answer is 412% and also . D) 4.12% and also Incorrect. To transform 4.12 come a percent, relocate the decimal allude two places to the right. The exactly answer is 412% and .See more: How To Build An Indoor Pitching Mound Plans: Step By Step Instructions Summary Percents space a common means to stand for fractional amounts, simply as decimals and fractions are. Any number that deserve to be composed as a decimal, fraction, or percent can also be written utilizing the various other two representations. .tags a { color: #fff; background: #909295; padding: 3px 10px; border-radius: 10px; font-size: 13px; line-height: 30px; white-space: nowrap; } .tags a:hover { background: #818182; } Home Contact - Advertising Copyright © 2022 dearteassociazione.org #footer {font-size: 14px;background: #ffffff;padding: 10px;text-align: center;} #footer a {color: #2c2b2b;margin-right: 10px;}
|
<MASK>
Notice the 12 that the 100 squares in the grid below have to be shaded green. This to represent 12 percent (12 per 100).
12% = 12 percent = 12 parts out the 100 =
How countless of the squares in the grid over are unshaded? due to the fact that 12 space shaded and there room a full of 100 squares, 88 space unshaded. The unshaded section of the totality grid is 88 components out of 100, or 88% of the grid. Notice that the shaded and also unshaded portions together make 100% of the network (100 out of 100 squares).
<MASK>
What percent that this network is shaded?
<MASK>
B) 11%
<MASK>
A) 3%
Incorrect. Three complete columns that 10 squares space shaded, plus an additional 8 squares indigenous the next column. So, there space 30 + 8, or 38, squares shaded the end of the 100 squares in the large square. The exactly answer is 38%.
<MASK>
Incorrect. Three complete columns of 10 squares room shaded, plus another 8 squares native the following column. So, there space 30 + 8, or 38, squares shaded the end of the 100 squares in the big square. The correct answer is 38%.
C) 38%
<MASK>
D) 62%
<MASK>
Rewriting Percents, Decimals, and also Fractions
It is often helpful to readjust the layout of a number. Because that example, girlfriend may find it less complicated to add decimals 보다 to include fractions. If you have the right to write the fractions together decimals, girlfriend can add them as decimals. Then you can rewrite your decimal amount as a fraction, if necessary.
Percents can be composed as fractions and also decimals in very few steps.
<MASK>
Notice that in the vault example, rewriting a percent together a decimal takes just a shift of the decimal point. You have the right to use fractions to recognize why this is the case. Any type of percentage x can be represented as the portion , and any fraction can be created as a decimal by moving the decimal suggest in x two places to the left. For example, 81% can be composed as
, and dividing 81 by 100 results in 0.81. People often skip end the intermediary portion step and just convert a percent come a decimal by relocating the decimal suggest two places to the left.
<MASK>
In this example, the percent is not a entirety number. You can handle this in the exact same way, yet it’s usually less complicated to convert the percent come a decimal and also then transform the decimal to a fraction.
<MASK>
Example Problem Write as a decimal and as a percent. Write together a decimal. Find one equivalent portion with 10, 100, 1,000, or various other power that 10 in the denominator. Due to the fact that 100 is a lot of of 4, you deserve to multiply 4 through 25 to obtain 100. Multiply both the numerator and also the denominator by 25. = 0.75 Write the fraction as a decimal through the 5 in the percentage percent place. Write as a percent. 0.75 = 75% To create the decimal together a percent, move the decimal suggest two locations to the right. Answer = 0.75 = 75%
<MASK>
Example Problem Write as a decimal and also as a percent. Write as a decimal. Divide the molecule by the denominator. 3 ÷ 8 = 0.375. Write as a percent. 0.375 = 37.5% To create the decimal together a percent, relocate the decimal allude two areas to the right. Answer = 0.375 = 37.5%
<MASK>
A) 80.0 and 0.8%
B) 0.4 and 4%
<MASK>
D) 0.8 and also 8%
A) 80.0 and also 0.8%
<MASK>
Incorrect. To uncover a decimal indistinguishable for , an initial convert the portion to tenths. Multiply the numerator and denominator by 2 to acquire . The tantamount decimal is 0.8. So, and 0.4 space not indistinguishable quantities. The correct answer is 0.8 and 80%.
C) 0.8 and also 80%
Correct. The price is = 0.8 = 80%.
<MASK>
Incorrect. It is true the = 0.8, however this does not equal 8%. To create 0.8 as a percent, relocate the decimal allude two locations to the right: 0.8 = 0.80 = 80%. The correct answer is 0.8 and also 80%.
<MASK>
In the diagram below, 115% is shaded. Every grid is taken into consideration a whole, and also you require two grids for 115%.
<MASK>
Write 4.12 as a percent and also as a simplified fraction. A) 0.0412% and B) 412% and also C) 412% and also D) 4.12% and also Show/Hide Answer A) 0.0412% and Incorrect. To convert 4.12 to a percent, move the decimal suggest two locations to the right, not the left. The exactly answer is 412% and also . B) 412% and also Correct. 4.12 amounts to 412%, and also the simplified kind of is . C) 412% and Incorrect. 4.12 does equal 412%, yet it is also equivalent to , no . The correct answer is 412% and also . D) 4.12% and also Incorrect. To transform 4.12 come a percent, relocate the decimal allude two places to the right. The exactly answer is 412% and .See more: How To Build An Indoor Pitching Mound Plans: Step By Step Instructions Summary Percents space a common means to stand for fractional amounts, simply as decimals and fractions are. Any number that deserve to be composed as a decimal, fraction, or percent can also be written utilizing the various other two representations. .tags a { color: #fff; background: #909295; padding: 3px 10px; border-radius: 10px; font-size: 13px; line-height: 30px; white-space: nowrap; } .tags a:hover { background: #818182; } Home Contact - Advertising Copyright © 2022 dearteassociazione.org #footer {font-size: 14px;background: #ffffff;padding: 10px;text-align: center;} #footer a {color: #2c2b2b;margin-right: 10px;}
<UNMASK>
Three common formats for numbers room fractions, decimals, and percents.
You are watching: How do you write 0.6 as a fraction
Percents are regularly used to connect a family member amount. You have probably seen them supplied for discounts, where the percent the discount can apply to different prices. Percents are likewise used when stating taxes and also interest rates on savings and also loans.
A percent is a proportion of a number come 100. Every cent way “per 100,” or “how numerous out that 100.” You usage the price % ~ a number to show percent.
Notice the 12 that the 100 squares in the grid below have to be shaded green. This to represent 12 percent (12 per 100).
12% = 12 percent = 12 parts out the 100 =
How countless of the squares in the grid over are unshaded? due to the fact that 12 space shaded and there room a full of 100 squares, 88 space unshaded. The unshaded section of the totality grid is 88 components out of 100, or 88% of the grid. Notice that the shaded and also unshaded portions together make 100% of the network (100 out of 100 squares).
<MASK>
Example Problem What percent of the big square is shaded? The net is divided into 10 rectangles. For percents, you need to look at 100 equal-sized parts of the whole. You can divide each of the 10 rectangles right into 10 pieces, providing 100 parts. 30 tiny squares out of 100 space shaded. Answer 30% of the huge square is shaded.
What percent that this network is shaded?
<MASK>
B) 11%
<MASK>
D) 62%
A) 3%
Incorrect. Three complete columns that 10 squares space shaded, plus an additional 8 squares indigenous the next column. So, there space 30 + 8, or 38, squares shaded the end of the 100 squares in the large square. The exactly answer is 38%.
B) 11%
Incorrect. Three complete columns of 10 squares room shaded, plus another 8 squares native the following column. So, there space 30 + 8, or 38, squares shaded the end of the 100 squares in the big square. The correct answer is 38%.
C) 38%
Correct. Three complete columns that 10 squares room shaded, plus an additional 8 squares from the next column. So, there space 30 + 8, or 38, squares shaded the end of the 100 squares in the large square. This means 38% that the huge square is shaded.
D) 62%
Incorrect. There room 62 tiny unshaded squares out of the 100 in the large square, therefore the percent of the large square the is unshaded is 62%. However, the inquiry asked what percent is shaded. There room 38 shaded squares that the 100 squares in the huge square, therefore the exactly answer is 38%.
Rewriting Percents, Decimals, and also Fractions
It is often helpful to readjust the layout of a number. Because that example, girlfriend may find it less complicated to add decimals 보다 to include fractions. If you have the right to write the fractions together decimals, girlfriend can add them as decimals. Then you can rewrite your decimal amount as a fraction, if necessary.
Percents can be composed as fractions and also decimals in very few steps.
<MASK>
Notice in the diagram listed below that 25% that a network is additionally of the grid, as you found in the example.
Notice that in the vault example, rewriting a percent together a decimal takes just a shift of the decimal point. You have the right to use fractions to recognize why this is the case. Any type of percentage x can be represented as the portion , and any fraction can be created as a decimal by moving the decimal suggest in x two places to the left. For example, 81% can be composed as
, and dividing 81 by 100 results in 0.81. People often skip end the intermediary portion step and just convert a percent come a decimal by relocating the decimal suggest two places to the left.
<MASK>
Example Problem Write 0.6 together a percent and also as a streamlined fraction. Write as a percent. 0.6 = 0.60 = 60% Write 0.6 as 0.60, i beg your pardon is 60 hundredths. 60 hundredths is 60 percent. You can additionally move the decimal point two places to the appropriate to discover the percent equivalent. Write as a fraction. 0.6 = To compose 0.6 together a fraction, you read the decimal, 6 tenths, and write 6 tenths in fraction form. Simplify the portion by splitting the numerator and also denominator by 2, a usual factor. Answer 0.6 = 60% =
In this example, the percent is not a entirety number. You can handle this in the exact same way, yet it’s usually less complicated to convert the percent come a decimal and also then transform the decimal to a fraction.
Example Problem Write 5.6% as a decimal and also as a streamlined fraction. Write as a decimal. 5.6% = 0.056 Move the decimal point two locations to the left. In this case, insert a 0 in front of the 5 (05.6) in bespeak to be able to move the decimal come the left two places. Write as a fraction. 0.056 = Write the portion as friend would check out the decimal. The last digit is in the thousandths place, therefore the denominator is 1,000. Simplify the portion by separating the numerator and also denominator through 8, a usual factor. Answer 5.6% = = 0.056
Write 0.645 together a percent and as a simplified fraction. A) 64.5% and B) 0.645% and also C) 645% and also D) 64.5% and also Show/Hide Answer A) 64.5% and Correct. 0.645 = 64.5% = . B) 0.645% and also Incorrect. 0.645 = 64.5%, not 0.645%. Psychic that when you convert a decimal to a percent you have to move the decimal suggest two locations to the right. The correct answer is 64.5% and . C) 645% and Incorrect. 0.645 = 64.5%, not 645%. Remember that when you convert a decimal to a percent you need to move the decimal point two areas to the right. The correct answer is 64.5% and . D) 64.5% and also Incorrect. To create 0.645 as a percent, move the decimal ar two locations to the right: 64.5%. To create 0.645 together a fraction, usage 645 as the numerator. The place value that the critical digit (the 5) is thousandths, for this reason the denominator is 1,000. The fraction is . The greatest common factor the 645 and also 1,000 is 5, therefore you deserve to divide the numerator and denominator by 5 to gain . The exactly answer is 64.5% and also .
<MASK>
Example Problem Write as a decimal and as a percent. Write together a decimal. Find one equivalent portion with 10, 100, 1,000, or various other power that 10 in the denominator. Due to the fact that 100 is a lot of of 4, you deserve to multiply 4 through 25 to obtain 100. Multiply both the numerator and also the denominator by 25. = 0.75 Write the fraction as a decimal through the 5 in the percentage percent place. Write as a percent. 0.75 = 75% To create the decimal together a percent, move the decimal suggest two locations to the right. Answer = 0.75 = 75%
If that is complicated to find an equivalent portion with a denominator of 10, 100, 1,000, and so on, friend can constantly divide the molecule by the denominator to discover the decimal equivalent.
Example Problem Write as a decimal and also as a percent. Write as a decimal. Divide the molecule by the denominator. 3 ÷ 8 = 0.375. Write as a percent. 0.375 = 37.5% To create the decimal together a percent, relocate the decimal allude two areas to the right. Answer = 0.375 = 37.5%
<MASK>
A) 80.0 and 0.8%
B) 0.4 and 4%
C) 0.8 and also 80%
D) 0.8 and also 8%
A) 80.0 and also 0.8%
<MASK>
Incorrect. To uncover a decimal indistinguishable for , an initial convert the portion to tenths. Multiply the numerator and denominator by 2 to acquire . The tantamount decimal is 0.8. So, and 0.4 space not indistinguishable quantities. The correct answer is 0.8 and 80%.
C) 0.8 and also 80%
Correct. The price is = 0.8 = 80%.
D) 0.8 and also 8%
Incorrect. It is true the = 0.8, however this does not equal 8%. To create 0.8 as a percent, relocate the decimal allude two locations to the right: 0.8 = 0.80 = 80%. The correct answer is 0.8 and also 80%.
Mixed Numbers
All the previous examples involve fractions and also decimals less than 1, so all of the percents you have actually seen so far have been much less than 100%.
Percents greater than 100% are feasible as well. Percents more than 100% are used to describe instances where there is more than one entirety (fractions and decimals higher than 1 are offered for the same reason).
In the diagram below, 115% is shaded. Every grid is taken into consideration a whole, and also you require two grids for 115%.
Expressed as a decimal, the percent 115% is 1.15; together a fraction, that is
, or
. Notice that you deserve to still convert amongst percents, fractions, and also decimals once the quantity is higher than one whole.
Numbers better than one that incorporate a fractional component can be composed as the sum of a totality number and also the fractional part. For instance, the mixed number is the amount of the entirety number 3 and the portion . = 3 + .
<MASK>
Example Problem Write 375% as a decimal and also as a streamlined fraction. Write together a decimal. 375% = 3.75 Move the decimal allude two areas to the left. Keep in mind that over there is a entirety number together with the decimal together the percent is more than 100%. Write as a fraction. 3.75 = 3 + 0.75 Write the decimal as a amount of the totality number and also the fractional part. 0.75 = Write the decimal part as a fraction. Simplify the portion by splitting the numerator and also denominator by a usual factor that 25. 3 + = Add the totality number component to the fraction. Answer 375% = 3.75=
Write 4.12 as a percent and also as a simplified fraction. A) 0.0412% and B) 412% and also C) 412% and also D) 4.12% and also Show/Hide Answer A) 0.0412% and Incorrect. To convert 4.12 to a percent, move the decimal suggest two locations to the right, not the left. The exactly answer is 412% and also . B) 412% and also Correct. 4.12 amounts to 412%, and also the simplified kind of is . C) 412% and Incorrect. 4.12 does equal 412%, yet it is also equivalent to , no . The correct answer is 412% and also . D) 4.12% and also Incorrect. To transform 4.12 come a percent, relocate the decimal allude two places to the right. The exactly answer is 412% and .See more: How To Build An Indoor Pitching Mound Plans: Step By Step Instructions Summary Percents space a common means to stand for fractional amounts, simply as decimals and fractions are. Any number that deserve to be composed as a decimal, fraction, or percent can also be written utilizing the various other two representations. .tags a { color: #fff; background: #909295; padding: 3px 10px; border-radius: 10px; font-size: 13px; line-height: 30px; white-space: nowrap; } .tags a:hover { background: #818182; } Home Contact - Advertising Copyright © 2022 dearteassociazione.org #footer {font-size: 14px;background: #ffffff;padding: 10px;text-align: center;} #footer a {color: #2c2b2b;margin-right: 10px;}
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Three common formats for numbers room fractions, decimals, and percents.
You are watching: How do you write 0.6 as a fraction
Percents are regularly used to connect a family member amount. You have probably seen them supplied for discounts, where the percent the discount can apply to different prices. Percents are likewise used when stating taxes and also interest rates on savings and also loans.
A percent is a proportion of a number come 100. Every cent way “per 100,” or “how numerous out that 100.” You usage the price % ~ a number to show percent.
Notice the 12 that the 100 squares in the grid below have to be shaded green. This to represent 12 percent (12 per 100).
12% = 12 percent = 12 parts out the 100 =
How countless of the squares in the grid over are unshaded? due to the fact that 12 space shaded and there room a full of 100 squares, 88 space unshaded. The unshaded section of the totality grid is 88 components out of 100, or 88% of the grid. Notice that the shaded and also unshaded portions together make 100% of the network (100 out of 100 squares).
<MASK>
Example Problem What percent of the big square is shaded? The net is divided into 10 rectangles. For percents, you need to look at 100 equal-sized parts of the whole. You can divide each of the 10 rectangles right into 10 pieces, providing 100 parts. 30 tiny squares out of 100 space shaded. Answer 30% of the huge square is shaded.
What percent that this network is shaded?
<MASK>
B) 11%
<MASK>
D) 62%
A) 3%
Incorrect. Three complete columns that 10 squares space shaded, plus an additional 8 squares indigenous the next column. So, there space 30 + 8, or 38, squares shaded the end of the 100 squares in the large square. The exactly answer is 38%.
B) 11%
Incorrect. Three complete columns of 10 squares room shaded, plus another 8 squares native the following column. So, there space 30 + 8, or 38, squares shaded the end of the 100 squares in the big square. The correct answer is 38%.
C) 38%
Correct. Three complete columns that 10 squares room shaded, plus an additional 8 squares from the next column. So, there space 30 + 8, or 38, squares shaded the end of the 100 squares in the large square. This means 38% that the huge square is shaded.
D) 62%
Incorrect. There room 62 tiny unshaded squares out of the 100 in the large square, therefore the percent of the large square the is unshaded is 62%. However, the inquiry asked what percent is shaded. There room 38 shaded squares that the 100 squares in the huge square, therefore the exactly answer is 38%.
Rewriting Percents, Decimals, and also Fractions
It is often helpful to readjust the layout of a number. Because that example, girlfriend may find it less complicated to add decimals 보다 to include fractions. If you have the right to write the fractions together decimals, girlfriend can add them as decimals. Then you can rewrite your decimal amount as a fraction, if necessary.
Percents can be composed as fractions and also decimals in very few steps.
<MASK>
Notice in the diagram listed below that 25% that a network is additionally of the grid, as you found in the example.
Notice that in the vault example, rewriting a percent together a decimal takes just a shift of the decimal point. You have the right to use fractions to recognize why this is the case. Any type of percentage x can be represented as the portion , and any fraction can be created as a decimal by moving the decimal suggest in x two places to the left. For example, 81% can be composed as
, and dividing 81 by 100 results in 0.81. People often skip end the intermediary portion step and just convert a percent come a decimal by relocating the decimal suggest two places to the left.
<MASK>
Example Problem Write 0.6 together a percent and also as a streamlined fraction. Write as a percent. 0.6 = 0.60 = 60% Write 0.6 as 0.60, i beg your pardon is 60 hundredths. 60 hundredths is 60 percent. You can additionally move the decimal point two places to the appropriate to discover the percent equivalent. Write as a fraction. 0.6 = To compose 0.6 together a fraction, you read the decimal, 6 tenths, and write 6 tenths in fraction form. Simplify the portion by splitting the numerator and also denominator by 2, a usual factor. Answer 0.6 = 60% =
In this example, the percent is not a entirety number. You can handle this in the exact same way, yet it’s usually less complicated to convert the percent come a decimal and also then transform the decimal to a fraction.
Example Problem Write 5.6% as a decimal and also as a streamlined fraction. Write as a decimal. 5.6% = 0.056 Move the decimal point two locations to the left. In this case, insert a 0 in front of the 5 (05.6) in bespeak to be able to move the decimal come the left two places. Write as a fraction. 0.056 = Write the portion as friend would check out the decimal. The last digit is in the thousandths place, therefore the denominator is 1,000. Simplify the portion by separating the numerator and also denominator through 8, a usual factor. Answer 5.6% = = 0.056
Write 0.645 together a percent and as a simplified fraction. A) 64.5% and B) 0.645% and also C) 645% and also D) 64.5% and also Show/Hide Answer A) 64.5% and Correct. 0.645 = 64.5% = . B) 0.645% and also Incorrect. 0.645 = 64.5%, not 0.645%. Psychic that when you convert a decimal to a percent you have to move the decimal suggest two locations to the right. The correct answer is 64.5% and . C) 645% and Incorrect. 0.645 = 64.5%, not 645%. Remember that when you convert a decimal to a percent you need to move the decimal point two areas to the right. The correct answer is 64.5% and . D) 64.5% and also Incorrect. To create 0.645 as a percent, move the decimal ar two locations to the right: 64.5%. To create 0.645 together a fraction, usage 645 as the numerator. The place value that the critical digit (the 5) is thousandths, for this reason the denominator is 1,000. The fraction is . The greatest common factor the 645 and also 1,000 is 5, therefore you deserve to divide the numerator and denominator by 5 to gain . The exactly answer is 64.5% and also .
<MASK>
Example Problem Write as a decimal and as a percent. Write together a decimal. Find one equivalent portion with 10, 100, 1,000, or various other power that 10 in the denominator. Due to the fact that 100 is a lot of of 4, you deserve to multiply 4 through 25 to obtain 100. Multiply both the numerator and also the denominator by 25. = 0.75 Write the fraction as a decimal through the 5 in the percentage percent place. Write as a percent. 0.75 = 75% To create the decimal together a percent, move the decimal suggest two locations to the right. Answer = 0.75 = 75%
If that is complicated to find an equivalent portion with a denominator of 10, 100, 1,000, and so on, friend can constantly divide the molecule by the denominator to discover the decimal equivalent.
Example Problem Write as a decimal and also as a percent. Write as a decimal. Divide the molecule by the denominator. 3 ÷ 8 = 0.375. Write as a percent. 0.375 = 37.5% To create the decimal together a percent, relocate the decimal allude two areas to the right. Answer = 0.375 = 37.5%
<MASK>
A) 80.0 and 0.8%
B) 0.4 and 4%
C) 0.8 and also 80%
D) 0.8 and also 8%
A) 80.0 and also 0.8%
<MASK>
Incorrect. To uncover a decimal indistinguishable for , an initial convert the portion to tenths. Multiply the numerator and denominator by 2 to acquire . The tantamount decimal is 0.8. So, and 0.4 space not indistinguishable quantities. The correct answer is 0.8 and 80%.
C) 0.8 and also 80%
Correct. The price is = 0.8 = 80%.
D) 0.8 and also 8%
Incorrect. It is true the = 0.8, however this does not equal 8%. To create 0.8 as a percent, relocate the decimal allude two locations to the right: 0.8 = 0.80 = 80%. The correct answer is 0.8 and also 80%.
Mixed Numbers
All the previous examples involve fractions and also decimals less than 1, so all of the percents you have actually seen so far have been much less than 100%.
Percents greater than 100% are feasible as well. Percents more than 100% are used to describe instances where there is more than one entirety (fractions and decimals higher than 1 are offered for the same reason).
In the diagram below, 115% is shaded. Every grid is taken into consideration a whole, and also you require two grids for 115%.
Expressed as a decimal, the percent 115% is 1.15; together a fraction, that is
, or
. Notice that you deserve to still convert amongst percents, fractions, and also decimals once the quantity is higher than one whole.
Numbers better than one that incorporate a fractional component can be composed as the sum of a totality number and also the fractional part. For instance, the mixed number is the amount of the entirety number 3 and the portion . = 3 + .
<MASK>
Example Problem Write 375% as a decimal and also as a streamlined fraction. Write together a decimal. 375% = 3.75 Move the decimal allude two areas to the left. Keep in mind that over there is a entirety number together with the decimal together the percent is more than 100%. Write as a fraction. 3.75 = 3 + 0.75 Write the decimal as a amount of the totality number and also the fractional part. 0.75 = Write the decimal part as a fraction. Simplify the portion by splitting the numerator and also denominator by a usual factor that 25. 3 + = Add the totality number component to the fraction. Answer 375% = 3.75=
Write 4.12 as a percent and also as a simplified fraction. A) 0.0412% and B) 412% and also C) 412% and also D) 4.12% and also Show/Hide Answer A) 0.0412% and Incorrect. To convert 4.12 to a percent, move the decimal suggest two locations to the right, not the left. The exactly answer is 412% and also . B) 412% and also Correct. 4.12 amounts to 412%, and also the simplified kind of is . C) 412% and Incorrect. 4.12 does equal 412%, yet it is also equivalent to , no . The correct answer is 412% and also . D) 4.12% and also Incorrect. To transform 4.12 come a percent, relocate the decimal allude two places to the right. The exactly answer is 412% and .See more: How To Build An Indoor Pitching Mound Plans: Step By Step Instructions Summary Percents space a common means to stand for fractional amounts, simply as decimals and fractions are. Any number that deserve to be composed as a decimal, fraction, or percent can also be written utilizing the various other two representations. .tags a { color: #fff; background: #909295; padding: 3px 10px; border-radius: 10px; font-size: 13px; line-height: 30px; white-space: nowrap; } .tags a:hover { background: #818182; } Home Contact - Advertising Copyright © 2022 dearteassociazione.org #footer {font-size: 14px;background: #ffffff;padding: 10px;text-align: center;} #footer a {color: #2c2b2b;margin-right: 10px;}
<UNMASK>
Three common formats for numbers room fractions, decimals, and percents.
You are watching: How do you write 0.6 as a fraction
Percents are regularly used to connect a family member amount. You have probably seen them supplied for discounts, where the percent the discount can apply to different prices. Percents are likewise used when stating taxes and also interest rates on savings and also loans.
A percent is a proportion of a number come 100. Every cent way “per 100,” or “how numerous out that 100.” You usage the price % ~ a number to show percent.
Notice the 12 that the 100 squares in the grid below have to be shaded green. This to represent 12 percent (12 per 100).
12% = 12 percent = 12 parts out the 100 =
How countless of the squares in the grid over are unshaded? due to the fact that 12 space shaded and there room a full of 100 squares, 88 space unshaded. The unshaded section of the totality grid is 88 components out of 100, or 88% of the grid. Notice that the shaded and also unshaded portions together make 100% of the network (100 out of 100 squares).
Example Problem What percent of the network is shaded? The net is separated into 100 smaller sized squares, v 10 squares in each row. 23 squares out of 100 squares room shaded. Answer 23% of the network is shaded.
Example Problem What percent of the big square is shaded? The net is divided into 10 rectangles. For percents, you need to look at 100 equal-sized parts of the whole. You can divide each of the 10 rectangles right into 10 pieces, providing 100 parts. 30 tiny squares out of 100 space shaded. Answer 30% of the huge square is shaded.
What percent that this network is shaded?
A) 3%
B) 11%
C) 38%
D) 62%
A) 3%
Incorrect. Three complete columns that 10 squares space shaded, plus an additional 8 squares indigenous the next column. So, there space 30 + 8, or 38, squares shaded the end of the 100 squares in the large square. The exactly answer is 38%.
B) 11%
Incorrect. Three complete columns of 10 squares room shaded, plus another 8 squares native the following column. So, there space 30 + 8, or 38, squares shaded the end of the 100 squares in the big square. The correct answer is 38%.
C) 38%
Correct. Three complete columns that 10 squares room shaded, plus an additional 8 squares from the next column. So, there space 30 + 8, or 38, squares shaded the end of the 100 squares in the large square. This means 38% that the huge square is shaded.
D) 62%
Incorrect. There room 62 tiny unshaded squares out of the 100 in the large square, therefore the percent of the large square the is unshaded is 62%. However, the inquiry asked what percent is shaded. There room 38 shaded squares that the 100 squares in the huge square, therefore the exactly answer is 38%.
Rewriting Percents, Decimals, and also Fractions
It is often helpful to readjust the layout of a number. Because that example, girlfriend may find it less complicated to add decimals 보다 to include fractions. If you have the right to write the fractions together decimals, girlfriend can add them as decimals. Then you can rewrite your decimal amount as a fraction, if necessary.
Percents can be composed as fractions and also decimals in very few steps.
Example Problem Write 25% as a simplified portion and as a decimal. Write together a fraction. 25% = Since % method “out the 100,” 25% way 25 the end of 100. You create this together a fraction, utilizing 100 together the denominator. Simplify the portion by separating the numerator and denominator through the usual factor 25. Write together a decimal. 25% = = 0.25 You can also just move the decimal suggest in the whole number 25 two locations to the left to acquire 0.25. Answer 25% = = 0.25
Notice in the diagram listed below that 25% that a network is additionally of the grid, as you found in the example.
Notice that in the vault example, rewriting a percent together a decimal takes just a shift of the decimal point. You have the right to use fractions to recognize why this is the case. Any type of percentage x can be represented as the portion , and any fraction can be created as a decimal by moving the decimal suggest in x two places to the left. For example, 81% can be composed as
, and dividing 81 by 100 results in 0.81. People often skip end the intermediary portion step and just convert a percent come a decimal by relocating the decimal suggest two places to the left.
In the same way, rewriting a decimal together a percent (or as a fraction) requires few steps.
Example Problem Write 0.6 together a percent and also as a streamlined fraction. Write as a percent. 0.6 = 0.60 = 60% Write 0.6 as 0.60, i beg your pardon is 60 hundredths. 60 hundredths is 60 percent. You can additionally move the decimal point two places to the appropriate to discover the percent equivalent. Write as a fraction. 0.6 = To compose 0.6 together a fraction, you read the decimal, 6 tenths, and write 6 tenths in fraction form. Simplify the portion by splitting the numerator and also denominator by 2, a usual factor. Answer 0.6 = 60% =
In this example, the percent is not a entirety number. You can handle this in the exact same way, yet it’s usually less complicated to convert the percent come a decimal and also then transform the decimal to a fraction.
Example Problem Write 5.6% as a decimal and also as a streamlined fraction. Write as a decimal. 5.6% = 0.056 Move the decimal point two locations to the left. In this case, insert a 0 in front of the 5 (05.6) in bespeak to be able to move the decimal come the left two places. Write as a fraction. 0.056 = Write the portion as friend would check out the decimal. The last digit is in the thousandths place, therefore the denominator is 1,000. Simplify the portion by separating the numerator and also denominator through 8, a usual factor. Answer 5.6% = = 0.056
Write 0.645 together a percent and as a simplified fraction. A) 64.5% and B) 0.645% and also C) 645% and also D) 64.5% and also Show/Hide Answer A) 64.5% and Correct. 0.645 = 64.5% = . B) 0.645% and also Incorrect. 0.645 = 64.5%, not 0.645%. Psychic that when you convert a decimal to a percent you have to move the decimal suggest two locations to the right. The correct answer is 64.5% and . C) 645% and Incorrect. 0.645 = 64.5%, not 645%. Remember that when you convert a decimal to a percent you need to move the decimal point two areas to the right. The correct answer is 64.5% and . D) 64.5% and also Incorrect. To create 0.645 as a percent, move the decimal ar two locations to the right: 64.5%. To create 0.645 together a fraction, usage 645 as the numerator. The place value that the critical digit (the 5) is thousandths, for this reason the denominator is 1,000. The fraction is . The greatest common factor the 645 and also 1,000 is 5, therefore you deserve to divide the numerator and denominator by 5 to gain . The exactly answer is 64.5% and also .
In stimulate to create a portion as a decimal or a percent, you have the right to write the fraction as an equivalent fraction with a denominator that 10 (or any kind of other strength of 10 such as 100 or 1,000), which deserve to be then converted to a decimal and then a percent.
Example Problem Write as a decimal and as a percent. Write together a decimal. Find one equivalent portion with 10, 100, 1,000, or various other power that 10 in the denominator. Due to the fact that 100 is a lot of of 4, you deserve to multiply 4 through 25 to obtain 100. Multiply both the numerator and also the denominator by 25. = 0.75 Write the fraction as a decimal through the 5 in the percentage percent place. Write as a percent. 0.75 = 75% To create the decimal together a percent, move the decimal suggest two locations to the right. Answer = 0.75 = 75%
If that is complicated to find an equivalent portion with a denominator of 10, 100, 1,000, and so on, friend can constantly divide the molecule by the denominator to discover the decimal equivalent.
Example Problem Write as a decimal and also as a percent. Write as a decimal. Divide the molecule by the denominator. 3 ÷ 8 = 0.375. Write as a percent. 0.375 = 37.5% To create the decimal together a percent, relocate the decimal allude two areas to the right. Answer = 0.375 = 37.5%
Write as a decimal and also as a percent.
A) 80.0 and 0.8%
B) 0.4 and 4%
C) 0.8 and also 80%
D) 0.8 and also 8%
A) 80.0 and also 0.8%
Incorrect. An alert that 10 is a multiple of 5, so you have the right to rewrite using 10 together the denominator. Main point the numerator and also denominator by 2 to gain . The indistinguishable decimal is 0.8. You deserve to write this together a percent by moving the decimal suggest two places to the right. Since 0.8 has only one location to the right, encompass 0 in the percentage percent place: 0.8 = 0.80 = 80%. The correct answer is 0.8 and also 80%.
B) 0.4 and also 4%
Incorrect. To uncover a decimal indistinguishable for , an initial convert the portion to tenths. Multiply the numerator and denominator by 2 to acquire . The tantamount decimal is 0.8. So, and 0.4 space not indistinguishable quantities. The correct answer is 0.8 and 80%.
C) 0.8 and also 80%
Correct. The price is = 0.8 = 80%.
D) 0.8 and also 8%
Incorrect. It is true the = 0.8, however this does not equal 8%. To create 0.8 as a percent, relocate the decimal allude two locations to the right: 0.8 = 0.80 = 80%. The correct answer is 0.8 and also 80%.
Mixed Numbers
All the previous examples involve fractions and also decimals less than 1, so all of the percents you have actually seen so far have been much less than 100%.
Percents greater than 100% are feasible as well. Percents more than 100% are used to describe instances where there is more than one entirety (fractions and decimals higher than 1 are offered for the same reason).
In the diagram below, 115% is shaded. Every grid is taken into consideration a whole, and also you require two grids for 115%.
Expressed as a decimal, the percent 115% is 1.15; together a fraction, that is
, or
. Notice that you deserve to still convert amongst percents, fractions, and also decimals once the quantity is higher than one whole.
Numbers better than one that incorporate a fractional component can be composed as the sum of a totality number and also the fractional part. For instance, the mixed number is the amount of the entirety number 3 and the portion . = 3 + .
Example Problem Write as a decimal and as a percent. Write the mixed fraction as 2 wholes to add the spring part. Write together a decimal. Write the fractional component as a decimal by splitting the numerator by the denominator. 7 ÷ 8 = 0.875. Add 2 come the decimal. Write together a percent. 2.875 = 287.5% Now you can move the decimal allude two areas to the right to create the decimal as a percent. Answer = 2.875 = 287.5%
Note that a totality number can be created as a percent. 100% means one whole; so 2 wholes would certainly be 200%.
Example Problem Write 375% as a decimal and also as a streamlined fraction. Write together a decimal. 375% = 3.75 Move the decimal allude two areas to the left. Keep in mind that over there is a entirety number together with the decimal together the percent is more than 100%. Write as a fraction. 3.75 = 3 + 0.75 Write the decimal as a amount of the totality number and also the fractional part. 0.75 = Write the decimal part as a fraction. Simplify the portion by splitting the numerator and also denominator by a usual factor that 25. 3 + = Add the totality number component to the fraction. Answer 375% = 3.75=
Write 4.12 as a percent and also as a simplified fraction. A) 0.0412% and B) 412% and also C) 412% and also D) 4.12% and also Show/Hide Answer A) 0.0412% and Incorrect. To convert 4.12 to a percent, move the decimal suggest two locations to the right, not the left. The exactly answer is 412% and also . B) 412% and also Correct. 4.12 amounts to 412%, and also the simplified kind of is . C) 412% and Incorrect. 4.12 does equal 412%, yet it is also equivalent to , no . The correct answer is 412% and also . D) 4.12% and also Incorrect. To transform 4.12 come a percent, relocate the decimal allude two places to the right. The exactly answer is 412% and .See more: How To Build An Indoor Pitching Mound Plans: Step By Step Instructions Summary Percents space a common means to stand for fractional amounts, simply as decimals and fractions are. Any number that deserve to be composed as a decimal, fraction, or percent can also be written utilizing the various other two representations. .tags a { color: #fff; background: #909295; padding: 3px 10px; border-radius: 10px; font-size: 13px; line-height: 30px; white-space: nowrap; } .tags a:hover { background: #818182; } Home Contact - Advertising Copyright © 2022 dearteassociazione.org #footer {font-size: 14px;background: #ffffff;padding: 10px;text-align: center;} #footer a {color: #2c2b2b;margin-right: 10px;}
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<MASK>
We don't need a unique voice over actor for each English actor. BUT we can't use the same voice over actor twice in a row in the order the they would appear in the film. And once a voice over actor is assigned to an English actor, that stays fixed. As in we can't just alternate back and forth between two voice over actors.
level 3
9 points · 1 year ago
<MASK>
level 4
Original Poster5 points · 1 year ago
This!
<MASK>
Thanks!
<MASK>
level 6
3 points · 1 year ago
Good question!
<MASK>
1. Separate the roles [1-17] by gender ahead of time, then run the algorithm once on each part, or
2. For roles of different genders, add an edge between them. Then run the algorithm once on the big graph.
<MASK>
level 6
Original Poster1 point · 1 year ago
<MASK>
Continue browsing in r/math
Community Details
<MASK>
Members
<MASK>
If you're asking for help understanding something mathematical, post in the Simple Question thread or /r/learnmath. This includes reference requests - also see our lists of recommended books and free online resources. Here is a more recent thread with book recommendations.
<MASK>
Everything about X - every Wednesday
<MASK>
MathJax userscript (install Greasemonkey or Tampermonkey first)
<MASK>
Post the equation above like this:
<MASK>
Calculus and Analysis Symbols
<MASK>
Other math subreddits
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74.2k members
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<UNMASK>
<MASK>
We don't need a unique voice over actor for each English actor. BUT we can't use the same voice over actor twice in a row in the order the they would appear in the film. And once a voice over actor is assigned to an English actor, that stays fixed. As in we can't just alternate back and forth between two voice over actors.
level 3
9 points · 1 year ago
<MASK>
In your particular case you only need 5 French actors. Here are the roles they would play:
<MASK>
level 4
Original Poster5 points · 1 year ago
This!
<MASK>
Thanks!
<MASK>
As for the guts of the algorithm, here's a place to start.
<MASK>
level 6
3 points · 1 year ago
Good question!
<MASK>
1. Separate the roles [1-17] by gender ahead of time, then run the algorithm once on each part, or
2. For roles of different genders, add an edge between them. Then run the algorithm once on the big graph.
<MASK>
level 6
Original Poster1 point · 1 year ago
<MASK>
Continue browsing in r/math
Community Details
<MASK>
Members
<MASK>
If you're asking for help understanding something mathematical, post in the Simple Question thread or /r/learnmath. This includes reference requests - also see our lists of recommended books and free online resources. Here is a more recent thread with book recommendations.
<MASK>
Everything about X - every Wednesday
<MASK>
Simple Questions - Posted Fridays
<MASK>
MathJax userscript (install Greasemonkey or Tampermonkey first)
<MASK>
Post the equation above like this:
<MASK>
Calculus and Analysis Symbols
<MASK>
Greek Letters
<MASK>
Other math subreddits
r/learnmath
<MASK>
r/algorithms
<MASK>
r/compsci
504k members
<MASK>
74.2k members
<MASK>
|
<MASK>
We don't need a unique voice over actor for each English actor. BUT we can't use the same voice over actor twice in a row in the order the they would appear in the film. And once a voice over actor is assigned to an English actor, that stays fixed. As in we can't just alternate back and forth between two voice over actors.
level 3
9 points · 1 year ago
<MASK>
In your particular case you only need 5 French actors. Here are the roles they would play:
<MASK>
level 4
Original Poster5 points · 1 year ago
This!
<MASK>
Thanks!
<MASK>
As for the guts of the algorithm, here's a place to start.
<MASK>
level 6
3 points · 1 year ago
Good question!
<MASK>
1. Separate the roles [1-17] by gender ahead of time, then run the algorithm once on each part, or
2. For roles of different genders, add an edge between them. Then run the algorithm once on the big graph.
<MASK>
level 6
Original Poster1 point · 1 year ago
<MASK>
Continue browsing in r/math
Community Details
<MASK>
Members
<MASK>
If you're asking for help understanding something mathematical, post in the Simple Question thread or /r/learnmath. This includes reference requests - also see our lists of recommended books and free online resources. Here is a more recent thread with book recommendations.
<MASK>
Everything about X - every Wednesday
<MASK>
Simple Questions - Posted Fridays
<MASK>
MathJax userscript (install Greasemonkey or Tampermonkey first)
<MASK>
Post the equation above like this:
<MASK>
Calculus and Analysis Symbols
<MASK>
Greek Letters
<MASK>
Other math subreddits
r/learnmath
<MASK>
r/algorithms
<MASK>
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504k members
<MASK>
74.2k members
<MASK>
<UNMASK>
Press J to jump to the feed. Press question mark to learn the rest of the keyboard shortcuts
Sort by
level 1
7 points · 1 year ago
<MASK>
We don't need a unique voice over actor for each English actor. BUT we can't use the same voice over actor twice in a row in the order the they would appear in the film. And once a voice over actor is assigned to an English actor, that stays fixed. As in we can't just alternate back and forth between two voice over actors.
level 3
9 points · 1 year ago
<MASK>
In your particular case you only need 5 French actors. Here are the roles they would play:
<MASK>
level 4
Original Poster5 points · 1 year ago
This!
<MASK>
Thanks!
<MASK>
As for the guts of the algorithm, here's a place to start.
<MASK>
level 6
3 points · 1 year ago
Good question!
<MASK>
1. Separate the roles [1-17] by gender ahead of time, then run the algorithm once on each part, or
2. For roles of different genders, add an edge between them. Then run the algorithm once on the big graph.
<MASK>
level 6
Original Poster1 point · 1 year ago
<MASK>
Just a hypothetical for now.
<MASK>
Continue browsing in r/math
Community Details
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Members
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Online
<MASK>
If you're asking for help understanding something mathematical, post in the Simple Question thread or /r/learnmath. This includes reference requests - also see our lists of recommended books and free online resources. Here is a more recent thread with book recommendations.
<MASK>
Everything about X - every Wednesday
What Are You Working On? - posted Mondays
<MASK>
Simple Questions - Posted Fridays
<MASK>
MathJax userscript (install Greasemonkey or Tampermonkey first)
<MASK>
Post the equation above like this:
<MASK>
Calculus and Analysis Symbols
<MASK>
Greek Letters
<MASK>
Other math subreddits
r/learnmath
<MASK>
r/CasualMath
9.2k members
<MASK>
4.7k members
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level 1
7 points · 1 year ago
<MASK>
We don't need a unique voice over actor for each English actor. BUT we can't use the same voice over actor twice in a row in the order the they would appear in the film. And once a voice over actor is assigned to an English actor, that stays fixed. As in we can't just alternate back and forth between two voice over actors.
level 3
9 points · 1 year ago
<MASK>
In your particular case you only need 5 French actors. Here are the roles they would play:
<MASK>
level 4
Original Poster5 points · 1 year ago
This!
<MASK>
Thanks!
<MASK>
As for the guts of the algorithm, here's a place to start.
<MASK>
level 6
3 points · 1 year ago
Good question!
<MASK>
1. Separate the roles [1-17] by gender ahead of time, then run the algorithm once on each part, or
2. For roles of different genders, add an edge between them. Then run the algorithm once on the big graph.
<MASK>
level 6
Original Poster1 point · 1 year ago
<MASK>
Just a hypothetical for now.
<MASK>
Continue browsing in r/math
Community Details
<MASK>
Members
<MASK>
Online
<MASK>
If you're asking for help understanding something mathematical, post in the Simple Question thread or /r/learnmath. This includes reference requests - also see our lists of recommended books and free online resources. Here is a more recent thread with book recommendations.
<MASK>
Everything about X - every Wednesday
What Are You Working On? - posted Mondays
<MASK>
Simple Questions - Posted Fridays
<MASK>
MathJax userscript (install Greasemonkey or Tampermonkey first)
<MASK>
Post the equation above like this:
<MASK>
Calculus and Analysis Symbols
<MASK>
Greek Letters
<MASK>
Other math subreddits
r/learnmath
<MASK>
r/CasualMath
9.2k members
<MASK>
4.7k members
<MASK>
r/sagemath
<MASK>
r/algorithms
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level 1
7 points · 1 year ago
<MASK>
We don't need a unique voice over actor for each English actor. BUT we can't use the same voice over actor twice in a row in the order the they would appear in the film. And once a voice over actor is assigned to an English actor, that stays fixed. As in we can't just alternate back and forth between two voice over actors.
level 3
9 points · 1 year ago
<MASK>
In your particular case you only need 5 French actors. Here are the roles they would play:
<MASK>
Here's the picture:
<MASK>
level 4
Original Poster5 points · 1 year ago
This!
<MASK>
I knew this would be an interesting math problem and there would be some sort of algorithm. Is it simply "vertex_coloring" in the code that solves this? I'd love to know how it's figured out.
Thanks!
level 5
6 points · 1 year ago
<MASK>
It looks like we could have also used chromatic_number(). The documentation..
As for the guts of the algorithm, here's a place to start.
<MASK>
level 6
3 points · 1 year ago
Good question!
<MASK>
1. Separate the roles [1-17] by gender ahead of time, then run the algorithm once on each part, or
2. For roles of different genders, add an edge between them. Then run the algorithm once on the big graph.
We add an edge between any two roles that cannot have the same French actor. OP originally stipulated that it was because of adjacent scenes, but it really doesn't matter the reason.
I suspect the first method will be much faster, but the second method is more general.
level 6
Original Poster1 point · 1 year ago
<MASK>
level 4
Original Poster3 points · 1 year ago
Alright Mr Smarty pants. While this uses 5 actors vs my 6 actors, if there are different solutions using only 5 actors, is there a way to spit out the solution that has the least amount of disparity in words between colors? Assuming I had the length in words of each numbers script.
Just a hypothetical for now.
<MASK>
The short answer is yes. The longer answer is I can't think of how to do that in practice without some serious machinery that might be too computationally intensive.
<MASK>
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level 1
7 points · 1 year ago
<MASK>
We don't need a unique voice over actor for each English actor. BUT we can't use the same voice over actor twice in a row in the order the they would appear in the film. And once a voice over actor is assigned to an English actor, that stays fixed. As in we can't just alternate back and forth between two voice over actors.
level 3
9 points · 1 year ago
<MASK>
In your particular case you only need 5 French actors. Here are the roles they would play:
<MASK>
Here's the picture:
<MASK>
level 4
Original Poster5 points · 1 year ago
This!
<MASK>
I knew this would be an interesting math problem and there would be some sort of algorithm. Is it simply "vertex_coloring" in the code that solves this? I'd love to know how it's figured out.
Thanks!
level 5
6 points · 1 year ago
<MASK>
It looks like we could have also used chromatic_number(). The documentation..
As for the guts of the algorithm, here's a place to start.
<MASK>
level 6
3 points · 1 year ago
Good question!
<MASK>
1. Separate the roles [1-17] by gender ahead of time, then run the algorithm once on each part, or
2. For roles of different genders, add an edge between them. Then run the algorithm once on the big graph.
We add an edge between any two roles that cannot have the same French actor. OP originally stipulated that it was because of adjacent scenes, but it really doesn't matter the reason.
I suspect the first method will be much faster, but the second method is more general.
level 6
Original Poster1 point · 1 year ago
<MASK>
level 4
Original Poster3 points · 1 year ago
Alright Mr Smarty pants. While this uses 5 actors vs my 6 actors, if there are different solutions using only 5 actors, is there a way to spit out the solution that has the least amount of disparity in words between colors? Assuming I had the length in words of each numbers script.
Just a hypothetical for now.
<MASK>
The short answer is yes. The longer answer is I can't think of how to do that in practice without some serious machinery that might be too computationally intensive.
<MASK>
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level 1
7 points · 1 year ago
1. What part of this is given to you (you have no control over)?
2. What part of this do you have control over?
3. What are you trying to accomplish?
I've determined I'd need 6 actors to make sure no two actors had the same voice AND were next to each other in a sequence.
This is confusing to me. I thought you already had 16 actors (labelled 1-17).
level 2
Original Poster10 points · 1 year ago
16 English actors need to be replaced with french voice over actors.
We don't need a unique voice over actor for each English actor. BUT we can't use the same voice over actor twice in a row in the order the they would appear in the film. And once a voice over actor is assigned to an English actor, that stays fixed. As in we can't just alternate back and forth between two voice over actors.
level 3
9 points · 1 year ago
Gotcha! That makes sense now. Thank you. This is literally the "Chromatic number problem". It is a computationally expensive problem for large collections of actors. For only 17 it isn't bad.
Here's some Sage code you can use to solve your problem (which you can run for free at, for example, cocalc.com )
https://gist.github.com/mpawliuk/ec91468365233b2d1faf57b4bbb56b21
In your particular case you only need 5 French actors. Here are the roles they would play:
You need 5 French actors.
These are the English roles the French actors will take:
French actor 1 will play the parts:
[6, 10, 13, 17]
French actor 2 will play the parts:
[7, 3, 5, 16, 14, 9]
French actor 3 will play the parts:
[2, 15, 11]
French actor 4 will play the parts:
[12, 4]
French actor 5 will play the parts:
[1]
Here's the picture:
https://cocalc.com/blobs//home/user/.sage/temp/project-fbeb3d9c-3251-4e88-9e27-82a1c37642e1/270/tmp_uijHct.svg?uuid=3877e5a6-2b20-41df-b57d-9d862c4d7394
level 4
Original Poster5 points · 1 year ago
This!
Wow this is so cool! I just googled Chromatic Number Problem.
I knew this would be an interesting math problem and there would be some sort of algorithm. Is it simply "vertex_coloring" in the code that solves this? I'd love to know how it's figured out.
Thanks!
level 5
6 points · 1 year ago
Yeah, vertex_coloring() is doing the heavy lifting. Here's the documentation, but it doesn't get into the nitty-gritty.
It looks like we could have also used chromatic_number(). The documentation..
As for the guts of the algorithm, here's a place to start.
level 6
Original Poster5 points · 1 year ago
I'll have to do the reading tonight after work.
Thank you so much!
level 5
2 points · 1 year ago
I really like that the Chromatic number problem has this unexpected application, but in practical terms, does your problem not have an additional constraint about the sex of the voice-over actors needing to match the sex of the parts? In mpaw976's solution, what if parts 6 and 10 are different sexes--will one French actor be able to do both?
level 6
3 points · 1 year ago
Good question!
There are two straightforward ways to deal with this:
1. Separate the roles [1-17] by gender ahead of time, then run the algorithm once on each part, or
2. For roles of different genders, add an edge between them. Then run the algorithm once on the big graph.
We add an edge between any two roles that cannot have the same French actor. OP originally stipulated that it was because of adjacent scenes, but it really doesn't matter the reason.
I suspect the first method will be much faster, but the second method is more general.
level 6
Original Poster1 point · 1 year ago
Thankfully all women! I could probably do it manually if it was mixed. Or just break down sequences to all the men and all the women. Not perfect efficiency but it will get the job done.
level 4
Original Poster3 points · 1 year ago
Alright Mr Smarty pants. While this uses 5 actors vs my 6 actors, if there are different solutions using only 5 actors, is there a way to spit out the solution that has the least amount of disparity in words between colors? Assuming I had the length in words of each numbers script.
Just a hypothetical for now.
level 5
2 points · 1 year ago
The short answer is yes. The longer answer is I can't think of how to do that in practice without some serious machinery that might be too computationally intensive.
One way to solve graph colouring is to basically just write down all the rules. (SAT of CSP if you're curious.) There's an extension to these techniques that allow you to specify a set of constraints that must be satisfied, and a set of constraints that you want the program to do its best on. (Fuzzy-CSP, Soft CSPs, and MAXSAT all fall into this category broadly speaking.)
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<MASK>
If the temperature is 86 degrees Fahrenheit, what is the temperature in Celsius?
First of all, it shouldn't matter. We're at home, indoors, mostly naked, and standing in the kitchen with the refrigerator door wide open.
<MASK>
<UNMASK>
<MASK>
# Temperatures
<MASK>
If the temperature is 86 degrees Fahrenheit, what is the temperature in Celsius?
First of all, it shouldn't matter. We're at home, indoors, mostly naked, and standing in the kitchen with the refrigerator door wide open.
<MASK>
|
<MASK>
# Temperatures
<MASK>
If the temperature is 86 degrees Fahrenheit, what is the temperature in Celsius?
First of all, it shouldn't matter. We're at home, indoors, mostly naked, and standing in the kitchen with the refrigerator door wide open.
<MASK>
<UNMASK>
We have changed our privacy policy. In addition, we use cookies on our website for various purposes. By continuing on our website, you consent to our use of cookies. You can learn about our practices by reading our privacy policy.
# Temperatures
<MASK>
If the temperature is 86 degrees Fahrenheit, what is the temperature in Celsius?
First of all, it shouldn't matter. We're at home, indoors, mostly naked, and standing in the kitchen with the refrigerator door wide open.
<MASK>
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# Temperatures
<MASK>
If the temperature is 86 degrees Fahrenheit, what is the temperature in Celsius?
First of all, it shouldn't matter. We're at home, indoors, mostly naked, and standing in the kitchen with the refrigerator door wide open.
<MASK>
<UNMASK>
We have changed our privacy policy. In addition, we use cookies on our website for various purposes. By continuing on our website, you consent to our use of cookies. You can learn about our practices by reading our privacy policy.
# Temperatures
Let F be degrees Fahrenheit, a unit commonly used in the United States, and let C be degrees Celsius, used almost everywhere else. Oh, but ours is the right one. Sure...
<MASK>
If the temperature is 86 degrees Fahrenheit, what is the temperature in Celsius?
First of all, it shouldn't matter. We're at home, indoors, mostly naked, and standing in the kitchen with the refrigerator door wide open.
<MASK>
Let F = 86. Then C = 5/9(86 – 32) = 5/9(54) = 30, so the temperature is 30 degrees Celsius.
<MASK>
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We have changed our privacy policy. In addition, we use cookies on our website for various purposes. By continuing on our website, you consent to our use of cookies. You can learn about our practices by reading our privacy policy.
# Temperatures
Let F be degrees Fahrenheit, a unit commonly used in the United States, and let C be degrees Celsius, used almost everywhere else. Oh, but ours is the right one. Sure...
<MASK>
If the temperature is 86 degrees Fahrenheit, what is the temperature in Celsius?
First of all, it shouldn't matter. We're at home, indoors, mostly naked, and standing in the kitchen with the refrigerator door wide open.
<MASK>
Let F = 86. Then C = 5/9(86 – 32) = 5/9(54) = 30, so the temperature is 30 degrees Celsius.
<MASK>
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We have changed our privacy policy. In addition, we use cookies on our website for various purposes. By continuing on our website, you consent to our use of cookies. You can learn about our practices by reading our privacy policy.
# Temperatures
Let F be degrees Fahrenheit, a unit commonly used in the United States, and let C be degrees Celsius, used almost everywhere else. Oh, but ours is the right one. Sure...
We can convert from one temperature system to the other using the following formulas:
### Sample Problem
If the temperature is 86 degrees Fahrenheit, what is the temperature in Celsius?
First of all, it shouldn't matter. We're at home, indoors, mostly naked, and standing in the kitchen with the refrigerator door wide open.
Okay, we'll play along.
Let F = 86. Then C = 5/9(86 – 32) = 5/9(54) = 30, so the temperature is 30 degrees Celsius.
That sounds deceptively cool. No wonder everywhere else is crazy.
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### Chapter 4 Notes
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### Chapter 4 Notes
<MASK>
<UNMASK>
### Chapter 4 Notes
```Chapter 4
Converting
• Fraction to Decimal to Percent
– ½ = .5 = 50% (decimal moves 2 places to right)
• Decimal to Percent to Fraction
– .75 = 75% = ¾ (decimal moves 2 places to right)
• Percent to Fraction to Decimal
– 150% = 1 ½ = 1.5 (decimal moves 2 places to left)
Multiplying & Dividing by a tenth,
hundredth, or thousandth
Multiplying by .1, .01, and .001
• 208 x 0.1 = 20.8 (decimal moves one places to left)
• 83 x 0.01 = .83 (decimal moves two places to left)
• 306 x 0.001 = .306 (decimal moves three places to left)
Dividing by .1, .01, and .001
• 816 / 0.1 = 8,160 (decimal moves one places to right)
• 51 / 0.01 = 5100 (decimal moves two places to right)
• 632 / 0.001 = 632,000 (decimal moves three places to right)
Deductions and Take-Home Pay
•
•
•
•
Income Tax
FICA Tax
Insurance
Parking
•
•
•
•
Uniforms
Dues
Commuting Costs
Etc.
Deductions & Income Tax
• Income Tax
– Withholding tax
– Withholding allowances
– More allowances
• Pay less
– Less allowances
• Pay more
– Use table
Deductions & FICA Tax
• Federal Insurance Contributions Act 7.65%
• Social Security 6.2%
• Medicare 1.45%
New Rate
Through 2012
Net Earnings Example
packet-problem 3 on p. 65
• Elaine Kaufman works a 40-hour week at \$8.75 an hour with
time and half for overtime. Last week she worked 43 hours.
From her earnings, her employer deducted FICA tax at a
rate of 0.0765 and income tax of \$32. Her employer also
deducted \$33.78 for health insurance and \$27.12 for union
dues.
–
–
–
–
–
Regular earnings = 40 * 8.75 = \$350.00
Overtime earnings = 3 * (8.75 * 1.5) = \$39.38
Total earnings = \$350 + \$39.38 = \$389.38
Deductions = \$32 + (\$389.38 * .0765) + \$33.78 + \$27.12 = \$122.69
Net earnings = \$389.38 - \$122.69 = \$266.69
More Percent Examples
•
•
•
•
•
•
•
•
•
67% of \$489 = .67 x \$489 = \$327.63
42 is ___% of 480 = 42 / 480 = .0875 = 8 ¾
20% of \$575 = .2 x \$575 = \$115
1% of \$57 = .01 x \$57 = \$0.57
10% of \$89 = .1 x \$89 = \$8.90
100% of \$76 = 1 x \$76 = \$76
1000% of \$87 = 10 x \$87 = \$870
½% of \$870 = ½ x \$8.70 = \$4.35
1/ % of \$255 = .003333 x 255 = \$0.85
3
Fringe Benefits
• Fringe benefits are extra payments/benefits received for
working for a company like pension, insurance, free parking,
tuition, uniforms, etc.
• Shari Traxler is paid \$9.75 an hour for a 40-hour week. Her
employer also provides these fringe benefits: yearly pension
contributions, \$1,622.40; health and accident insurance per
year, \$956; free parking, \$520 per year; free tuition for evening
classes, \$1,200 per year. (a) What is Shari’s annual wage? (b)
What are her total yearly fringe benefits? (c) What are her total
yearly job benefits?
– (a) \$9.75 x 40 = \$390 (weekly pay) x 52 (weeks per year) = \$20,280
– (b) \$1,622.40 + \$956 + \$520 + \$1,200 = \$4,298.40
– (c) \$20,280 + \$4,298.40 = \$24,578.40
Net Job Benefits
• Job expenses are expenses paid for working for a company like dues,
uniforms, commuting costs, insurance, tools, etc.
• Duane McCoy’s job pays him \$11.25 per hour for a 40-hour week. He
estimates his fringe benefits to be 29% of his yearly wages. His yearly job
expenses are estimated to be dues, \$375; uniforms, \$580; commuting costs,
\$934. (a) What is Duane’s total annual pay? (b) What is the amount of
Duane’s fringe benefits per year? (c) What are Duane’s total yearly job
benefits? (d) What are Duane’s total yearly job expenses? (e) What are
Duane’s net yearly job benefits?
–
–
–
–
–
(a) \$11.25 x 40 = \$450 (weekly pay) x 52 (weeks per year) = \$23,400 (annual pay)
(b) \$23,400 x .29 (29%) = \$6,786 (annual fringe benefits)
(c) \$23,400 + \$6,786 = \$30,186 (total yearly job benefits)
(d) \$375 + \$580 + \$934 = \$1,889 (total yearly job expenses)
(e) \$30,186 - \$1,889 = \$28,297 (net yearly job benefits)
Percent Relationships
• ___ is 20% more than 50. 50 x .2 = 10, 10 + 50
= 60
• 40 plus 6% of itself = ___. 40 x .06 = 2.4, 2.4 +
40 = 42.4
• ___ is 10% less than 80. 80 x .1 = 8, 80 – 8 = 72
• 60 minus 40% of itself = ___. 60 x .4 = 24, 60 –
24 = 36
• 240 is ___% more than 180. 240 - 180 = 60, 60 /
180 = .3333 = 33 1/3%
• 45 is ___% less than 60. 60 – 45 = 15, 15 / 60 =
.25 = 25%
Straight Commission
• Straight commission is earned when an
employee sells a specific product for a company.
It can be calculated as a rate per item or it can
be a percentage of a sale.
– A salesperson who works a straight commission basis
sold 5 copy machines at \$4,500 each. The
commission rate was 6%. The amount of commission
was \$___.
• \$4,500 x 5 = \$22,500 total sales
• \$22,500 x 0.06 = \$1,350 amount of commission
Salary Plus Commission
• Salary plus commission is when an employee is
paid a set amount per hour plus a commission
when they sell set amounts of certain items to
stimulate sales.
– Mary Banjavic is paid a salary of \$200 a week plus
4/ % commission on weekly sales over \$7,500. Her
5
sales last week totaled \$14,100. Her total earnings
for the week were \$___.
• \$14,100 - \$7,500 = \$6,600
• \$6,600 x .008 (4/5%) = \$52.80 commission
• \$200 + \$52.80 = \$252.80 total earnings for week
• Graduated commission is when an employee is paid
commission an amount on a tier basis.
– Tony Bollini sells encyclopedias. His monthly commission is
based on the number of sets sold in a month. He earns \$45
each for the first 25 sets, \$60 each for the next 25 sets, and
\$75 each for each set over 50 sets he sells. Bollini sold 27
sets in November and 55 in December. His total
commission for the two months was \$___.
25 sets x \$45 = \$1,125
2 sets x \$60 = \$120
\$1,125 + \$120 = \$1,245 for November
25 sets x \$45 = \$1,125
\$1,245 + \$3,000 = \$4,245 for the two months
25 sets x \$60 = \$1,500
5 sets x \$75 = \$375
\$1,125 + \$1,500 + \$375 = \$3,000 for December
Finding Commission Rates
• Commission divided by sales.
• On sales of \$34,000, a sales person earns
\$2,720 commission. The rate of commission is
___%.
– \$2,720 / \$34,000 = 0.08 = 8% rate of commission
More Finding Commission
• Susan Favre sold her home through Tri-Town
Realty Company, which charges a 6% sales
commission. Her agent was Vince Pineta.
at \$175,900, but was able to sell it for only
\$165,500. If Vince’s share of the commission
was 3 ½%, he earned \$___ commission on
the sale.
– \$165,500 x 0.035 = \$5,792.50 commission
Finding Net Proceeds
• Joe Popoff, a collection agent, collected 90%
of a debt of \$5,600 which had been overdue
90 days. This collection rate was 5% more
than the average collection rate for that agent.
The agent charged 25% commission. The net
proceeds of the debt were \$___.
– \$5,600 x 0.90 = \$5,040 (amount collected)
– \$5,040 x 0.25 = \$1,260 (commission)
– \$5,040 - \$1,260 = \$3,780 (net proceeds)
```
|
<MASK>
Pseudocode is also known as fake codes. It is used to give a simple human-friendly description of the steps used in an algorithm. It is an informal description. It is often used to summarise the steps or flow of the algorithm but it does not specify the detail of the algorithm. It is written by the system designers so that aligned codes and requirements can be understood by the programmers.
<MASK>
<UNMASK>
<MASK>
Difference Between Algorithm and Pseudocode: In a programming language, both algorithm and pseudocode play an important role. Where an algorithm is considered the foundation of the programming language pseudocode is used to make the programming language more human-friendly. The major difference between algorithm and pseudocode is that pseudocode is a method of writing an algorithm and an algorithm is a step-by-step description of the procedure of a task.
<MASK>
Algorithm Pseudocode It is a step-by-step description of the solution. It is an easy way of writing algorithms for users to understand. It is always a real algorithm and not fake codes. These are fake codes. They are a sequence of solutions to a problem. They are representations of algorithms. It is a systematically written code. These are simpler ways of writing codes. They are an unambiguous way of writing codes. They are a method of describing codes written in an algorithm. They can be considered pseudocode. They can not be considered algorithms There are no rules to writing algorithms. Certain rules to writing pseudocode are there.
<MASK>
The algorithm will have a well-defined set of steps. Problems are solved with a specific solution. Natural languages, flow charts, etc can be used to represent an algorithm. Candidates can check out Prim’s Algorithm to know more about Algorithm.
<MASK>
Pseudocode is also known as fake codes. It is used to give a simple human-friendly description of the steps used in an algorithm. It is an informal description. It is often used to summarise the steps or flow of the algorithm but it does not specify the detail of the algorithm. It is written by the system designers so that aligned codes and requirements can be understood by the programmers.
<MASK>
|
<MASK>
Difference Between Algorithm and Pseudocode: In a programming language, both algorithm and pseudocode play an important role. Where an algorithm is considered the foundation of the programming language pseudocode is used to make the programming language more human-friendly. The major difference between algorithm and pseudocode is that pseudocode is a method of writing an algorithm and an algorithm is a step-by-step description of the procedure of a task.
<MASK>
Algorithm Pseudocode It is a step-by-step description of the solution. It is an easy way of writing algorithms for users to understand. It is always a real algorithm and not fake codes. These are fake codes. They are a sequence of solutions to a problem. They are representations of algorithms. It is a systematically written code. These are simpler ways of writing codes. They are an unambiguous way of writing codes. They are a method of describing codes written in an algorithm. They can be considered pseudocode. They can not be considered algorithms There are no rules to writing algorithms. Certain rules to writing pseudocode are there.
<MASK>
The algorithm will have a well-defined set of steps. Problems are solved with a specific solution. Natural languages, flow charts, etc can be used to represent an algorithm. Candidates can check out Prim’s Algorithm to know more about Algorithm.
<MASK>
Pseudocode is also known as fake codes. It is used to give a simple human-friendly description of the steps used in an algorithm. It is an informal description. It is often used to summarise the steps or flow of the algorithm but it does not specify the detail of the algorithm. It is written by the system designers so that aligned codes and requirements can be understood by the programmers.
<MASK>
<UNMASK>
<MASK>
By BYJU'S Exam Prep
<MASK>
Difference Between Algorithm and Pseudocode: In a programming language, both algorithm and pseudocode play an important role. Where an algorithm is considered the foundation of the programming language pseudocode is used to make the programming language more human-friendly. The major difference between algorithm and pseudocode is that pseudocode is a method of writing an algorithm and an algorithm is a step-by-step description of the procedure of a task.
<MASK>
Algorithm Pseudocode It is a step-by-step description of the solution. It is an easy way of writing algorithms for users to understand. It is always a real algorithm and not fake codes. These are fake codes. They are a sequence of solutions to a problem. They are representations of algorithms. It is a systematically written code. These are simpler ways of writing codes. They are an unambiguous way of writing codes. They are a method of describing codes written in an algorithm. They can be considered pseudocode. They can not be considered algorithms There are no rules to writing algorithms. Certain rules to writing pseudocode are there.
<MASK>
## What is an Algorithm?
<MASK>
The algorithm will have a well-defined set of steps. Problems are solved with a specific solution. Natural languages, flow charts, etc can be used to represent an algorithm. Candidates can check out Prim’s Algorithm to know more about Algorithm.
## What is a Pseudocode?
Pseudocode is also known as fake codes. It is used to give a simple human-friendly description of the steps used in an algorithm. It is an informal description. It is often used to summarise the steps or flow of the algorithm but it does not specify the detail of the algorithm. It is written by the system designers so that aligned codes and requirements can be understood by the programmers.
<MASK>
POPULAR EXAMS
SSC and Bank
Other Exams
GradeStack Learning Pvt. Ltd.Windsor IT Park, Tower - A, 2nd Floor, Sector 125, Noida, Uttar Pradesh 201303 [email protected]
|
<MASK>
By BYJU'S Exam Prep
<MASK>
Difference Between Algorithm and Pseudocode: In a programming language, both algorithm and pseudocode play an important role. Where an algorithm is considered the foundation of the programming language pseudocode is used to make the programming language more human-friendly. The major difference between algorithm and pseudocode is that pseudocode is a method of writing an algorithm and an algorithm is a step-by-step description of the procedure of a task.
<MASK>
Algorithm Pseudocode It is a step-by-step description of the solution. It is an easy way of writing algorithms for users to understand. It is always a real algorithm and not fake codes. These are fake codes. They are a sequence of solutions to a problem. They are representations of algorithms. It is a systematically written code. These are simpler ways of writing codes. They are an unambiguous way of writing codes. They are a method of describing codes written in an algorithm. They can be considered pseudocode. They can not be considered algorithms There are no rules to writing algorithms. Certain rules to writing pseudocode are there.
<MASK>
## What is an Algorithm?
<MASK>
The algorithm will have a well-defined set of steps. Problems are solved with a specific solution. Natural languages, flow charts, etc can be used to represent an algorithm. Candidates can check out Prim’s Algorithm to know more about Algorithm.
## What is a Pseudocode?
Pseudocode is also known as fake codes. It is used to give a simple human-friendly description of the steps used in an algorithm. It is an informal description. It is often used to summarise the steps or flow of the algorithm but it does not specify the detail of the algorithm. It is written by the system designers so that aligned codes and requirements can be understood by the programmers.
<MASK>
POPULAR EXAMS
SSC and Bank
Other Exams
GradeStack Learning Pvt. Ltd.Windsor IT Park, Tower - A, 2nd Floor, Sector 125, Noida, Uttar Pradesh 201303 [email protected]
<UNMASK>
<MASK>
By BYJU'S Exam Prep
Updated on: September 25th, 2023
Difference Between Algorithm and Pseudocode: In a programming language, both algorithm and pseudocode play an important role. Where an algorithm is considered the foundation of the programming language pseudocode is used to make the programming language more human-friendly. The major difference between algorithm and pseudocode is that pseudocode is a method of writing an algorithm and an algorithm is a step-by-step description of the procedure of a task.
Here, we will first read what is algorithm and pseudocode in brief then we will discuss the difference between algorithm and pseudocode on various factors.
Table of content
<MASK>
### Key Differences Between Algorithm and Pseudocode
Algorithm Pseudocode It is a step-by-step description of the solution. It is an easy way of writing algorithms for users to understand. It is always a real algorithm and not fake codes. These are fake codes. They are a sequence of solutions to a problem. They are representations of algorithms. It is a systematically written code. These are simpler ways of writing codes. They are an unambiguous way of writing codes. They are a method of describing codes written in an algorithm. They can be considered pseudocode. They can not be considered algorithms There are no rules to writing algorithms. Certain rules to writing pseudocode are there.
<MASK>
## What is an Algorithm?
In the programming language, algorithms are a procedure to solve a given problem with step by step description of the solution. The steps are carried out in a finite amount of time. The problems of complex nature can be solved by a simple step-by-step description of an algorithm.
The algorithm will have a well-defined set of steps. Problems are solved with a specific solution. Natural languages, flow charts, etc can be used to represent an algorithm. Candidates can check out Prim’s Algorithm to know more about Algorithm.
## What is a Pseudocode?
Pseudocode is also known as fake codes. It is used to give a simple human-friendly description of the steps used in an algorithm. It is an informal description. It is often used to summarise the steps or flow of the algorithm but it does not specify the detail of the algorithm. It is written by the system designers so that aligned codes and requirements can be understood by the programmers.
Pseudocode is used to plan an algorithm. They are not used in complex programming languages. As we have seen the algorithm and pseudocode, let us now see the major differences between the two in the next section.
Check out some important topics related to the difference between Algorithm and Pseudocode:
POPULAR EXAMS
SSC and Bank
Other Exams
GradeStack Learning Pvt. Ltd.Windsor IT Park, Tower - A, 2nd Floor, Sector 125, Noida, Uttar Pradesh 201303 [email protected]
|
<MASK>
By BYJU'S Exam Prep
Updated on: September 25th, 2023
Difference Between Algorithm and Pseudocode: In a programming language, both algorithm and pseudocode play an important role. Where an algorithm is considered the foundation of the programming language pseudocode is used to make the programming language more human-friendly. The major difference between algorithm and pseudocode is that pseudocode is a method of writing an algorithm and an algorithm is a step-by-step description of the procedure of a task.
Here, we will first read what is algorithm and pseudocode in brief then we will discuss the difference between algorithm and pseudocode on various factors.
Table of content
<MASK>
### Key Differences Between Algorithm and Pseudocode
Algorithm Pseudocode It is a step-by-step description of the solution. It is an easy way of writing algorithms for users to understand. It is always a real algorithm and not fake codes. These are fake codes. They are a sequence of solutions to a problem. They are representations of algorithms. It is a systematically written code. These are simpler ways of writing codes. They are an unambiguous way of writing codes. They are a method of describing codes written in an algorithm. They can be considered pseudocode. They can not be considered algorithms There are no rules to writing algorithms. Certain rules to writing pseudocode are there.
<MASK>
## What is an Algorithm?
In the programming language, algorithms are a procedure to solve a given problem with step by step description of the solution. The steps are carried out in a finite amount of time. The problems of complex nature can be solved by a simple step-by-step description of an algorithm.
The algorithm will have a well-defined set of steps. Problems are solved with a specific solution. Natural languages, flow charts, etc can be used to represent an algorithm. Candidates can check out Prim’s Algorithm to know more about Algorithm.
## What is a Pseudocode?
Pseudocode is also known as fake codes. It is used to give a simple human-friendly description of the steps used in an algorithm. It is an informal description. It is often used to summarise the steps or flow of the algorithm but it does not specify the detail of the algorithm. It is written by the system designers so that aligned codes and requirements can be understood by the programmers.
Pseudocode is used to plan an algorithm. They are not used in complex programming languages. As we have seen the algorithm and pseudocode, let us now see the major differences between the two in the next section.
Check out some important topics related to the difference between Algorithm and Pseudocode:
POPULAR EXAMS
SSC and Bank
Other Exams
GradeStack Learning Pvt. Ltd.Windsor IT Park, Tower - A, 2nd Floor, Sector 125, Noida, Uttar Pradesh 201303 [email protected]
<UNMASK>
# Difference Between Algorithm and Pseudocode
By BYJU'S Exam Prep
Updated on: September 25th, 2023
Difference Between Algorithm and Pseudocode: In a programming language, both algorithm and pseudocode play an important role. Where an algorithm is considered the foundation of the programming language pseudocode is used to make the programming language more human-friendly. The major difference between algorithm and pseudocode is that pseudocode is a method of writing an algorithm and an algorithm is a step-by-step description of the procedure of a task.
Here, we will first read what is algorithm and pseudocode in brief then we will discuss the difference between algorithm and pseudocode on various factors.
Table of content
## Difference Between Algorithm and Pseudocode
Although there are various similarities between algorithm and pseudocode, there are a few differences between the two which are explained in the table provided below:
### Key Differences Between Algorithm and Pseudocode
Algorithm Pseudocode It is a step-by-step description of the solution. It is an easy way of writing algorithms for users to understand. It is always a real algorithm and not fake codes. These are fake codes. They are a sequence of solutions to a problem. They are representations of algorithms. It is a systematically written code. These are simpler ways of writing codes. They are an unambiguous way of writing codes. They are a method of describing codes written in an algorithm. They can be considered pseudocode. They can not be considered algorithms There are no rules to writing algorithms. Certain rules to writing pseudocode are there.
The Difference Between Algorithm, Pseudocode, and Program to know more about these topics.
## What is an Algorithm?
In the programming language, algorithms are a procedure to solve a given problem with step by step description of the solution. The steps are carried out in a finite amount of time. The problems of complex nature can be solved by a simple step-by-step description of an algorithm.
The algorithm will have a well-defined set of steps. Problems are solved with a specific solution. Natural languages, flow charts, etc can be used to represent an algorithm. Candidates can check out Prim’s Algorithm to know more about Algorithm.
## What is a Pseudocode?
Pseudocode is also known as fake codes. It is used to give a simple human-friendly description of the steps used in an algorithm. It is an informal description. It is often used to summarise the steps or flow of the algorithm but it does not specify the detail of the algorithm. It is written by the system designers so that aligned codes and requirements can be understood by the programmers.
Pseudocode is used to plan an algorithm. They are not used in complex programming languages. As we have seen the algorithm and pseudocode, let us now see the major differences between the two in the next section.
Check out some important topics related to the difference between Algorithm and Pseudocode:
POPULAR EXAMS
SSC and Bank
Other Exams
GradeStack Learning Pvt. Ltd.Windsor IT Park, Tower - A, 2nd Floor, Sector 125, Noida, Uttar Pradesh 201303 [email protected]
|
FREE ASSISTANCE FOR THE INQUISITIVE PEOPLE
Tutorial Topics
Write a Java program to transpose of a matrix. JAVA Practical ISC 2016 Solve - Start and End Vowel
JAVA Practical Question ISC 2016 Solve - Circular Prime - Java
2780 Arnab De 09/08/2019
<MASK>
A Circular prime is a prime number that remains a prime under cyclic shifts of its digits. When left most digits is removed and replaced at the end of the remaining string of the digits, the generated number is still prime. The process is repeated until the original number is reached again.
<MASK>
Examples 1:
<MASK>
Test with the no 1193
Enter A Number : 197
197
971
719
197 is a Circular Prime No
Test with the no 131
Enter A Number : 131
131
311
113
131 is a Circular Prime No
<MASK>
<UNMASK>
FREE ASSISTANCE FOR THE INQUISITIVE PEOPLE
Tutorial Topics
Write a Java program to transpose of a matrix. JAVA Practical ISC 2016 Solve - Start and End Vowel
JAVA Practical Question ISC 2016 Solve - Circular Prime - Java
2780 Arnab De 09/08/2019
This program is selected from ISC 2016 Computer Science or Class 12 practical paper.
A Circular prime is a prime number that remains a prime under cyclic shifts of its digits. When left most digits is removed and replaced at the end of the remaining string of the digits, the generated number is still prime. The process is repeated until the original number is reached again.
<MASK>
Examples 1:
<MASK>
Test with the no 1193
Enter A Number : 197
197
971
719
197 is a Circular Prime No
Test with the no 131
Enter A Number : 131
131
311
113
131 is a Circular Prime No
Test with the no 1193
Enter A Number : 1193
1193
1931
9311
3119
1193 is a Circular Prime No
<MASK>
|
FREE ASSISTANCE FOR THE INQUISITIVE PEOPLE
Tutorial Topics
Write a Java program to transpose of a matrix. JAVA Practical ISC 2016 Solve - Start and End Vowel
JAVA Practical Question ISC 2016 Solve - Circular Prime - Java
2780 Arnab De 09/08/2019
This program is selected from ISC 2016 Computer Science or Class 12 practical paper.
A Circular prime is a prime number that remains a prime under cyclic shifts of its digits. When left most digits is removed and replaced at the end of the remaining string of the digits, the generated number is still prime. The process is repeated until the original number is reached again.
<MASK>
Examples 1:
<MASK>
Test with the no 1193
Enter A Number : 197
197
971
719
197 is a Circular Prime No
Test with the no 131
Enter A Number : 131
131
311
113
131 is a Circular Prime No
Test with the no 1193
Enter A Number : 1193
1193
1931
9311
3119
1193 is a Circular Prime No
<MASK>
<UNMASK>
FREE ASSISTANCE FOR THE INQUISITIVE PEOPLE
Tutorial Topics
Write a Java program to transpose of a matrix. JAVA Practical ISC 2016 Solve - Start and End Vowel
JAVA Practical Question ISC 2016 Solve - Circular Prime - Java
2780 Arnab De 09/08/2019
This program is selected from ISC 2016 Computer Science or Class 12 practical paper.
A Circular prime is a prime number that remains a prime under cyclic shifts of its digits. When left most digits is removed and replaced at the end of the remaining string of the digits, the generated number is still prime. The process is repeated until the original number is reached again.
<MASK>
Examples 1:
• 131
• 311
• 113
<MASK>
Test with the no 1193
Enter A Number : 197
197
971
719
197 is a Circular Prime No
Test with the no 131
Enter A Number : 131
131
311
113
131 is a Circular Prime No
Test with the no 1193
Enter A Number : 1193
1193
1931
9311
3119
1193 is a Circular Prime No
<MASK>
|
FREE ASSISTANCE FOR THE INQUISITIVE PEOPLE
Tutorial Topics
Write a Java program to transpose of a matrix. JAVA Practical ISC 2016 Solve - Start and End Vowel
JAVA Practical Question ISC 2016 Solve - Circular Prime - Java
2780 Arnab De 09/08/2019
This program is selected from ISC 2016 Computer Science or Class 12 practical paper.
A Circular prime is a prime number that remains a prime under cyclic shifts of its digits. When left most digits is removed and replaced at the end of the remaining string of the digits, the generated number is still prime. The process is repeated until the original number is reached again.
<MASK>
Examples 1:
• 131
• 311
• 113
<MASK>
Test with the no 1193
Enter A Number : 197
197
971
719
197 is a Circular Prime No
Test with the no 131
Enter A Number : 131
131
311
113
131 is a Circular Prime No
Test with the no 1193
Enter A Number : 1193
1193
1931
9311
3119
1193 is a Circular Prime No
<MASK>
<UNMASK>
FREE ASSISTANCE FOR THE INQUISITIVE PEOPLE
Tutorial Topics
Write a Java program to transpose of a matrix. JAVA Practical ISC 2016 Solve - Start and End Vowel
JAVA Practical Question ISC 2016 Solve - Circular Prime - Java
2780 Arnab De 09/08/2019
This program is selected from ISC 2016 Computer Science or Class 12 practical paper.
A Circular prime is a prime number that remains a prime under cyclic shifts of its digits. When left most digits is removed and replaced at the end of the remaining string of the digits, the generated number is still prime. The process is repeated until the original number is reached again.
<MASK>
Examples 1:
• 131
• 311
• 113
<MASK>
}
nos=cp.changeNumber(nos);
}
if(flag)
{
System.out.print(noi + " is a Circular Prime No");
}
else
{
System.out.print(noi + " is not a Circular Prime No");
}
}
String changeNumber(String n)
{
String s="";
s=n.substring(1)+n.substring(0,1);
return s;
}
boolean IsPrime(String n)
{
int no=Integer.parseInt(n);
boolean b=true;
int d=2;
while(d<=Math.sqrt(no))
{
if(no%d==0)
{
b=false;
break;
}
d++;
}
return b;
}
}
```
Test with the no 1193
Enter A Number : 197
197
971
719
197 is a Circular Prime No
Test with the no 131
Enter A Number : 131
131
311
113
131 is a Circular Prime No
Test with the no 1193
Enter A Number : 1193
1193
1931
9311
3119
1193 is a Circular Prime No
<MASK>
|
FREE ASSISTANCE FOR THE INQUISITIVE PEOPLE
Tutorial Topics
Write a Java program to transpose of a matrix. JAVA Practical ISC 2016 Solve - Start and End Vowel
JAVA Practical Question ISC 2016 Solve - Circular Prime - Java
2780 Arnab De 09/08/2019
This program is selected from ISC 2016 Computer Science or Class 12 practical paper.
A Circular prime is a prime number that remains a prime under cyclic shifts of its digits. When left most digits is removed and replaced at the end of the remaining string of the digits, the generated number is still prime. The process is repeated until the original number is reached again.
<MASK>
Examples 1:
• 131
• 311
• 113
<MASK>
}
nos=cp.changeNumber(nos);
}
if(flag)
{
System.out.print(noi + " is a Circular Prime No");
}
else
{
System.out.print(noi + " is not a Circular Prime No");
}
}
String changeNumber(String n)
{
String s="";
s=n.substring(1)+n.substring(0,1);
return s;
}
boolean IsPrime(String n)
{
int no=Integer.parseInt(n);
boolean b=true;
int d=2;
while(d<=Math.sqrt(no))
{
if(no%d==0)
{
b=false;
break;
}
d++;
}
return b;
}
}
```
Test with the no 1193
Enter A Number : 197
197
971
719
197 is a Circular Prime No
Test with the no 131
Enter A Number : 131
131
311
113
131 is a Circular Prime No
Test with the no 1193
Enter A Number : 1193
1193
1931
9311
3119
1193 is a Circular Prime No
<MASK>
<UNMASK>
FREE ASSISTANCE FOR THE INQUISITIVE PEOPLE
Tutorial Topics
Write a Java program to transpose of a matrix. JAVA Practical ISC 2016 Solve - Start and End Vowel
JAVA Practical Question ISC 2016 Solve - Circular Prime - Java
2780 Arnab De 09/08/2019
This program is selected from ISC 2016 Computer Science or Class 12 practical paper.
A Circular prime is a prime number that remains a prime under cyclic shifts of its digits. When left most digits is removed and replaced at the end of the remaining string of the digits, the generated number is still prime. The process is repeated until the original number is reached again.
A number is said to be prime if it has only two factors 1 and itself.
Examples 1:
• 131
• 311
• 113
Hence,131 is a circular prime
Accept a positive number N and check whether it is a circular prime or not. The new number formed after the shifting of the digits should also be displayed.
```import java.util.*;
public class CircularPrime
{
public static void main(String []args)
{
Scanner sc=new Scanner(System.in);
CircularPrime cp=new CircularPrime();
Boolean flag=true;
System.out.print("Enter A Number : ");
int noi=sc.nextInt();
String nos=String.valueOf(noi);
int len=nos.length();
for(int i=1;i<=len;i++)
{
System.out.println(nos);
if(!cp.IsPrime(nos))
{
flag=false;
}
nos=cp.changeNumber(nos);
}
if(flag)
{
System.out.print(noi + " is a Circular Prime No");
}
else
{
System.out.print(noi + " is not a Circular Prime No");
}
}
String changeNumber(String n)
{
String s="";
s=n.substring(1)+n.substring(0,1);
return s;
}
boolean IsPrime(String n)
{
int no=Integer.parseInt(n);
boolean b=true;
int d=2;
while(d<=Math.sqrt(no))
{
if(no%d==0)
{
b=false;
break;
}
d++;
}
return b;
}
}
```
Test with the no 1193
Enter A Number : 197
197
971
719
197 is a Circular Prime No
Test with the no 131
Enter A Number : 131
131
311
113
131 is a Circular Prime No
Test with the no 1193
Enter A Number : 1193
1193
1931
9311
3119
1193 is a Circular Prime No
Test with the no 29
Enter A Number : 29
29
92
29 is not a Circular Prime No
Write a Java program to transpose of a matrix. JAVA Practical ISC 2016 Solve - Start and End Vowel
Author Details
Arnab De
I have over 16 years of experience working as an IT professional, ranging from teaching at my own institute to being a computer faculty at different leading institute across Kolkata. I also work as a web developer and designer, having worked for renowned companies and brand. Through tutorialathome, I wish to share my years of knowledge with the readers.
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<MASK>
<UNMASK>
<MASK>
I plugged in a + bi for z and attempted to simplify.
• Jan 3rd 2012, 09:08 AM
FernandoRevilla
Re: A few complex number problems
Use that $\displaystyle \textrm{Re}(w)=\frac{1}{2}(w+\bar{w})$ and $\displaystyle |z|^2=z\bar{z}=1$ .
• Jan 3rd 2012, 12:50 PM
Opalg
Re: A few complex number problems
Quote:
<MASK>
|
<MASK>
I plugged in a + bi for z and attempted to simplify.
• Jan 3rd 2012, 09:08 AM
FernandoRevilla
Re: A few complex number problems
Use that $\displaystyle \textrm{Re}(w)=\frac{1}{2}(w+\bar{w})$ and $\displaystyle |z|^2=z\bar{z}=1$ .
• Jan 3rd 2012, 12:50 PM
Opalg
Re: A few complex number problems
Quote:
<MASK>
<UNMASK>
<MASK>
• Jan 3rd 2012, 08:19 AM
Lemons123
A few complex number problems
I have attempted to solve it but arrive at either no solution or a solution much different from the textbook's.
<MASK>
I plugged in a + bi for z and attempted to simplify.
• Jan 3rd 2012, 09:08 AM
FernandoRevilla
Re: A few complex number problems
Use that $\displaystyle \textrm{Re}(w)=\frac{1}{2}(w+\bar{w})$ and $\displaystyle |z|^2=z\bar{z}=1$ .
• Jan 3rd 2012, 12:50 PM
Opalg
Re: A few complex number problems
Quote:
<MASK>
1. If w = $\displaystyle \frac{z + 1}{z - 1}$ and |z| = 1, find Re(w).
I plugged in a + bi for z and attempted to simplify.
<MASK>
|
<MASK>
• Jan 3rd 2012, 08:19 AM
Lemons123
A few complex number problems
I have attempted to solve it but arrive at either no solution or a solution much different from the textbook's.
<MASK>
I plugged in a + bi for z and attempted to simplify.
• Jan 3rd 2012, 09:08 AM
FernandoRevilla
Re: A few complex number problems
Use that $\displaystyle \textrm{Re}(w)=\frac{1}{2}(w+\bar{w})$ and $\displaystyle |z|^2=z\bar{z}=1$ .
• Jan 3rd 2012, 12:50 PM
Opalg
Re: A few complex number problems
Quote:
<MASK>
1. If w = $\displaystyle \frac{z + 1}{z - 1}$ and |z| = 1, find Re(w).
I plugged in a + bi for z and attempted to simplify.
<MASK>
<UNMASK>
<MASK>
• Jan 3rd 2012, 08:19 AM
Lemons123
A few complex number problems
I have attempted to solve it but arrive at either no solution or a solution much different from the textbook's.
<MASK>
I plugged in a + bi for z and attempted to simplify.
• Jan 3rd 2012, 09:08 AM
FernandoRevilla
Re: A few complex number problems
Use that $\displaystyle \textrm{Re}(w)=\frac{1}{2}(w+\bar{w})$ and $\displaystyle |z|^2=z\bar{z}=1$ .
• Jan 3rd 2012, 12:50 PM
Opalg
Re: A few complex number problems
Quote:
<MASK>
1. If w = $\displaystyle \frac{z + 1}{z - 1}$ and |z| = 1, find Re(w).
I plugged in a + bi for z and attempted to simplify.
If If $\displaystyle w=\frac{z + 1}{z - 1}$ then $\displaystyle w(z-1) = z+1.$ Solve that for z to get $\displaystyle z = \frac{w+1}{w-1}.$ If $\displaystyle |z|=1$ it follows that $\displaystyle |w+1| = |w-1|.$ Thus w is equidistant from 1 and –1, and so Re(w) = 0.
• Jan 3rd 2012, 02:04 PM
FernandoRevilla
Re: A few complex number problems
Or (using $\displaystyle z\bar{z}=1$) :
<MASK>
|
<MASK>
• Jan 3rd 2012, 08:19 AM
Lemons123
A few complex number problems
I have attempted to solve it but arrive at either no solution or a solution much different from the textbook's.
<MASK>
I plugged in a + bi for z and attempted to simplify.
• Jan 3rd 2012, 09:08 AM
FernandoRevilla
Re: A few complex number problems
Use that $\displaystyle \textrm{Re}(w)=\frac{1}{2}(w+\bar{w})$ and $\displaystyle |z|^2=z\bar{z}=1$ .
• Jan 3rd 2012, 12:50 PM
Opalg
Re: A few complex number problems
Quote:
<MASK>
1. If w = $\displaystyle \frac{z + 1}{z - 1}$ and |z| = 1, find Re(w).
I plugged in a + bi for z and attempted to simplify.
If If $\displaystyle w=\frac{z + 1}{z - 1}$ then $\displaystyle w(z-1) = z+1.$ Solve that for z to get $\displaystyle z = \frac{w+1}{w-1}.$ If $\displaystyle |z|=1$ it follows that $\displaystyle |w+1| = |w-1|.$ Thus w is equidistant from 1 and –1, and so Re(w) = 0.
• Jan 3rd 2012, 02:04 PM
FernandoRevilla
Re: A few complex number problems
Or (using $\displaystyle z\bar{z}=1$) :
<MASK>
<UNMASK>
# A few complex number problems
• Jan 3rd 2012, 08:19 AM
Lemons123
A few complex number problems
I have attempted to solve it but arrive at either no solution or a solution much different from the textbook's.
1. If w = $\displaystyle \frac{z + 1}{z - 1}$ and |z| = 1, find Re(w).
I plugged in a + bi for z and attempted to simplify.
• Jan 3rd 2012, 09:08 AM
FernandoRevilla
Re: A few complex number problems
Use that $\displaystyle \textrm{Re}(w)=\frac{1}{2}(w+\bar{w})$ and $\displaystyle |z|^2=z\bar{z}=1$ .
• Jan 3rd 2012, 12:50 PM
Opalg
Re: A few complex number problems
Quote:
Originally Posted by Lemons123
I have attempted to solve it but arrive at either no solution or a solution much different from the textbook's.
1. If w = $\displaystyle \frac{z + 1}{z - 1}$ and |z| = 1, find Re(w).
I plugged in a + bi for z and attempted to simplify.
If If $\displaystyle w=\frac{z + 1}{z - 1}$ then $\displaystyle w(z-1) = z+1.$ Solve that for z to get $\displaystyle z = \frac{w+1}{w-1}.$ If $\displaystyle |z|=1$ it follows that $\displaystyle |w+1| = |w-1|.$ Thus w is equidistant from 1 and –1, and so Re(w) = 0.
• Jan 3rd 2012, 02:04 PM
FernandoRevilla
Re: A few complex number problems
Or (using $\displaystyle z\bar{z}=1$) :
$\displaystyle \textrm{Re}(w)=\frac{1}{2}(w+\bar{w})=\frac{1}{2} \left(\frac{z+1}{z-1}+\frac{\bar{z}+1}{\bar{z}-1} \right)=\frac{1}{2}\dfrac {0}{(z-1)(\bar{z}-1)}=0$
|
# Into Math Grade 2 Module 12 Lesson 3 Answer Key Represent and Record Two-Digit Addition
<MASK>
How can you represent Brianna’s cat and dog books? How many books about cats or dogs does she have?
<MASK>
Read the following: Brianna has 12 books about cats. She has 11 books about dogs. How many books about cats or dogs does she have?
Given that,
The total number of books about cats near Brianna is 12
The total number of books about dogs near Brianna is 11
Therefore 12 + 11 = 23
There are 23 books she has.
<MASK>
B. Are there 10 ones to regroup?
Yes, there are 10 ones to regroup.
Adding 57 + 35 in this case you need to regroup the numbers.
when you add the ones place digits 7 + 5, you get 12 which means 1 ten and 2 ones.
Know to regroup the tens into the tens place and leave the ones. Then 57 + 35 = 92.
<MASK>
D. How many ones are left after regrouping? Write the number of ones left over in the ones place.
After regrouping the number of ones left over in the one place is 2.
<MASK>
A. How can you draw quick pictures to help you find the sum of 26 and 46?
<MASK>
A. Find How many ones in all. Regroup if you need to. Write a I in the tens column to show the regrouped ten.
<MASK>
Question 6.
Add 16 and 23.
<MASK>
<UNMASK>
# Into Math Grade 2 Module 12 Lesson 3 Answer Key Represent and Record Two-Digit Addition
<MASK>
I Can represent and record two-digit addition with and without regrouping.
How can you represent Brianna’s cat and dog books? How many books about cats or dogs does she have?
<MASK>
Read the following: Brianna has 12 books about cats. She has 11 books about dogs. How many books about cats or dogs does she have?
Given that,
The total number of books about cats near Brianna is 12
The total number of books about dogs near Brianna is 11
Therefore 12 + 11 = 23
There are 23 books she has.
<MASK>
Question 1.
Kurt has 57¢. His friend gives him 35¢. How much money does Kurt hove now?
<MASK>
B. Are there 10 ones to regroup?
Yes, there are 10 ones to regroup.
Adding 57 + 35 in this case you need to regroup the numbers.
when you add the ones place digits 7 + 5, you get 12 which means 1 ten and 2 ones.
Know to regroup the tens into the tens place and leave the ones. Then 57 + 35 = 92.
<MASK>
D. How many ones are left after regrouping? Write the number of ones left over in the ones place.
After regrouping the number of ones left over in the one place is 2.
E. How many tens are there in all? Write the number of tens ¡n the tens place.
The number of tens in the tens place is 9.
F. How much money does Kurt have now?
________ ¢
Given that
Kurt has money = 57 cents.
Her friend given = 35 cents.
The total money near Kurt = 57 + 35 = 92
Kurt has 92 cents.
<MASK>
A. How can you draw quick pictures to help you find the sum of 26 and 46?
<MASK>
D. What is the sum?
26 + 46 = 72
Adding 26 with 46 then we get 72.
Turn and Talk Are there two numbers from that Mateo could add without regrouping?
52, 11, 25 and 74
Any two numbers can add without regrouping. Because the addition of one’s place digit is less than the 10.
<MASK>
Question 1.
Add 47 and 37.
A. Find How many ones in all. Regroup if you need to. Write a I in the tens column to show the regrouped ten.
<MASK>
Question 3.
Reason Did you need to regroup 10 ones as 1 ten in Problem 2? Explain.
No need to regroup 10 ones as 1 ten. Because the addition of one’s place digits is less than 10.
So, there is no need to regroup.
<MASK>
Question 6.
Add 16 and 23.
<MASK>
|
# Into Math Grade 2 Module 12 Lesson 3 Answer Key Represent and Record Two-Digit Addition
<MASK>
I Can represent and record two-digit addition with and without regrouping.
How can you represent Brianna’s cat and dog books? How many books about cats or dogs does she have?
<MASK>
Read the following: Brianna has 12 books about cats. She has 11 books about dogs. How many books about cats or dogs does she have?
Given that,
The total number of books about cats near Brianna is 12
The total number of books about dogs near Brianna is 11
Therefore 12 + 11 = 23
There are 23 books she has.
<MASK>
Question 1.
Kurt has 57¢. His friend gives him 35¢. How much money does Kurt hove now?
<MASK>
B. Are there 10 ones to regroup?
Yes, there are 10 ones to regroup.
Adding 57 + 35 in this case you need to regroup the numbers.
when you add the ones place digits 7 + 5, you get 12 which means 1 ten and 2 ones.
Know to regroup the tens into the tens place and leave the ones. Then 57 + 35 = 92.
<MASK>
D. How many ones are left after regrouping? Write the number of ones left over in the ones place.
After regrouping the number of ones left over in the one place is 2.
E. How many tens are there in all? Write the number of tens ¡n the tens place.
The number of tens in the tens place is 9.
F. How much money does Kurt have now?
________ ¢
Given that
Kurt has money = 57 cents.
Her friend given = 35 cents.
The total money near Kurt = 57 + 35 = 92
Kurt has 92 cents.
<MASK>
A. How can you draw quick pictures to help you find the sum of 26 and 46?
<MASK>
D. What is the sum?
26 + 46 = 72
Adding 26 with 46 then we get 72.
Turn and Talk Are there two numbers from that Mateo could add without regrouping?
52, 11, 25 and 74
Any two numbers can add without regrouping. Because the addition of one’s place digit is less than the 10.
<MASK>
Question 1.
Add 47 and 37.
A. Find How many ones in all. Regroup if you need to. Write a I in the tens column to show the regrouped ten.
<MASK>
Question 3.
Reason Did you need to regroup 10 ones as 1 ten in Problem 2? Explain.
No need to regroup 10 ones as 1 ten. Because the addition of one’s place digits is less than 10.
So, there is no need to regroup.
<MASK>
Question 6.
Add 16 and 23.
<MASK>
<UNMASK>
# Into Math Grade 2 Module 12 Lesson 3 Answer Key Represent and Record Two-Digit Addition
<MASK>
I Can represent and record two-digit addition with and without regrouping.
How can you represent Brianna’s cat and dog books? How many books about cats or dogs does she have?
<MASK>
Read the following: Brianna has 12 books about cats. She has 11 books about dogs. How many books about cats or dogs does she have?
Given that,
The total number of books about cats near Brianna is 12
The total number of books about dogs near Brianna is 11
Therefore 12 + 11 = 23
There are 23 books she has.
<MASK>
Question 1.
Kurt has 57¢. His friend gives him 35¢. How much money does Kurt hove now?
<MASK>
B. Are there 10 ones to regroup?
Yes, there are 10 ones to regroup.
Adding 57 + 35 in this case you need to regroup the numbers.
when you add the ones place digits 7 + 5, you get 12 which means 1 ten and 2 ones.
Know to regroup the tens into the tens place and leave the ones. Then 57 + 35 = 92.
<MASK>
D. How many ones are left after regrouping? Write the number of ones left over in the ones place.
After regrouping the number of ones left over in the one place is 2.
E. How many tens are there in all? Write the number of tens ¡n the tens place.
The number of tens in the tens place is 9.
F. How much money does Kurt have now?
________ ¢
Given that
Kurt has money = 57 cents.
Her friend given = 35 cents.
The total money near Kurt = 57 + 35 = 92
Kurt has 92 cents.
Question 2.
Mateo and his friends make a list of two-digit numbers. He chooses two of the numbers to add.
A. How can you draw quick pictures to help you find the sum of 26 and 46?
<MASK>
D. What is the sum?
26 + 46 = 72
Adding 26 with 46 then we get 72.
Turn and Talk Are there two numbers from that Mateo could add without regrouping?
52, 11, 25 and 74
Any two numbers can add without regrouping. Because the addition of one’s place digit is less than the 10.
<MASK>
Question 1.
Add 47 and 37.
A. Find How many ones in all. Regroup if you need to. Write a I in the tens column to show the regrouped ten.
<MASK>
Question 3.
Reason Did you need to regroup 10 ones as 1 ten in Problem 2? Explain.
No need to regroup 10 ones as 1 ten. Because the addition of one’s place digits is less than 10.
So, there is no need to regroup.
<MASK>
Question 6.
Add 16 and 23.
<MASK>
|
# Into Math Grade 2 Module 12 Lesson 3 Answer Key Represent and Record Two-Digit Addition
<MASK>
I Can represent and record two-digit addition with and without regrouping.
How can you represent Brianna’s cat and dog books? How many books about cats or dogs does she have?
<MASK>
Read the following: Brianna has 12 books about cats. She has 11 books about dogs. How many books about cats or dogs does she have?
Given that,
The total number of books about cats near Brianna is 12
The total number of books about dogs near Brianna is 11
Therefore 12 + 11 = 23
There are 23 books she has.
<MASK>
Question 1.
Kurt has 57¢. His friend gives him 35¢. How much money does Kurt hove now?
<MASK>
B. Are there 10 ones to regroup?
Yes, there are 10 ones to regroup.
Adding 57 + 35 in this case you need to regroup the numbers.
when you add the ones place digits 7 + 5, you get 12 which means 1 ten and 2 ones.
Know to regroup the tens into the tens place and leave the ones. Then 57 + 35 = 92.
<MASK>
D. How many ones are left after regrouping? Write the number of ones left over in the ones place.
After regrouping the number of ones left over in the one place is 2.
E. How many tens are there in all? Write the number of tens ¡n the tens place.
The number of tens in the tens place is 9.
F. How much money does Kurt have now?
________ ¢
Given that
Kurt has money = 57 cents.
Her friend given = 35 cents.
The total money near Kurt = 57 + 35 = 92
Kurt has 92 cents.
Question 2.
Mateo and his friends make a list of two-digit numbers. He chooses two of the numbers to add.
A. How can you draw quick pictures to help you find the sum of 26 and 46?
<MASK>
D. What is the sum?
26 + 46 = 72
Adding 26 with 46 then we get 72.
Turn and Talk Are there two numbers from that Mateo could add without regrouping?
52, 11, 25 and 74
Any two numbers can add without regrouping. Because the addition of one’s place digit is less than the 10.
<MASK>
Question 1.
Add 47 and 37.
A. Find How many ones in all. Regroup if you need to. Write a I in the tens column to show the regrouped ten.
<MASK>
Question 3.
Reason Did you need to regroup 10 ones as 1 ten in Problem 2? Explain.
No need to regroup 10 ones as 1 ten. Because the addition of one’s place digits is less than 10.
So, there is no need to regroup.
<MASK>
Question 6.
Add 16 and 23.
<MASK>
<UNMASK>
# Into Math Grade 2 Module 12 Lesson 3 Answer Key Represent and Record Two-Digit Addition
<MASK>
## HMH Into Math Grade 2 Module 12 Lesson 3 Answer Key Represent and Record Two-Digit Addition
I Can represent and record two-digit addition with and without regrouping.
How can you represent Brianna’s cat and dog books? How many books about cats or dogs does she have?
<MASK>
Read the following: Brianna has 12 books about cats. She has 11 books about dogs. How many books about cats or dogs does she have?
Given that,
The total number of books about cats near Brianna is 12
The total number of books about dogs near Brianna is 11
Therefore 12 + 11 = 23
There are 23 books she has.
Build Understanding
Question 1.
Kurt has 57¢. His friend gives him 35¢. How much money does Kurt hove now?
A. How can you use tools to show the two addends for this problem? Draw to show what you did.
Given that
Kurt has money = 57 cents.
Her friend given = 35 cents.
The total money near Kurt = 57 + 35 = 92
Kurt has 92 cents.
B. Are there 10 ones to regroup?
Yes, there are 10 ones to regroup.
Adding 57 + 35 in this case you need to regroup the numbers.
when you add the ones place digits 7 + 5, you get 12 which means 1 ten and 2 ones.
Know to regroup the tens into the tens place and leave the ones. Then 57 + 35 = 92.
C. Regroup 10 ones as 1 ten. Write a 1 in the tens column to show the regrouped ten.
D. How many ones are left after regrouping? Write the number of ones left over in the ones place.
After regrouping the number of ones left over in the one place is 2.
E. How many tens are there in all? Write the number of tens ¡n the tens place.
The number of tens in the tens place is 9.
F. How much money does Kurt have now?
________ ¢
Given that
Kurt has money = 57 cents.
Her friend given = 35 cents.
The total money near Kurt = 57 + 35 = 92
Kurt has 92 cents.
Question 2.
Mateo and his friends make a list of two-digit numbers. He chooses two of the numbers to add.
A. How can you draw quick pictures to help you find the sum of 26 and 46?
<MASK>
C. How can you odd the tens? Show your work in the chart.
D. What is the sum?
26 + 46 = 72
Adding 26 with 46 then we get 72.
Turn and Talk Are there two numbers from that Mateo could add without regrouping?
52, 11, 25 and 74
Any two numbers can add without regrouping. Because the addition of one’s place digit is less than the 10.
Step It Out
Question 1.
Add 47 and 37.
A. Find How many ones in all. Regroup if you need to. Write a I in the tens column to show the regrouped ten.
<MASK>
B. Write the number of ones left over in the ones place.
Number of ones left over in the ones place is 4.
<MASK>
D. Write the sum.
47 + 37 = 84
Adding 47 with 37 then we get 84.
<MASK>
________ apples
Given that,
The total number of apples on the tree = 65
The total number of apple on the another tree = 28
The total number of apples = 65 + 28 = 93.
Question 2.
Attend to Precision Mrs. Meyers plants 34 flowers. Mrs. Owens plants 42 flowers. How many flowers do they plant? Draw to show the addition.
_________ flowers
Given that,
Mrs. Meyers plants 34 flowers.
Mrs. Owens plants 42 flowers.
The total number of flowers = 34 + 42 = 76.
Question 3.
Reason Did you need to regroup 10 ones as 1 ten in Problem 2? Explain.
No need to regroup 10 ones as 1 ten. Because the addition of one’s place digits is less than 10.
So, there is no need to regroup.
<MASK>
_________ dogs
Given that,
The total number of big dogs = 25.
The total number of small dogs = 19.
The total number of dogs = 25 + 19 = 44.
Question 6.
Add 16 and 23.
<MASK>
Question 7.
Add 44 + 49
|
# Into Math Grade 2 Module 12 Lesson 3 Answer Key Represent and Record Two-Digit Addition
<MASK>
## HMH Into Math Grade 2 Module 12 Lesson 3 Answer Key Represent and Record Two-Digit Addition
I Can represent and record two-digit addition with and without regrouping.
How can you represent Brianna’s cat and dog books? How many books about cats or dogs does she have?
<MASK>
Read the following: Brianna has 12 books about cats. She has 11 books about dogs. How many books about cats or dogs does she have?
Given that,
The total number of books about cats near Brianna is 12
The total number of books about dogs near Brianna is 11
Therefore 12 + 11 = 23
There are 23 books she has.
Build Understanding
Question 1.
Kurt has 57¢. His friend gives him 35¢. How much money does Kurt hove now?
A. How can you use tools to show the two addends for this problem? Draw to show what you did.
Given that
Kurt has money = 57 cents.
Her friend given = 35 cents.
The total money near Kurt = 57 + 35 = 92
Kurt has 92 cents.
B. Are there 10 ones to regroup?
Yes, there are 10 ones to regroup.
Adding 57 + 35 in this case you need to regroup the numbers.
when you add the ones place digits 7 + 5, you get 12 which means 1 ten and 2 ones.
Know to regroup the tens into the tens place and leave the ones. Then 57 + 35 = 92.
C. Regroup 10 ones as 1 ten. Write a 1 in the tens column to show the regrouped ten.
D. How many ones are left after regrouping? Write the number of ones left over in the ones place.
After regrouping the number of ones left over in the one place is 2.
E. How many tens are there in all? Write the number of tens ¡n the tens place.
The number of tens in the tens place is 9.
F. How much money does Kurt have now?
________ ¢
Given that
Kurt has money = 57 cents.
Her friend given = 35 cents.
The total money near Kurt = 57 + 35 = 92
Kurt has 92 cents.
Question 2.
Mateo and his friends make a list of two-digit numbers. He chooses two of the numbers to add.
A. How can you draw quick pictures to help you find the sum of 26 and 46?
<MASK>
C. How can you odd the tens? Show your work in the chart.
D. What is the sum?
26 + 46 = 72
Adding 26 with 46 then we get 72.
Turn and Talk Are there two numbers from that Mateo could add without regrouping?
52, 11, 25 and 74
Any two numbers can add without regrouping. Because the addition of one’s place digit is less than the 10.
Step It Out
Question 1.
Add 47 and 37.
A. Find How many ones in all. Regroup if you need to. Write a I in the tens column to show the regrouped ten.
<MASK>
B. Write the number of ones left over in the ones place.
Number of ones left over in the ones place is 4.
<MASK>
D. Write the sum.
47 + 37 = 84
Adding 47 with 37 then we get 84.
<MASK>
________ apples
Given that,
The total number of apples on the tree = 65
The total number of apple on the another tree = 28
The total number of apples = 65 + 28 = 93.
Question 2.
Attend to Precision Mrs. Meyers plants 34 flowers. Mrs. Owens plants 42 flowers. How many flowers do they plant? Draw to show the addition.
_________ flowers
Given that,
Mrs. Meyers plants 34 flowers.
Mrs. Owens plants 42 flowers.
The total number of flowers = 34 + 42 = 76.
Question 3.
Reason Did you need to regroup 10 ones as 1 ten in Problem 2? Explain.
No need to regroup 10 ones as 1 ten. Because the addition of one’s place digits is less than 10.
So, there is no need to regroup.
<MASK>
_________ dogs
Given that,
The total number of big dogs = 25.
The total number of small dogs = 19.
The total number of dogs = 25 + 19 = 44.
Question 6.
Add 16 and 23.
<MASK>
Question 7.
Add 44 + 49
<UNMASK>
# Into Math Grade 2 Module 12 Lesson 3 Answer Key Represent and Record Two-Digit Addition
We included HMH Into Math Grade 2 Answer Key PDF Module 12 Lesson 3 Represent and Record Two-Digit Addition to make students experts in learning maths.
## HMH Into Math Grade 2 Module 12 Lesson 3 Answer Key Represent and Record Two-Digit Addition
I Can represent and record two-digit addition with and without regrouping.
How can you represent Brianna’s cat and dog books? How many books about cats or dogs does she have?
Brianna has _________ cat or dog books.
Read the following: Brianna has 12 books about cats. She has 11 books about dogs. How many books about cats or dogs does she have?
Given that,
The total number of books about cats near Brianna is 12
The total number of books about dogs near Brianna is 11
Therefore 12 + 11 = 23
There are 23 books she has.
Build Understanding
Question 1.
Kurt has 57¢. His friend gives him 35¢. How much money does Kurt hove now?
A. How can you use tools to show the two addends for this problem? Draw to show what you did.
Given that
Kurt has money = 57 cents.
Her friend given = 35 cents.
The total money near Kurt = 57 + 35 = 92
Kurt has 92 cents.
B. Are there 10 ones to regroup?
Yes, there are 10 ones to regroup.
Adding 57 + 35 in this case you need to regroup the numbers.
when you add the ones place digits 7 + 5, you get 12 which means 1 ten and 2 ones.
Know to regroup the tens into the tens place and leave the ones. Then 57 + 35 = 92.
C. Regroup 10 ones as 1 ten. Write a 1 in the tens column to show the regrouped ten.
D. How many ones are left after regrouping? Write the number of ones left over in the ones place.
After regrouping the number of ones left over in the one place is 2.
E. How many tens are there in all? Write the number of tens ¡n the tens place.
The number of tens in the tens place is 9.
F. How much money does Kurt have now?
________ ¢
Given that
Kurt has money = 57 cents.
Her friend given = 35 cents.
The total money near Kurt = 57 + 35 = 92
Kurt has 92 cents.
Question 2.
Mateo and his friends make a list of two-digit numbers. He chooses two of the numbers to add.
A. How can you draw quick pictures to help you find the sum of 26 and 46?
B. How can you add the ones? Regroup if you need to. Show your work in the chart.
26 + 46 = 72
Adding 26 + 46 in this case you need to regroup the numbers.
when you add the ones place digits 6 + 6, you get 12 which means 1 ten and 2 ones.
Know to regroup the tens into the tens place and leave the ones. Then 26 + 46 = 72.
C. How can you odd the tens? Show your work in the chart.
D. What is the sum?
26 + 46 = 72
Adding 26 with 46 then we get 72.
Turn and Talk Are there two numbers from that Mateo could add without regrouping?
52, 11, 25 and 74
Any two numbers can add without regrouping. Because the addition of one’s place digit is less than the 10.
Step It Out
Question 1.
Add 47 and 37.
A. Find How many ones in all. Regroup if you need to. Write a I in the tens column to show the regrouped ten.
Adding 47 + 37 in this case you need to regroup the numbers.
when you add the ones place digits 7 + 7, you get 14 which means 1 ten and 4 ones.
Know to regroup the tens into the tens place and leave the ones. Then 47 + 37 = 84.
B. Write the number of ones left over in the ones place.
Number of ones left over in the ones place is 4.
C. Write the number of tens in the tens place.
Number of tens in the tens place is 8.
D. Write the sum.
47 + 37 = 84
Adding 47 with 37 then we get 84.
Check Understanding
Question 1.
There are 65 apples on a tree. There are 28 apples on another tree. How many apples are on the trees? Draw to show the addition.
________ apples
Given that,
The total number of apples on the tree = 65
The total number of apple on the another tree = 28
The total number of apples = 65 + 28 = 93.
Question 2.
Attend to Precision Mrs. Meyers plants 34 flowers. Mrs. Owens plants 42 flowers. How many flowers do they plant? Draw to show the addition.
_________ flowers
Given that,
Mrs. Meyers plants 34 flowers.
Mrs. Owens plants 42 flowers.
The total number of flowers = 34 + 42 = 76.
Question 3.
Reason Did you need to regroup 10 ones as 1 ten in Problem 2? Explain.
No need to regroup 10 ones as 1 ten. Because the addition of one’s place digits is less than 10.
So, there is no need to regroup.
Question 4.
Open Ended Rewrite Problem 2 with different numbers so that you need to regroup when you odd. Then solve.
Mrs. Meyers plants 36 flowers. Mrs. Owens plants 45 flowers. How many flowers do they plant? Draw to show the addition.
36 + 45 = 81
Adding 36 + 45 in this case you need to regroup the numbers.
when you add the ones place digits 6 + 5, you get 11 which means 1 ten and 1 ones.
Know to regroup the tens into the tens place and leave the ones.
Question 5.
Use Structure There are 25 big dogs and 19 small dogs at the dog park. How many dogs are at the park?
_________ dogs
Given that,
The total number of big dogs = 25.
The total number of small dogs = 19.
The total number of dogs = 25 + 19 = 44.
Question 6.
Add 16 and 23.
16 + 23 = 39
There is no need of regrouping.
Question 7.
Add 44 + 49
|
<MASK>
For example, to convert 2 mol to mmol, you can use the following formula:
<MASK>
mole = mmol / 1000
<MASK>
<UNMASK>
<MASK>
Below, you will find information on how many millimol in a mol and how to accurately convert mol to mmol and vice versa.
<MASK>
For example, to convert 2 mol to mmol, you can use the following formula:
<MASK>
Using the simple formulas below, you can easily convert mol to mmol.
<MASK>
mmol to mole conversion formula:
<MASK>
mole = mmol / 1000
<MASK>
|
<MASK>
Below, you will find information on how many millimol in a mol and how to accurately convert mol to mmol and vice versa.
<MASK>
For example, to convert 2 mol to mmol, you can use the following formula:
<MASK>
Using the simple formulas below, you can easily convert mol to mmol.
<MASK>
mmol to mole conversion formula:
<MASK>
mole = mmol / 1000
<MASK>
<UNMASK>
<MASK>
Below, you will find information on how many millimol in a mol and how to accurately convert mol to mmol and vice versa.
<MASK>
For example, to convert 2 mol to mmol, you can use the following formula:
<MASK>
Using the simple formulas below, you can easily convert mol to mmol.
<MASK>
mmol = mole * 1000
<MASK>
multiply 100 by 0.001:
<MASK>
mmol to mole conversion formula:
<MASK>
mole = mmol / 1000
<MASK>
|
<MASK>
Below, you will find information on how many millimol in a mol and how to accurately convert mol to mmol and vice versa.
<MASK>
For example, to convert 2 mol to mmol, you can use the following formula:
<MASK>
Using the simple formulas below, you can easily convert mol to mmol.
<MASK>
mmol = mole * 1000
<MASK>
multiply 100 by 0.001:
<MASK>
mmol to mole conversion formula:
<MASK>
mole = mmol / 1000
<MASK>
<UNMASK>
# Moles to Millimoles (mol to mmol) Converter
<MASK>
The mol to millimol converter is a simple tool to convert mol to mmol. It works by taking the input value in mol and applying the conversion factor of 1000 millimols per mol. The converter calculates the equivalent flow molar in millimol and displays the result.
Below, you will find information on how many millimol in a mol and how to accurately convert mol to mmol and vice versa.
<MASK>
For example, to convert 2 mol to mmol, you can use the following formula:
mmol = mol * 1000
multiply 2 by 1000:
<MASK>
Using the simple formulas below, you can easily convert mol to mmol.
mole to mmol conversion formula:
mmol = mole * 1000
<MASK>
1 Millimole (mmol) is equal to 0.001 mole (mol). To convert millimoles to moles, multiply the millimole value by 0.001 or divide by 1000.
<MASK>
mol = mmol * 0.001
multiply 100 by 0.001:
mol = 100 * 0.001 = 0.1 mol
Therefore, 100 mmol equal to 0.1 mol.
Using the simple formulas below, you can easily convert mmol to mol.
mmol to mole conversion formula:
mole = mmol * 0.001
mole = mmol / 1000
What is a Mole?
Mole is a metric system molar unit. 1 mol = 1000 mmol. The symbol is "mol".
What is a Millimole?
Millimole is a metric system molar unit. 1 mmol = 0.001 mol. The symbol is "mmol".
<MASK>
Create Conversion Table
Click "Create Table". Enter a "Start" value (5, 100 etc). Select an "Increment" value (0.01, 5 etc) and select "Accuracy" to round the result.
|
# Moles to Millimoles (mol to mmol) Converter
<MASK>
The mol to millimol converter is a simple tool to convert mol to mmol. It works by taking the input value in mol and applying the conversion factor of 1000 millimols per mol. The converter calculates the equivalent flow molar in millimol and displays the result.
Below, you will find information on how many millimol in a mol and how to accurately convert mol to mmol and vice versa.
<MASK>
For example, to convert 2 mol to mmol, you can use the following formula:
mmol = mol * 1000
multiply 2 by 1000:
<MASK>
Using the simple formulas below, you can easily convert mol to mmol.
mole to mmol conversion formula:
mmol = mole * 1000
<MASK>
1 Millimole (mmol) is equal to 0.001 mole (mol). To convert millimoles to moles, multiply the millimole value by 0.001 or divide by 1000.
<MASK>
mol = mmol * 0.001
multiply 100 by 0.001:
mol = 100 * 0.001 = 0.1 mol
Therefore, 100 mmol equal to 0.1 mol.
Using the simple formulas below, you can easily convert mmol to mol.
mmol to mole conversion formula:
mole = mmol * 0.001
mole = mmol / 1000
What is a Mole?
Mole is a metric system molar unit. 1 mol = 1000 mmol. The symbol is "mol".
What is a Millimole?
Millimole is a metric system molar unit. 1 mmol = 0.001 mol. The symbol is "mmol".
<MASK>
Create Conversion Table
Click "Create Table". Enter a "Start" value (5, 100 etc). Select an "Increment" value (0.01, 5 etc) and select "Accuracy" to round the result.
<UNMASK>
# Moles to Millimoles (mol to mmol) Converter
Mol to millimol converter. 1 Mol is equal to 1000 mmillimoles.
conversion table ←→
mol 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 500 1000 mmol 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000 14000 15000 16000 17000 18000 19000 20000 21000 22000 23000 24000 25000 26000 27000 28000 29000 30000 31000 32000 33000 34000 35000 36000 37000 38000 39000 40000 41000 42000 43000 44000 45000 46000 47000 48000 49000 50000 51000 52000 53000 54000 55000 56000 57000 58000 59000 60000 61000 62000 63000 64000 65000 66000 67000 68000 69000 70000 71000 72000 73000 74000 75000 76000 77000 78000 79000 80000 81000 82000 83000 84000 85000 86000 87000 88000 89000 90000 91000 92000 93000 94000 95000 96000 97000 98000 99000 100000 500000 1000000
Round:
Moles:
Millimoles:
The mol to millimol converter is a simple tool to convert mol to mmol. It works by taking the input value in mol and applying the conversion factor of 1000 millimols per mol. The converter calculates the equivalent flow molar in millimol and displays the result.
Below, you will find information on how many millimol in a mol and how to accurately convert mol to mmol and vice versa.
## How many millimoles are in a mole?
1 Mole (mol) is equal to 1000 millimoles (mmol). To convert moles to millimoles, multiply the mole value by 1000.
For example, to convert 2 mol to mmol, you can use the following formula:
mmol = mol * 1000
multiply 2 by 1000:
mmol = 2 * 1000 = 2000 mmol
Therefore, 2 mol equal to 2000 mmol.
Using the simple formulas below, you can easily convert mol to mmol.
mole to mmol conversion formula:
mmol = mole * 1000
## How to convert millimoles to moles?
1 Millimole (mmol) is equal to 0.001 mole (mol). To convert millimoles to moles, multiply the millimole value by 0.001 or divide by 1000.
For example, to convert 100 mmol to mol, you can use the following formula:
mol = mmol * 0.001
multiply 100 by 0.001:
mol = 100 * 0.001 = 0.1 mol
Therefore, 100 mmol equal to 0.1 mol.
Using the simple formulas below, you can easily convert mmol to mol.
mmol to mole conversion formula:
mole = mmol * 0.001
mole = mmol / 1000
What is a Mole?
Mole is a metric system molar unit. 1 mol = 1000 mmol. The symbol is "mol".
What is a Millimole?
Millimole is a metric system molar unit. 1 mmol = 0.001 mol. The symbol is "mmol".
To convert all molar flow units, please visit all molar flow units converter.
Below, you have the option to create your own customized mol to millimol conversion table to meet your specific needs. This feature allows you to set the starting value, choose the increments between each entry, and select the desired level of accuracy. By tailoring the mol to mmol table according to your preferences, you can generate precise and personalized conversion results.
Create Conversion Table
Click "Create Table". Enter a "Start" value (5, 100 etc). Select an "Increment" value (0.01, 5 etc) and select "Accuracy" to round the result.
|
<MASK>
VIEWS: 19 PAGES: 5
<MASK>
3. Attach your solutions to the Summer Mathematics Fun Reflection Sheet and
Summer Mathematics Fun Log.
<MASK>
Algebra Four
http://www.shodor.org/interactivate/activities/AlgebraFour/
<MASK>
<UNMASK>
<MASK>
VIEWS: 19 PAGES: 5
<MASK>
3. Attach your solutions to the Summer Mathematics Fun Reflection Sheet and
Summer Mathematics Fun Log.
<MASK>
Close to One (Directions) and (Recording Sheet)
Fraction Track (Directions), (Board 1), (Board 2)
Small Array, Big Array (Directions) and (Recording Sheet)
Array Cards
Missing Factors (Directions), (Recording Sheet) and (Cards)
Numeral Cards
(Decimal Cards Set A) and (Decimal Cards Set B)
Smaller to Larger (Directions)
Division Compare (Directions) and (Recording Sheet)
Decimal Compare (Directions) and (Recording Sheet)
Multiplication Compare (Directions) and (Recording Sheet)
Compare Cards
Information for Parents
Information for Parents and Students
Middle School Mathematics Games (from Teaching Middle School Mathematics)
Learning Multiplication Combinations
Double-Digit Multiplication Checklist
Information for Parents and Students
Middle School Mathematics Games (from Teaching Middle School Mathematics)
CMP2 Parent Guides
The Factor Game Activity
The Product Game Activity
Locker Problem Activity
<MASK>
Angle Sum Activity
<MASK>
Information for Parents and Students
Middle School Mathematics Games (from Teaching Middle School Mathematics)
CMP2 Parent Guides
<MASK>
Algebra Four
http://www.shodor.org/interactivate/activities/AlgebraFour/
<MASK>
http://www.gamequarium.com/algebra.htm
Operation Order (Three Levels)
<MASK>
http://classroom.jc-schools.net/basic/math-integ.html
```
To top
|
<MASK>
VIEWS: 19 PAGES: 5
<MASK>
3. Attach your solutions to the Summer Mathematics Fun Reflection Sheet and
Summer Mathematics Fun Log.
<MASK>
Close to One (Directions) and (Recording Sheet)
Fraction Track (Directions), (Board 1), (Board 2)
Small Array, Big Array (Directions) and (Recording Sheet)
Array Cards
Missing Factors (Directions), (Recording Sheet) and (Cards)
Numeral Cards
(Decimal Cards Set A) and (Decimal Cards Set B)
Smaller to Larger (Directions)
Division Compare (Directions) and (Recording Sheet)
Decimal Compare (Directions) and (Recording Sheet)
Multiplication Compare (Directions) and (Recording Sheet)
Compare Cards
Information for Parents
Information for Parents and Students
Middle School Mathematics Games (from Teaching Middle School Mathematics)
Learning Multiplication Combinations
Double-Digit Multiplication Checklist
Information for Parents and Students
Middle School Mathematics Games (from Teaching Middle School Mathematics)
CMP2 Parent Guides
The Factor Game Activity
The Product Game Activity
Locker Problem Activity
<MASK>
Angle Sum Activity
<MASK>
Information for Parents and Students
Middle School Mathematics Games (from Teaching Middle School Mathematics)
CMP2 Parent Guides
<MASK>
Algebra Four
http://www.shodor.org/interactivate/activities/AlgebraFour/
<MASK>
http://www.gamequarium.com/algebra.htm
Operation Order (Three Levels)
<MASK>
http://classroom.jc-schools.net/basic/math-integ.html
```
To top
<UNMASK>
<MASK>
VIEWS: 19 PAGES: 5
<MASK>
3. Attach your solutions to the Summer Mathematics Fun Reflection Sheet and
Summer Mathematics Fun Log.
<MASK>
Close to One (Directions) and (Recording Sheet)
Fraction Track (Directions), (Board 1), (Board 2)
Small Array, Big Array (Directions) and (Recording Sheet)
Array Cards
Missing Factors (Directions), (Recording Sheet) and (Cards)
Numeral Cards
(Decimal Cards Set A) and (Decimal Cards Set B)
Smaller to Larger (Directions)
Division Compare (Directions) and (Recording Sheet)
Decimal Compare (Directions) and (Recording Sheet)
Multiplication Compare (Directions) and (Recording Sheet)
Compare Cards
Information for Parents
Information for Parents and Students
Middle School Mathematics Games (from Teaching Middle School Mathematics)
Learning Multiplication Combinations
Double-Digit Multiplication Checklist
Information for Parents and Students
Middle School Mathematics Games (from Teaching Middle School Mathematics)
CMP2 Parent Guides
The Factor Game Activity
The Product Game Activity
Locker Problem Activity
<MASK>
Angle Sum Activity
Information for Parents and Students
Middle School Mathematics Games (from Teaching Middle School Mathematics)
CMP2 Parent Guides
<MASK>
Information for Parents and Students
Middle School Mathematics Games (from Teaching Middle School Mathematics)
CMP2 Parent Guides
Virtual Bridge Experiment
(Explore bridges with the Virtual Bridge Experiment)
Interactive Pythagoras
(Use Interactive Pythagoras to explore the Pythagorean Theorem)
Painted Cubes Activity
<MASK>
http://www.classzone.com/books/algebra_1/index.cfm
Algebra Four
http://www.shodor.org/interactivate/activities/AlgebraFour/
<MASK>
http://www.gamequarium.com/algebra.htm
Operation Order (Three Levels)
<MASK>
http://classroom.jc-schools.net/basic/math-integ.html
```
To top
|
<MASK>
VIEWS: 19 PAGES: 5
<MASK>
3. Attach your solutions to the Summer Mathematics Fun Reflection Sheet and
Summer Mathematics Fun Log.
<MASK>
Close to One (Directions) and (Recording Sheet)
Fraction Track (Directions), (Board 1), (Board 2)
Small Array, Big Array (Directions) and (Recording Sheet)
Array Cards
Missing Factors (Directions), (Recording Sheet) and (Cards)
Numeral Cards
(Decimal Cards Set A) and (Decimal Cards Set B)
Smaller to Larger (Directions)
Division Compare (Directions) and (Recording Sheet)
Decimal Compare (Directions) and (Recording Sheet)
Multiplication Compare (Directions) and (Recording Sheet)
Compare Cards
Information for Parents
Information for Parents and Students
Middle School Mathematics Games (from Teaching Middle School Mathematics)
Learning Multiplication Combinations
Double-Digit Multiplication Checklist
Information for Parents and Students
Middle School Mathematics Games (from Teaching Middle School Mathematics)
CMP2 Parent Guides
The Factor Game Activity
The Product Game Activity
Locker Problem Activity
<MASK>
Angle Sum Activity
Information for Parents and Students
Middle School Mathematics Games (from Teaching Middle School Mathematics)
CMP2 Parent Guides
<MASK>
Information for Parents and Students
Middle School Mathematics Games (from Teaching Middle School Mathematics)
CMP2 Parent Guides
Virtual Bridge Experiment
(Explore bridges with the Virtual Bridge Experiment)
Interactive Pythagoras
(Use Interactive Pythagoras to explore the Pythagorean Theorem)
Painted Cubes Activity
<MASK>
http://www.classzone.com/books/algebra_1/index.cfm
Algebra Four
http://www.shodor.org/interactivate/activities/AlgebraFour/
<MASK>
http://www.gamequarium.com/algebra.htm
Operation Order (Three Levels)
<MASK>
http://classroom.jc-schools.net/basic/math-integ.html
```
To top
<UNMASK>
# Grade 6 CMP2 Games Online by dZb6J59n
VIEWS: 19 PAGES: 5
<MASK>
Palette of Problems 1 (from Teaching Middle School Mathematics)
Palette of Problems 2 (from Teaching Middle School Mathematics)
Palette of Problems 3 (from Teaching Middle School Mathematics)
2. Honor System: Do not read the solutions section until you are finished solving the
problem(s) and have explained your thinking using the rubric referenced above.
3. Attach your solutions to the Summer Mathematics Fun Reflection Sheet and
Summer Mathematics Fun Log.
<MASK>
Close to One (Directions) and (Recording Sheet)
Fraction Track (Directions), (Board 1), (Board 2)
Small Array, Big Array (Directions) and (Recording Sheet)
Array Cards
Missing Factors (Directions), (Recording Sheet) and (Cards)
Numeral Cards
(Decimal Cards Set A) and (Decimal Cards Set B)
Smaller to Larger (Directions)
Division Compare (Directions) and (Recording Sheet)
Decimal Compare (Directions) and (Recording Sheet)
Multiplication Compare (Directions) and (Recording Sheet)
Compare Cards
Information for Parents
Information for Parents and Students
Middle School Mathematics Games (from Teaching Middle School Mathematics)
Learning Multiplication Combinations
Double-Digit Multiplication Checklist
Information for Parents and Students
Middle School Mathematics Games (from Teaching Middle School Mathematics)
CMP2 Parent Guides
The Factor Game Activity
The Product Game Activity
Locker Problem Activity
<MASK>
The Target Game Activity
Tessellations
Bee Dance and Angles Activity
Angle Sum Activity
Information for Parents and Students
Middle School Mathematics Games (from Teaching Middle School Mathematics)
CMP2 Parent Guides
Virtual Box Activity
Cylinder Wrapping Activity
Designer Dart Boards Activity
Interactive Chip Model Activity
(Explore adding and subtracting using chips)
Integer Product Game Activity
Information for Parents and Students
Middle School Mathematics Games (from Teaching Middle School Mathematics)
CMP2 Parent Guides
Virtual Bridge Experiment
(Explore bridges with the Virtual Bridge Experiment)
Interactive Pythagoras
(Use Interactive Pythagoras to explore the Pythagorean Theorem)
Painted Cubes Activity
2005 http://www.necompact.org/ea/gle_support/NECAP_2005.asp
2006 http://www.ride.ri.gov/assessment/necap_releaseditems.aspx
Online Games for Algebra
Algebra 1 (McDougal Littell)
http://www.classzone.com/books/algebra_1/index.cfm
Algebra Four
http://www.shodor.org/interactivate/activities/AlgebraFour/
Interactive Algebra Games
http://www.gamequarium.com/algebra.htm
Operation Order (Three Levels)
http://www.funbrain.com/algebra/index.html
Integer Games
http://classroom.jc-schools.net/basic/math-integ.html
```
To top
|
# Grade 6 CMP2 Games Online by dZb6J59n
VIEWS: 19 PAGES: 5
<MASK>
Palette of Problems 1 (from Teaching Middle School Mathematics)
Palette of Problems 2 (from Teaching Middle School Mathematics)
Palette of Problems 3 (from Teaching Middle School Mathematics)
2. Honor System: Do not read the solutions section until you are finished solving the
problem(s) and have explained your thinking using the rubric referenced above.
3. Attach your solutions to the Summer Mathematics Fun Reflection Sheet and
Summer Mathematics Fun Log.
<MASK>
Close to One (Directions) and (Recording Sheet)
Fraction Track (Directions), (Board 1), (Board 2)
Small Array, Big Array (Directions) and (Recording Sheet)
Array Cards
Missing Factors (Directions), (Recording Sheet) and (Cards)
Numeral Cards
(Decimal Cards Set A) and (Decimal Cards Set B)
Smaller to Larger (Directions)
Division Compare (Directions) and (Recording Sheet)
Decimal Compare (Directions) and (Recording Sheet)
Multiplication Compare (Directions) and (Recording Sheet)
Compare Cards
Information for Parents
Information for Parents and Students
Middle School Mathematics Games (from Teaching Middle School Mathematics)
Learning Multiplication Combinations
Double-Digit Multiplication Checklist
Information for Parents and Students
Middle School Mathematics Games (from Teaching Middle School Mathematics)
CMP2 Parent Guides
The Factor Game Activity
The Product Game Activity
Locker Problem Activity
<MASK>
The Target Game Activity
Tessellations
Bee Dance and Angles Activity
Angle Sum Activity
Information for Parents and Students
Middle School Mathematics Games (from Teaching Middle School Mathematics)
CMP2 Parent Guides
Virtual Box Activity
Cylinder Wrapping Activity
Designer Dart Boards Activity
Interactive Chip Model Activity
(Explore adding and subtracting using chips)
Integer Product Game Activity
Information for Parents and Students
Middle School Mathematics Games (from Teaching Middle School Mathematics)
CMP2 Parent Guides
Virtual Bridge Experiment
(Explore bridges with the Virtual Bridge Experiment)
Interactive Pythagoras
(Use Interactive Pythagoras to explore the Pythagorean Theorem)
Painted Cubes Activity
2005 http://www.necompact.org/ea/gle_support/NECAP_2005.asp
2006 http://www.ride.ri.gov/assessment/necap_releaseditems.aspx
Online Games for Algebra
Algebra 1 (McDougal Littell)
http://www.classzone.com/books/algebra_1/index.cfm
Algebra Four
http://www.shodor.org/interactivate/activities/AlgebraFour/
Interactive Algebra Games
http://www.gamequarium.com/algebra.htm
Operation Order (Three Levels)
http://www.funbrain.com/algebra/index.html
Integer Games
http://classroom.jc-schools.net/basic/math-integ.html
```
To top
<UNMASK>
# Grade 6 CMP2 Games Online by dZb6J59n
VIEWS: 19 PAGES: 5
• pg 1
``` Problem Solving Tasks for Grades 6-8
Directions:
1. Select tasks that are the appropriate level of challenge for you. Use the Exemplars
rubric as a guide for explaining your solutions to the problems you choose from the
“Palette of Problems” challenges below.
Palette of Problems 1 (from Teaching Middle School Mathematics)
Palette of Problems 2 (from Teaching Middle School Mathematics)
Palette of Problems 3 (from Teaching Middle School Mathematics)
2. Honor System: Do not read the solutions section until you are finished solving the
problem(s) and have explained your thinking using the rubric referenced above.
3. Attach your solutions to the Summer Mathematics Fun Reflection Sheet and
Summer Mathematics Fun Log.
Directions: Explore mathematics games from all grade levels!
Close to One (Directions) and (Recording Sheet)
Fraction Track (Directions), (Board 1), (Board 2)
Small Array, Big Array (Directions) and (Recording Sheet)
Array Cards
Missing Factors (Directions), (Recording Sheet) and (Cards)
Numeral Cards
(Decimal Cards Set A) and (Decimal Cards Set B)
Smaller to Larger (Directions)
Division Compare (Directions) and (Recording Sheet)
Decimal Compare (Directions) and (Recording Sheet)
Multiplication Compare (Directions) and (Recording Sheet)
Compare Cards
Information for Parents
Information for Parents and Students
Middle School Mathematics Games (from Teaching Middle School Mathematics)
Learning Multiplication Combinations
Double-Digit Multiplication Checklist
Information for Parents and Students
Middle School Mathematics Games (from Teaching Middle School Mathematics)
CMP2 Parent Guides
The Factor Game Activity
The Product Game Activity
Locker Problem Activity
The Fraction Game Activity
The Target Game Activity
Tessellations
Bee Dance and Angles Activity
Angle Sum Activity
Information for Parents and Students
Middle School Mathematics Games (from Teaching Middle School Mathematics)
CMP2 Parent Guides
Virtual Box Activity
Cylinder Wrapping Activity
Designer Dart Boards Activity
Interactive Chip Model Activity
(Explore adding and subtracting using chips)
Integer Product Game Activity
Information for Parents and Students
Middle School Mathematics Games (from Teaching Middle School Mathematics)
CMP2 Parent Guides
Virtual Bridge Experiment
(Explore bridges with the Virtual Bridge Experiment)
Interactive Pythagoras
(Use Interactive Pythagoras to explore the Pythagorean Theorem)
Painted Cubes Activity
2005 http://www.necompact.org/ea/gle_support/NECAP_2005.asp
2006 http://www.ride.ri.gov/assessment/necap_releaseditems.aspx
Online Games for Algebra
Algebra 1 (McDougal Littell)
http://www.classzone.com/books/algebra_1/index.cfm
Algebra Four
http://www.shodor.org/interactivate/activities/AlgebraFour/
Interactive Algebra Games
http://www.gamequarium.com/algebra.htm
Operation Order (Three Levels)
http://www.funbrain.com/algebra/index.html
Integer Games
http://classroom.jc-schools.net/basic/math-integ.html
```
To top
|
<MASK>
<UNMASK>
<MASK>
### Astronomy Wavelength Notes:
Visible Light: 0.39 to 0.75 micrometres
Near Infrared IR: 0.78 to 3 micrometres
Medium Wavelength IR: 3 to 50 micrometres
Long Wavelength IR: 50 to 1000 micrometres
1 inch: 25,400 micrometers
1 cm: 10,000 micrometres
<MASK>
Degrees = ArcSeconds / 3600
Radians = Degrees • ( π / 180)
EXAMPLE: Our Space telescope can resolve down to 0.05 arc-seconds. What is this in radians? First, we convert arc-seconds to Degrees. 0.05 / 3600 = 1.389E-05 degrees Then to Radians 1.389E-05 • ( π / 180) = 2.42E-07 radians
### Calculating Angular Diameter for distant objects when given Actual Diameters and Distances
<MASK>
### Calculating Distance when given Angular and Actual Diameters for distant objects
<MASK>
δ: Angular Diameter of object in radians
d: Diameter of object
D: Distance between observer and object.
NOTE: d/D must be expressed in the same unit.
EXAMPLE: The Hubble Space Telescope has a visual resolution of 0.1 arc-seconds (0.00000048 radians). How far away can it see an object 100 meters in diameter? 100 / [ 2 * TAN(0.00000048/2) ] = 208,333,333.33 meters or 208,333.33 kilometers
<MASK>
Where:
<MASK>
Where:
θ: Angular resolution of imaging system in radians
|
<MASK>
### Astronomy Wavelength Notes:
Visible Light: 0.39 to 0.75 micrometres
Near Infrared IR: 0.78 to 3 micrometres
Medium Wavelength IR: 3 to 50 micrometres
Long Wavelength IR: 50 to 1000 micrometres
1 inch: 25,400 micrometers
1 cm: 10,000 micrometres
<MASK>
Degrees = ArcSeconds / 3600
Radians = Degrees • ( π / 180)
EXAMPLE: Our Space telescope can resolve down to 0.05 arc-seconds. What is this in radians? First, we convert arc-seconds to Degrees. 0.05 / 3600 = 1.389E-05 degrees Then to Radians 1.389E-05 • ( π / 180) = 2.42E-07 radians
### Calculating Angular Diameter for distant objects when given Actual Diameters and Distances
<MASK>
### Calculating Distance when given Angular and Actual Diameters for distant objects
<MASK>
δ: Angular Diameter of object in radians
d: Diameter of object
D: Distance between observer and object.
NOTE: d/D must be expressed in the same unit.
EXAMPLE: The Hubble Space Telescope has a visual resolution of 0.1 arc-seconds (0.00000048 radians). How far away can it see an object 100 meters in diameter? 100 / [ 2 * TAN(0.00000048/2) ] = 208,333,333.33 meters or 208,333.33 kilometers
<MASK>
Where:
<MASK>
Where:
θ: Angular resolution of imaging system in radians
<UNMASK>
### Astronomy Angle Notes:
<MASK>
### Astronomy Wavelength Notes:
Visible Light: 0.39 to 0.75 micrometres
Near Infrared IR: 0.78 to 3 micrometres
Medium Wavelength IR: 3 to 50 micrometres
Long Wavelength IR: 50 to 1000 micrometres
1 inch: 25,400 micrometers
1 cm: 10,000 micrometres
A Microsoft Excel file with the most important equations already laid out is available HERE.
### Converting from Arc-Seconds to Radians
Degrees = ArcSeconds / 3600
Radians = Degrees • ( π / 180)
EXAMPLE: Our Space telescope can resolve down to 0.05 arc-seconds. What is this in radians? First, we convert arc-seconds to Degrees. 0.05 / 3600 = 1.389E-05 degrees Then to Radians 1.389E-05 • ( π / 180) = 2.42E-07 radians
### Calculating Angular Diameter for distant objects when given Actual Diameters and Distances
<MASK>
Where:
<MASK>
### Calculating Distance when given Angular and Actual Diameters for distant objects
D = d / [ 2 • TAN(δ/2) ]
Where:
δ: Angular Diameter of object in radians
d: Diameter of object
D: Distance between observer and object.
NOTE: d/D must be expressed in the same unit.
EXAMPLE: The Hubble Space Telescope has a visual resolution of 0.1 arc-seconds (0.00000048 radians). How far away can it see an object 100 meters in diameter? 100 / [ 2 * TAN(0.00000048/2) ] = 208,333,333.33 meters or 208,333.33 kilometers
<MASK>
Where:
<MASK>
### Rayleigh Criterion
sin θ = 1.220 * (λ / D)
<MASK>
θ: Angular resolution of imaging system in radians
D: Diameter of the lens aperture.
NOTE: Both the lens aperture diameter and the wavelength must use the same measurement units.
<MASK>
Where:
θ: Angular resolution of imaging system in radians
|
### Astronomy Angle Notes:
<MASK>
### Astronomy Wavelength Notes:
Visible Light: 0.39 to 0.75 micrometres
Near Infrared IR: 0.78 to 3 micrometres
Medium Wavelength IR: 3 to 50 micrometres
Long Wavelength IR: 50 to 1000 micrometres
1 inch: 25,400 micrometers
1 cm: 10,000 micrometres
A Microsoft Excel file with the most important equations already laid out is available HERE.
### Converting from Arc-Seconds to Radians
Degrees = ArcSeconds / 3600
Radians = Degrees • ( π / 180)
EXAMPLE: Our Space telescope can resolve down to 0.05 arc-seconds. What is this in radians? First, we convert arc-seconds to Degrees. 0.05 / 3600 = 1.389E-05 degrees Then to Radians 1.389E-05 • ( π / 180) = 2.42E-07 radians
### Calculating Angular Diameter for distant objects when given Actual Diameters and Distances
<MASK>
Where:
<MASK>
### Calculating Distance when given Angular and Actual Diameters for distant objects
D = d / [ 2 • TAN(δ/2) ]
Where:
δ: Angular Diameter of object in radians
d: Diameter of object
D: Distance between observer and object.
NOTE: d/D must be expressed in the same unit.
EXAMPLE: The Hubble Space Telescope has a visual resolution of 0.1 arc-seconds (0.00000048 radians). How far away can it see an object 100 meters in diameter? 100 / [ 2 * TAN(0.00000048/2) ] = 208,333,333.33 meters or 208,333.33 kilometers
<MASK>
Where:
<MASK>
### Rayleigh Criterion
sin θ = 1.220 * (λ / D)
<MASK>
θ: Angular resolution of imaging system in radians
D: Diameter of the lens aperture.
NOTE: Both the lens aperture diameter and the wavelength must use the same measurement units.
<MASK>
Where:
θ: Angular resolution of imaging system in radians
<UNMASK>
### Astronomy Angle Notes:
<MASK>
### Astronomy Wavelength Notes:
Visible Light: 0.39 to 0.75 micrometres
Near Infrared IR: 0.78 to 3 micrometres
Medium Wavelength IR: 3 to 50 micrometres
Long Wavelength IR: 50 to 1000 micrometres
1 inch: 25,400 micrometers
1 cm: 10,000 micrometres
A Microsoft Excel file with the most important equations already laid out is available HERE.
### Converting from Arc-Seconds to Radians
Degrees = ArcSeconds / 3600
Radians = Degrees • ( π / 180)
EXAMPLE: Our Space telescope can resolve down to 0.05 arc-seconds. What is this in radians? First, we convert arc-seconds to Degrees. 0.05 / 3600 = 1.389E-05 degrees Then to Radians 1.389E-05 • ( π / 180) = 2.42E-07 radians
### Calculating Angular Diameter for distant objects when given Actual Diameters and Distances
<MASK>
Where:
<MASK>
### Calculating Distance when given Angular and Actual Diameters for distant objects
D = d / [ 2 • TAN(δ/2) ]
Where:
δ: Angular Diameter of object in radians
d: Diameter of object
D: Distance between observer and object.
NOTE: d/D must be expressed in the same unit.
EXAMPLE: The Hubble Space Telescope has a visual resolution of 0.1 arc-seconds (0.00000048 radians). How far away can it see an object 100 meters in diameter? 100 / [ 2 * TAN(0.00000048/2) ] = 208,333,333.33 meters or 208,333.33 kilometers
<MASK>
Resolution = 4.56 / Diameter
Where:
<MASK>
### Rayleigh Criterion
sin θ = 1.220 * (λ / D)
<MASK>
θ: Angular resolution of imaging system in radians
D: Diameter of the lens aperture.
NOTE: Both the lens aperture diameter and the wavelength must use the same measurement units.
<MASK>
Where:
θ: Angular resolution of imaging system in radians
|
### Astronomy Angle Notes:
<MASK>
### Astronomy Wavelength Notes:
Visible Light: 0.39 to 0.75 micrometres
Near Infrared IR: 0.78 to 3 micrometres
Medium Wavelength IR: 3 to 50 micrometres
Long Wavelength IR: 50 to 1000 micrometres
1 inch: 25,400 micrometers
1 cm: 10,000 micrometres
A Microsoft Excel file with the most important equations already laid out is available HERE.
### Converting from Arc-Seconds to Radians
Degrees = ArcSeconds / 3600
Radians = Degrees • ( π / 180)
EXAMPLE: Our Space telescope can resolve down to 0.05 arc-seconds. What is this in radians? First, we convert arc-seconds to Degrees. 0.05 / 3600 = 1.389E-05 degrees Then to Radians 1.389E-05 • ( π / 180) = 2.42E-07 radians
### Calculating Angular Diameter for distant objects when given Actual Diameters and Distances
<MASK>
Where:
<MASK>
### Calculating Distance when given Angular and Actual Diameters for distant objects
D = d / [ 2 • TAN(δ/2) ]
Where:
δ: Angular Diameter of object in radians
d: Diameter of object
D: Distance between observer and object.
NOTE: d/D must be expressed in the same unit.
EXAMPLE: The Hubble Space Telescope has a visual resolution of 0.1 arc-seconds (0.00000048 radians). How far away can it see an object 100 meters in diameter? 100 / [ 2 * TAN(0.00000048/2) ] = 208,333,333.33 meters or 208,333.33 kilometers
<MASK>
Resolution = 4.56 / Diameter
Where:
<MASK>
### Rayleigh Criterion
sin θ = 1.220 * (λ / D)
<MASK>
θ: Angular resolution of imaging system in radians
D: Diameter of the lens aperture.
NOTE: Both the lens aperture diameter and the wavelength must use the same measurement units.
<MASK>
Where:
θ: Angular resolution of imaging system in radians
<UNMASK>
### Astronomy Angle Notes:
1 degree = 60 arc-minutes or 3,600 arc-seconds (written as 3600”)
1 arc-minute = 60 arc-seconds
### Astronomy Wavelength Notes:
Visible Light: 0.39 to 0.75 micrometres
Near Infrared IR: 0.78 to 3 micrometres
Medium Wavelength IR: 3 to 50 micrometres
Long Wavelength IR: 50 to 1000 micrometres
1 inch: 25,400 micrometers
1 cm: 10,000 micrometres
A Microsoft Excel file with the most important equations already laid out is available HERE.
### Converting from Arc-Seconds to Radians
Degrees = ArcSeconds / 3600
Radians = Degrees • ( π / 180)
EXAMPLE: Our Space telescope can resolve down to 0.05 arc-seconds. What is this in radians? First, we convert arc-seconds to Degrees. 0.05 / 3600 = 1.389E-05 degrees Then to Radians 1.389E-05 • ( π / 180) = 2.42E-07 radians
### Calculating Angular Diameter for distant objects when given Actual Diameters and Distances
δ = 2 • arctan (½ • d / D)
Where:
δ: Angular Diameter of object in radians
d: Diameter of object
D: Distance between observer and object.
NOTE: d/D must be expressed in the same unit.
EXAMPLE: Earth's moon has a diameter of about 3,474 km and is about 384,000~ km from Earth. What is its angular size? 2 • arctan (½ • 3,474 / 384,000) = 0.009 radians
### Calculating Distance when given Angular and Actual Diameters for distant objects
D = d / [ 2 • TAN(δ/2) ]
Where:
δ: Angular Diameter of object in radians
d: Diameter of object
D: Distance between observer and object.
NOTE: d/D must be expressed in the same unit.
EXAMPLE: The Hubble Space Telescope has a visual resolution of 0.1 arc-seconds (0.00000048 radians). How far away can it see an object 100 meters in diameter? 100 / [ 2 * TAN(0.00000048/2) ] = 208,333,333.33 meters or 208,333.33 kilometers
### Dawes Limit for Resolution of an Visual Light Optical Telescope
This was based off of empirical studies done by W.R. Dawes. It is for light with a wavelength of about 562 nm.
Resolution = 4.56 / Diameter
Where:
Resolution: Resolution of the telescope in arc seconds
Diameter: Diameter of the Telescope optic in inches.
EXAMPLE: What is the resolution in arc seconds of a 8-foot (96-inch) diameter optical telescope? 4.56 / 96 = 0.0475 arc-seconds
### Rayleigh Criterion
sin θ = 1.220 * (λ / D)
Where:
θ: Angular resolution of imaging system in radians
D: Diameter of the lens aperture.
NOTE: Both the lens aperture diameter and the wavelength must use the same measurement units.
### Quick Angular Resolution Approximation via Wavelength for a Single Telescope
θ = (λ / D)
Where:
θ: Angular resolution of imaging system in radians
|
<MASK>
How old is John?
SherlockHolmes Expert Asked on 23rd January 2018 in
<MASK>
A traveller, on his way to Mexico City, reaches a road junction, where he can turn left or right. He ...Read More »
• ### FIND THE CULPRIT
<MASK>
You have a microwave whose timer is damaged and you don’t have any other watch except two hourglasses, Hourglass A ...Read More »
• ### Count the Dirt in Hole
<MASK>
What’s the largest amount of money you can have in change and still not have change for a dollar?Read More »
• ### Make the Ring drop
<MASK>
Whats the next number in the below number sequence pattern.Read More »
• ### Connect the Stars
<MASK>
<UNMASK>
<MASK>
1,047.0K Views
<MASK>
How old is John?
SherlockHolmes Expert Asked on 23rd January 2018 in
<MASK>
1. Let Tony’s age be X. Since his father who is 45, is 15 yrs older than twice his age, 2X + 15 = 45 => X = 15.
2. Let Jacob’s age be Y, and John be Z.
Since John is twice as old as Jacob, Z = 2Y.
3 years from now, their ages will be Y + 3 and Z + 3. But since Z = 2Y, this implies that the ages will be Y + 3 and 2Y + 3.
The sum of the ages = Y + 3 + 2Y + 3 = 3Y + 6 = 42. Hence Y = 12; Z = 24.
<MASK>
A lift is on the ground floor. There are 4 people in the lift including me. When the lift reaches ...Read More »
• ### Sister 7
<MASK>
A traveller, on his way to Mexico City, reaches a road junction, where he can turn left or right. He ...Read More »
• ### FIND THE CULPRIT
<MASK>
During the African-US summit last year, 10 presidents left the conference room and greeted one another. Assuming no 2 presidents ...Read More »
• ### Answer if you know
Swallowing one is fine. Swallowing two together is fine. But Swallow them separately and all shall fall. What are they?Read More »
• ### Make vegetable pizza in damaged microwave puzzle
You have a microwave whose timer is damaged and you don’t have any other watch except two hourglasses, Hourglass A ...Read More »
• ### Count the Dirt in Hole
<MASK>
There is a house. One enters it blind and leaves it seeing. What is it?Read More »
• ### Horse, Car & Helicopter riddle
<MASK>
What’s the largest amount of money you can have in change and still not have change for a dollar?Read More »
• ### Make the Ring drop
<MASK>
Whats the next number in the below number sequence pattern.Read More »
• ### Connect the Stars
<MASK>
|
<MASK>
1,047.0K Views
<MASK>
How old is John?
SherlockHolmes Expert Asked on 23rd January 2018 in
<MASK>
1. Let Tony’s age be X. Since his father who is 45, is 15 yrs older than twice his age, 2X + 15 = 45 => X = 15.
2. Let Jacob’s age be Y, and John be Z.
Since John is twice as old as Jacob, Z = 2Y.
3 years from now, their ages will be Y + 3 and Z + 3. But since Z = 2Y, this implies that the ages will be Y + 3 and 2Y + 3.
The sum of the ages = Y + 3 + 2Y + 3 = 3Y + 6 = 42. Hence Y = 12; Z = 24.
<MASK>
A lift is on the ground floor. There are 4 people in the lift including me. When the lift reaches ...Read More »
• ### Sister 7
<MASK>
A traveller, on his way to Mexico City, reaches a road junction, where he can turn left or right. He ...Read More »
• ### FIND THE CULPRIT
<MASK>
During the African-US summit last year, 10 presidents left the conference room and greeted one another. Assuming no 2 presidents ...Read More »
• ### Answer if you know
Swallowing one is fine. Swallowing two together is fine. But Swallow them separately and all shall fall. What are they?Read More »
• ### Make vegetable pizza in damaged microwave puzzle
You have a microwave whose timer is damaged and you don’t have any other watch except two hourglasses, Hourglass A ...Read More »
• ### Count the Dirt in Hole
<MASK>
There is a house. One enters it blind and leaves it seeing. What is it?Read More »
• ### Horse, Car & Helicopter riddle
<MASK>
What’s the largest amount of money you can have in change and still not have change for a dollar?Read More »
• ### Make the Ring drop
<MASK>
Whats the next number in the below number sequence pattern.Read More »
• ### Connect the Stars
<MASK>
<UNMASK>
<MASK>
1,047.0K Views
<MASK>
How old is John?
SherlockHolmes Expert Asked on 23rd January 2018 in
<MASK>
1. Let Tony’s age be X. Since his father who is 45, is 15 yrs older than twice his age, 2X + 15 = 45 => X = 15.
2. Let Jacob’s age be Y, and John be Z.
Since John is twice as old as Jacob, Z = 2Y.
3 years from now, their ages will be Y + 3 and Z + 3. But since Z = 2Y, this implies that the ages will be Y + 3 and 2Y + 3.
The sum of the ages = Y + 3 + 2Y + 3 = 3Y + 6 = 42. Hence Y = 12; Z = 24.
<MASK>
• ## More puzzles to try-
<MASK>
A lift is on the ground floor. There are 4 people in the lift including me. When the lift reaches ...Read More »
• ### Sister 7
<MASK>
A traveller, on his way to Mexico City, reaches a road junction, where he can turn left or right. He ...Read More »
• ### FIND THE CULPRIT
<MASK>
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• ### Make vegetable pizza in damaged microwave puzzle
You have a microwave whose timer is damaged and you don’t have any other watch except two hourglasses, Hourglass A ...Read More »
• ### Count the Dirt in Hole
<MASK>
There was a minor accident with a doctor’s son but the doctor noticed no major injury. After the treatment, the ...Read More »
• ### Enters it blind and leaves it seeing
There is a house. One enters it blind and leaves it seeing. What is it?Read More »
• ### Horse, Car & Helicopter riddle
You are riding a horse. In front of you, there is a fire engine. A helicopter is following you. To ...Read More »
• ### Largest amount of money change
What’s the largest amount of money you can have in change and still not have change for a dollar?Read More »
• ### Make the Ring drop
<MASK>
Whats the next number in the below number sequence pattern.Read More »
• ### Connect the Stars
<MASK>
|
<MASK>
1,047.0K Views
<MASK>
How old is John?
SherlockHolmes Expert Asked on 23rd January 2018 in
<MASK>
1. Let Tony’s age be X. Since his father who is 45, is 15 yrs older than twice his age, 2X + 15 = 45 => X = 15.
2. Let Jacob’s age be Y, and John be Z.
Since John is twice as old as Jacob, Z = 2Y.
3 years from now, their ages will be Y + 3 and Z + 3. But since Z = 2Y, this implies that the ages will be Y + 3 and 2Y + 3.
The sum of the ages = Y + 3 + 2Y + 3 = 3Y + 6 = 42. Hence Y = 12; Z = 24.
<MASK>
• ## More puzzles to try-
<MASK>
A lift is on the ground floor. There are 4 people in the lift including me. When the lift reaches ...Read More »
• ### Sister 7
<MASK>
A traveller, on his way to Mexico City, reaches a road junction, where he can turn left or right. He ...Read More »
• ### FIND THE CULPRIT
<MASK>
A boy at a carnival went to a booth ran by a man who said “If I can write your ...Read More »
• ### How many handshakes in African-US summit ?
During the African-US summit last year, 10 presidents left the conference room and greeted one another. Assuming no 2 presidents ...Read More »
• ### Answer if you know
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• ### Make vegetable pizza in damaged microwave puzzle
You have a microwave whose timer is damaged and you don’t have any other watch except two hourglasses, Hourglass A ...Read More »
• ### Count the Dirt in Hole
<MASK>
There was a minor accident with a doctor’s son but the doctor noticed no major injury. After the treatment, the ...Read More »
• ### Enters it blind and leaves it seeing
There is a house. One enters it blind and leaves it seeing. What is it?Read More »
• ### Horse, Car & Helicopter riddle
You are riding a horse. In front of you, there is a fire engine. A helicopter is following you. To ...Read More »
• ### Largest amount of money change
What’s the largest amount of money you can have in change and still not have change for a dollar?Read More »
• ### Make the Ring drop
<MASK>
Whats the next number in the below number sequence pattern.Read More »
• ### Connect the Stars
<MASK>
<UNMASK>
<MASK>
1,047.0K Views
<MASK>
How old is John?
SherlockHolmes Expert Asked on 23rd January 2018 in
<MASK>
Explanation:
1. Let Tony’s age be X. Since his father who is 45, is 15 yrs older than twice his age, 2X + 15 = 45 => X = 15.
2. Let Jacob’s age be Y, and John be Z.
Since John is twice as old as Jacob, Z = 2Y.
3 years from now, their ages will be Y + 3 and Z + 3. But since Z = 2Y, this implies that the ages will be Y + 3 and 2Y + 3.
The sum of the ages = Y + 3 + 2Y + 3 = 3Y + 6 = 42. Hence Y = 12; Z = 24.
<MASK>
• ## More puzzles to try-
<MASK>
At a farm, you are asked to identify these common plants from their blooms:Read More »
• ### How do i survive after elevator crash puzzle
A lift is on the ground floor. There are 4 people in the lift including me. When the lift reaches ...Read More »
• ### Sister 7
<MASK>
The one who has it does not keep it. It is large and small. It is any shape.Read More »
• ### Distressed Traveller Riddle
A traveller, on his way to Mexico City, reaches a road junction, where he can turn left or right. He ...Read More »
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<MASK>
There was a minor accident with a doctor’s son but the doctor noticed no major injury. After the treatment, the ...Read More »
• ### Enters it blind and leaves it seeing
There is a house. One enters it blind and leaves it seeing. What is it?Read More »
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You are riding a horse. In front of you, there is a fire engine. A helicopter is following you. To ...Read More »
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What’s the largest amount of money you can have in change and still not have change for a dollar?Read More »
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<MASK>
Whats the next number in the below number sequence pattern.Read More »
• ### Connect the Stars
<MASK>
|
<MASK>
1,047.0K Views
<MASK>
How old is John?
SherlockHolmes Expert Asked on 23rd January 2018 in
<MASK>
Explanation:
1. Let Tony’s age be X. Since his father who is 45, is 15 yrs older than twice his age, 2X + 15 = 45 => X = 15.
2. Let Jacob’s age be Y, and John be Z.
Since John is twice as old as Jacob, Z = 2Y.
3 years from now, their ages will be Y + 3 and Z + 3. But since Z = 2Y, this implies that the ages will be Y + 3 and 2Y + 3.
The sum of the ages = Y + 3 + 2Y + 3 = 3Y + 6 = 42. Hence Y = 12; Z = 24.
<MASK>
• ## More puzzles to try-
<MASK>
At a farm, you are asked to identify these common plants from their blooms:Read More »
• ### How do i survive after elevator crash puzzle
A lift is on the ground floor. There are 4 people in the lift including me. When the lift reaches ...Read More »
• ### Sister 7
<MASK>
The one who has it does not keep it. It is large and small. It is any shape.Read More »
• ### Distressed Traveller Riddle
A traveller, on his way to Mexico City, reaches a road junction, where he can turn left or right. He ...Read More »
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• ### Answer if you know
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• ### Make vegetable pizza in damaged microwave puzzle
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• ### Count the Dirt in Hole
<MASK>
There was a minor accident with a doctor’s son but the doctor noticed no major injury. After the treatment, the ...Read More »
• ### Enters it blind and leaves it seeing
There is a house. One enters it blind and leaves it seeing. What is it?Read More »
• ### Horse, Car & Helicopter riddle
You are riding a horse. In front of you, there is a fire engine. A helicopter is following you. To ...Read More »
• ### Largest amount of money change
What’s the largest amount of money you can have in change and still not have change for a dollar?Read More »
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<MASK>
Whats the next number in the below number sequence pattern.Read More »
• ### Connect the Stars
<MASK>
<UNMASK>
# Know the age puzzle
1,047.0K Views
Tony’s father is 45. He is 15 years older than twice Tony’s age. How old is Tony? John is twice as old as Jacob. Three years from now, the sum of their ages will be 42.
How old is John?
SherlockHolmes Expert Asked on 23rd January 2018 in
Tony is 15, John is 24, Jacob, 12
Explanation:
1. Let Tony’s age be X. Since his father who is 45, is 15 yrs older than twice his age, 2X + 15 = 45 => X = 15.
2. Let Jacob’s age be Y, and John be Z.
Since John is twice as old as Jacob, Z = 2Y.
3 years from now, their ages will be Y + 3 and Z + 3. But since Z = 2Y, this implies that the ages will be Y + 3 and 2Y + 3.
The sum of the ages = Y + 3 + 2Y + 3 = 3Y + 6 = 42. Hence Y = 12; Z = 24.
Viji_Pinarayi Expert Answered on 23rd January 2018.
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|
## Chapter 3. Expressions
This chapter contains the following subsections:
<MASK>
• arithmetic
• character
<MASK>
• logical
<MASK>
## Arithmetic Expressions
<MASK>
• an unsigned arithmetic constant
<MASK>
• an arithmetic array element reference
<MASK>
You can form more complicated arithmetic expressions from one or more operands together with arithmetic operators and parentheses.
<MASK>
### Arithmetic Operators
Table 3-1 shows the arithmetic operators.
<MASK>
Operator
Function
<MASK>
Exponentiation
*
<MASK>
/
<MASK>
+
<MASK>
### Interpretation of Arithmetic Expressions
Table 3-2 interprets sample arithmetic expressions.
<MASK>
Operator
Use
<MASK>
x1 ** x2
<MASK>
x1 * x2
<MASK>
/
x1 / x2
Divide x1 by x2
+
x1 + x2
<MASK>
x (identity)
x1 – x2
Subtract x1 from x2
<MASK>
An arithmetic expression containing two or more operators is interpreted based on a precedence relation among the arithmetic operators. This precedence, from highest to lowest, is
<MASK>
The following is an example of an arithmetic expression:
<MASK>
The operators are executed in the following sequence:
<MASK>
3. The result of C**D is subtracted from the result of A/B to give the final result.
A unary operator (–) can follow another operator. Specifying the unary operator after the exponentiation operator produces a variation on the standard order of operations. The unary operator is evaluated first in that case, resulting in exponentiation taking a lower precedence in the expression.
For example, the following expression
<MASK>
is interpreted as
```A ** ( - B * C ) ```
### Arithmetic Operands
Arithmetic operands must specify values with integer, real, double-precision, complex, or double-complex data types. You can combine specific operands in an arithmetic expression. The arithmetic operands, in order of increasing complexity, are
<MASK>
• factor
<MASK>
• arithmetic expression
<MASK>
• an unsigned arithmetic constant
• a symbolic name of an arithmetic constant
• an arithmetic variable reference
<MASK>
• an arithmetic expression enclosed in parentheses
<MASK>
The term incorporates the multiplicative operators into arithmetic expressions. Its forms are
<MASK>
• term * factor
The above definition indicates that factors are combined from left to right in a term containing two or more multiplication or division operators.
<MASK>
• arithmetic expression + term
• arithmetic expression – term
An arithmetic expression consists of one or more terms separated by an addition operator or a subtraction operator. The terms are combined from left to right. For example, A+B-C has the same interpretation as the expression (A+B)-C. Expressions such as A*-B and A+-B are not allowed. The correct forms are A*(–B) and A+(-B).
An arithmetic expression can begin with a plus or minus sign.
### Arithmetic Constant Expressions
An arithmetic constant expression is an arithmetic expression containing no variables. Therefore, each primary in an arithmetic constant expression must be one of the following:
<MASK>
• arithmetic constant expression enclosed in parentheses
In an arithmetic constant expression, do not specify the exponentiation operator unless the exponent is of type integer. Variable, array element, and function references are not allowed. Examples of integer constant expressions are
``` 7 –7 –7+5 3**2 x+3 (where x is the symbolic name of a constant) ```
### Integer Constant Expressions
<MASK>
### Evaluating Arithmetic Expressions
<MASK>
#### Mixed-Mode Expressions
<MASK>
Table 3-3. Data Type Ranks
<MASK>
Rank
INTEGER*1
<MASK>
REAL*4
4
REAL*8 (double precision)
5
COMPLEX*8
<MASK>
COMPLEX*16
<MASK>
Operations that combine REAL*8 (DOUBLE PRECISION) and COMPLEX*8 (COMPLEX) are not allowed. The REAL*8 operand must be explicitly converted (for example, by using the SNGL intrinsic function).
<MASK>
Exponentiation is an exception to the above rules for mixed-mode expressions. When raising a value to an integer power, the integer is not converted. The result is assigned the type of the left operand.
<MASK>
```xy = EXP (y * LOG(x)) ```
### Integer Division
One operand of type integer can be divided by another operand of type integer. The result of an integer division operation is a value of type integer, referred to as an integer quotient. The integer quotient is obtained as follows:
<MASK>
A character expression yields a character string value on evaluation. The simplest form of a character expression can be one of these types of characters:
<MASK>
• function reference
<MASK>
### Concatenate Operator
The concatenate operator (//) is the only character operator defined in Fortran. A character expression formed from the concatenation of two character operands x1 and x2 is specified as
```x1 // x2 ```
The result of this operation is a character string with a value of x1 extended on the right with the value of x2. The length of the result is the sum of the lengths of the character operands. For example,
```'HEL' // 'LO2' ```
The result of the above expression is the string HELLO2 of length six.
<MASK>
• character constant
<MASK>
• character array element reference
<MASK>
• character function reference
<MASK>
A character expression consists of one or more character primaries separated by the concatenation operator. Its forms are
• character primary
<MASK>
In a character expression containing two or more concatenation operators, the primaries are combined from left to right. Thus, the character expression
<MASK>
is interpreted the same as
```('A' // 'BCD') // 'EF' ```
The value of the above character expression is ABCDEF.
Except in a character assignment statement, concatenation of an operand with an asterisk (*) as its length specification is not allowed unless the operand is the symbolic name of a constant.
### Character Constant Expressions
<MASK>
• symbolic name of a character constant
<MASK>
A relational expression yields a logical value of either .TRUE. or .FALSE. on evaluation and comparison of two arithmetic expressions or two character expressions. A relational expression can appear only within a logical expression. Refer to “Logical Expressions” for details about logical expressions.
### Relational Operators
<MASK>
Table 3-4. Fortran Relational Operators
<MASK>
Meaning
<MASK>
Equal to
.NE.
<MASK>
.GE.
Greater than or equal to
<MASK>
.LE.
Less than or equal to
<MASK>
### Relational Operands
The operands of a relational operator can be arithmetic or character expressions. The relational expression requires exactly two operands and is written in the following form:
e1 relop e2
<MASK>
e1 and e2 are arithmetic or character expressions. relop is the relational operator.
<MASK>
### Evaluating Relational Expressions
<MASK>
### Arithmetic Relational Expressions
<MASK>
You can use complex type operands only when specifying either the .EQ. or .NE. relational operator.
<MASK>
If the two arithmetic expressions e1 and e2 differ in type, the expression is evaluated as follows:
```((e1) - (e2)) relop 0 ```
<MASK>
### Character Relational Expressions
<MASK>
A character relational expression has the logical value .TRUE. only if the values of the operands satisfy the relation specified by the operator. Otherwise, the value is .FALSE.. The result of a character relational expression depends on the collating sequence as follows:
• If e1 and e2 are single characters, their relationship in the collating sequence determines the value of the operator. e1 is less than or greater than e2 if e1 is before or after e2, respectively, in the collating sequence.
• If either e1 or e2 are character strings with lengths greater than 1, corresponding individual characters are compared from left to right until a relationship other than .EQ. can be determined.
• If the operands are of unequal length, the shorter operand is extended on the right with blanks to the length of the longer operand for the comparison.
• If no other relationship can be determined after the strings are exhausted, the strings are equal.
<MASK>
• logical variable reference
• logical array element reference
• logical function reference
• relational expression
Construct complicated logical expressions from one or more logical operands together with logical operators and parentheses.
<MASK>
Table 3-5. Logical Operators
<MASK>
.NOT.
Logical negation
.AND.
Logical conjunt
.OR.
<MASK>
.EQV.
Logical equivalence
<MASK>
.XOR.
Same as .NEQV.
All logical operators require at least two operands, except the logical negation operator .NOT. , which requires only one.
A logical expression containing two or more logical operators is evaluated based on a precedence relation between the logical operators. This precedence, from highest to lowest, is
• .NOT.
<MASK>
• .OR.
<MASK>
• .XOR.
<MASK>
```W .NEQV. X .OR. Y .AND. Z ```
the operators are executed in the following sequence:
<MASK>
2. X .OR. A is evaluated second (B represents the result).
<MASK>
You can use parentheses to override the precedence of the operators.
### Logical Operands
Logical operands specify values with a logical data type. The forms of a logical operands are
<MASK>
• logical term
• logical disjunct
<MASK>
#### Logical Primary
The logical primary is the basic component of a logical expression. The forms of a logical primary are
• logical constant
<MASK>
• logical array element reference
<MASK>
• integer or logical expression in parentheses
When an integer appears as an operand to a logical operator, the other operand is promoted to type integer if necessary and the operation is performed on a bit-by-bit basis producing an integer result. Whenever an arithmetic datum appears in a logical expression, the result of that expression will be of type integer because of type promotion rules. If necessary, the result can be converted back to LOGICAL.
Do not specify two logical operators consecutively and do not use implied logical operators.
#### Logical Factor
The logical factor uses the logical negation operator .NOT. to reverse the logical value to which it is applied. For example, applying .NOT. to a false relational expression makes the expression true. Therefore, if UP is true, .NOT. UP is false. The logical factor has the following forms:
• logical primary
• .NOT. logical primary
<MASK>
• Logical factor
• Logical term .AND. logical factor
In evaluating a logical term with two or more .AND. operators, the logical factors are combined from left to right. For example, X .AND. Y .AND. Z has the same interpretation as (X .AND. Y) .AND. Z.
#### Logical Disjunct
<MASK>
• Logical term
<MASK>
• logical disjunct
<MASK>
• logical expression .NEQV. logical disjunct
<MASK>
A logical constant expression is a logical expression in which each primary is a logical constant, the symbolic name of a logical constant, a relational expression in which each primary is a constant, or a logical constant expression enclosed in parentheses. A logical constant expression can contain arithmetic and character constant expressions but not variables, array elements, or function references.
### Interpretation of Logical Expressions
<MASK>
IFA=
<MASK>
THEN
.NOT.B
<MASK>
A.OR.B
A.EQV.B
<MASK>
F
F
T
<MASK>
T
<MASK>
F
<MASK>
F
<MASK>
T
<MASK>
F
F
T
F
<MASK>
T
T
T
T
T
<MASK>
Several rules are applied to the general evaluation of Fortran expressions. This section covers the priority of the different Fortran operators, the use of parentheses in specifying the order of evaluation, and the rules for combining operators with operands.
<MASK>
Certain Fortran operators have precedence over others when combined in an expression. The previous sections have listed the precedence among the arithmetic, logical, and expression operators. No precedence exists between the relational operators and the single character operator (//). On the highest level, the precedence among the types of expression operators, from highest to lowest, is
<MASK>
• character
<MASK>
Use parentheses to specify the order in which operators are evaluated within an expression. Expressions within parentheses are treated as an entity.
In an expression containing more than one operation, the processor first evaluates any expressions within parentheses. Subexpressions within parentheses are evaluated beginning with the innermost subexpression and proceeding sequentially to the outermost. The processor then scans the expression from left to right and performs the operations according to the operator precedence described previously.
<UNMASK>
## Chapter 3. Expressions
This chapter contains the following subsections:
<MASK>
• arithmetic
• character
<MASK>
• logical
<MASK>
## Arithmetic Expressions
<MASK>
• an unsigned arithmetic constant
<MASK>
• an arithmetic array element reference
• an arithmetic function reference
You can form more complicated arithmetic expressions from one or more operands together with arithmetic operators and parentheses.
An arithmetic element can include logical entities because logical data is treated as integer data when used in an arithmetic context. When both arithmetic and logical operands exist for a given operator, the logical operand is promoted to type INTEGER of the same byte length as the original logical length. For example, a LOGICAL*2 will be promoted to INTEGER*2 and a LOGICAL*4 will be promoted to INTEGER*4.
### Arithmetic Operators
Table 3-1 shows the arithmetic operators.
<MASK>
Operator
Function
**
Exponentiation
*
<MASK>
/
<MASK>
+
Subtraction or negation
<MASK>
### Interpretation of Arithmetic Expressions
Table 3-2 interprets sample arithmetic expressions.
<MASK>
Operator
Use
<MASK>
x1 ** x2
<MASK>
x1 * x2
<MASK>
/
x1 / x2
Divide x1 by x2
+
x1 + x2
<MASK>
x (identity)
x1 – x2
Subtract x1 from x2
<MASK>
An arithmetic expression containing two or more operators is interpreted based on a precedence relation among the arithmetic operators. This precedence, from highest to lowest, is
<MASK>
The following is an example of an arithmetic expression:
```A/B-C**D ```
The operators are executed in the following sequence:
<MASK>
3. The result of C**D is subtracted from the result of A/B to give the final result.
A unary operator (–) can follow another operator. Specifying the unary operator after the exponentiation operator produces a variation on the standard order of operations. The unary operator is evaluated first in that case, resulting in exponentiation taking a lower precedence in the expression.
For example, the following expression
<MASK>
is interpreted as
```A ** ( - B * C ) ```
### Arithmetic Operands
Arithmetic operands must specify values with integer, real, double-precision, complex, or double-complex data types. You can combine specific operands in an arithmetic expression. The arithmetic operands, in order of increasing complexity, are
<MASK>
• factor
<MASK>
• arithmetic expression
<MASK>
• an unsigned arithmetic constant
• a symbolic name of an arithmetic constant
• an arithmetic variable reference
<MASK>
• an arithmetic function reference
• an arithmetic expression enclosed in parentheses
<MASK>
The term incorporates the multiplicative operators into arithmetic expressions. Its forms are
<MASK>
• term * factor
The above definition indicates that factors are combined from left to right in a term containing two or more multiplication or division operators.
<MASK>
• arithmetic expression + term
• arithmetic expression – term
An arithmetic expression consists of one or more terms separated by an addition operator or a subtraction operator. The terms are combined from left to right. For example, A+B-C has the same interpretation as the expression (A+B)-C. Expressions such as A*-B and A+-B are not allowed. The correct forms are A*(–B) and A+(-B).
An arithmetic expression can begin with a plus or minus sign.
### Arithmetic Constant Expressions
An arithmetic constant expression is an arithmetic expression containing no variables. Therefore, each primary in an arithmetic constant expression must be one of the following:
<MASK>
• arithmetic constant expression enclosed in parentheses
In an arithmetic constant expression, do not specify the exponentiation operator unless the exponent is of type integer. Variable, array element, and function references are not allowed. Examples of integer constant expressions are
``` 7 –7 –7+5 3**2 x+3 (where x is the symbolic name of a constant) ```
### Integer Constant Expressions
<MASK>
### Evaluating Arithmetic Expressions
<MASK>
#### Mixed-Mode Expressions
<MASK>
Table 3-3. Data Type Ranks
<MASK>
Rank
INTEGER*1
<MASK>
REAL*4
4
REAL*8 (double precision)
5
COMPLEX*8
<MASK>
COMPLEX*16
<MASK>
Operations that combine REAL*8 (DOUBLE PRECISION) and COMPLEX*8 (COMPLEX) are not allowed. The REAL*8 operand must be explicitly converted (for example, by using the SNGL intrinsic function).
<MASK>
Exponentiation is an exception to the above rules for mixed-mode expressions. When raising a value to an integer power, the integer is not converted. The result is assigned the type of the left operand.
<MASK>
```xy = EXP (y * LOG(x)) ```
### Integer Division
One operand of type integer can be divided by another operand of type integer. The result of an integer division operation is a value of type integer, referred to as an integer quotient. The integer quotient is obtained as follows:
<MASK>
A character expression yields a character string value on evaluation. The simplest form of a character expression can be one of these types of characters:
<MASK>
• function reference
<MASK>
### Concatenate Operator
The concatenate operator (//) is the only character operator defined in Fortran. A character expression formed from the concatenation of two character operands x1 and x2 is specified as
```x1 // x2 ```
The result of this operation is a character string with a value of x1 extended on the right with the value of x2. The length of the result is the sum of the lengths of the character operands. For example,
```'HEL' // 'LO2' ```
The result of the above expression is the string HELLO2 of length six.
<MASK>
• character constant
<MASK>
• character array element reference
<MASK>
• character function reference
<MASK>
A character expression consists of one or more character primaries separated by the concatenation operator. Its forms are
• character primary
<MASK>
In a character expression containing two or more concatenation operators, the primaries are combined from left to right. Thus, the character expression
<MASK>
is interpreted the same as
```('A' // 'BCD') // 'EF' ```
The value of the above character expression is ABCDEF.
Except in a character assignment statement, concatenation of an operand with an asterisk (*) as its length specification is not allowed unless the operand is the symbolic name of a constant.
### Character Constant Expressions
<MASK>
• symbolic name of a character constant
<MASK>
A relational expression yields a logical value of either .TRUE. or .FALSE. on evaluation and comparison of two arithmetic expressions or two character expressions. A relational expression can appear only within a logical expression. Refer to “Logical Expressions” for details about logical expressions.
### Relational Operators
<MASK>
Table 3-4. Fortran Relational Operators
<MASK>
Meaning
<MASK>
Equal to
.NE.
<MASK>
.GE.
Greater than or equal to
<MASK>
.LE.
Less than or equal to
<MASK>
### Relational Operands
The operands of a relational operator can be arithmetic or character expressions. The relational expression requires exactly two operands and is written in the following form:
e1 relop e2
<MASK>
e1 and e2 are arithmetic or character expressions. relop is the relational operator.
<MASK>
### Evaluating Relational Expressions
<MASK>
### Arithmetic Relational Expressions
<MASK>
You can use complex type operands only when specifying either the .EQ. or .NE. relational operator.
<MASK>
If the two arithmetic expressions e1 and e2 differ in type, the expression is evaluated as follows:
```((e1) - (e2)) relop 0 ```
<MASK>
### Character Relational Expressions
In a character relational expression, e1 and e2 are character expressions and relop is a relational operator.
<MASK>
A character relational expression has the logical value .TRUE. only if the values of the operands satisfy the relation specified by the operator. Otherwise, the value is .FALSE.. The result of a character relational expression depends on the collating sequence as follows:
• If e1 and e2 are single characters, their relationship in the collating sequence determines the value of the operator. e1 is less than or greater than e2 if e1 is before or after e2, respectively, in the collating sequence.
• If either e1 or e2 are character strings with lengths greater than 1, corresponding individual characters are compared from left to right until a relationship other than .EQ. can be determined.
• If the operands are of unequal length, the shorter operand is extended on the right with blanks to the length of the longer operand for the comparison.
• If no other relationship can be determined after the strings are exhausted, the strings are equal.
<MASK>
• logical variable reference
• logical array element reference
• logical function reference
• relational expression
Construct complicated logical expressions from one or more logical operands together with logical operators and parentheses.
<MASK>
Table 3-5. Logical Operators
<MASK>
.NOT.
Logical negation
.AND.
Logical conjunt
.OR.
<MASK>
.EQV.
Logical equivalence
<MASK>
.XOR.
Same as .NEQV.
All logical operators require at least two operands, except the logical negation operator .NOT. , which requires only one.
A logical expression containing two or more logical operators is evaluated based on a precedence relation between the logical operators. This precedence, from highest to lowest, is
• .NOT.
<MASK>
• .OR.
• .EQV. and .NEQV.
• .XOR.
For example, in the following expression
```W .NEQV. X .OR. Y .AND. Z ```
the operators are executed in the following sequence:
<MASK>
2. X .OR. A is evaluated second (B represents the result).
<MASK>
You can use parentheses to override the precedence of the operators.
### Logical Operands
Logical operands specify values with a logical data type. The forms of a logical operands are
<MASK>
• logical term
• logical disjunct
<MASK>
#### Logical Primary
The logical primary is the basic component of a logical expression. The forms of a logical primary are
• logical constant
<MASK>
• logical array element reference
<MASK>
• integer or logical expression in parentheses
When an integer appears as an operand to a logical operator, the other operand is promoted to type integer if necessary and the operation is performed on a bit-by-bit basis producing an integer result. Whenever an arithmetic datum appears in a logical expression, the result of that expression will be of type integer because of type promotion rules. If necessary, the result can be converted back to LOGICAL.
Do not specify two logical operators consecutively and do not use implied logical operators.
#### Logical Factor
The logical factor uses the logical negation operator .NOT. to reverse the logical value to which it is applied. For example, applying .NOT. to a false relational expression makes the expression true. Therefore, if UP is true, .NOT. UP is false. The logical factor has the following forms:
• logical primary
• .NOT. logical primary
<MASK>
• Logical factor
• Logical term .AND. logical factor
In evaluating a logical term with two or more .AND. operators, the logical factors are combined from left to right. For example, X .AND. Y .AND. Z has the same interpretation as (X .AND. Y) .AND. Z.
#### Logical Disjunct
<MASK>
• Logical term
<MASK>
At the highest level of complexity is the logical expression. A logical expression is a sequence of logical disjuncts separated by the .EQV., .NEQV., or .XOR. operators. Its forms are
• logical disjunct
<MASK>
• logical expression .NEQV. logical disjunct
• logical expression .XOR. logical disjunct
<MASK>
A logical constant expression is a logical expression in which each primary is a logical constant, the symbolic name of a logical constant, a relational expression in which each primary is a constant, or a logical constant expression enclosed in parentheses. A logical constant expression can contain arithmetic and character constant expressions but not variables, array elements, or function references.
### Interpretation of Logical Expressions
<MASK>
IFA=
<MASK>
THEN
.NOT.B
<MASK>
A.OR.B
A.EQV.B
<MASK>
F
F
T
<MASK>
T
<MASK>
F
<MASK>
F
<MASK>
T
<MASK>
F
F
T
F
<MASK>
T
T
T
T
T
<MASK>
Several rules are applied to the general evaluation of Fortran expressions. This section covers the priority of the different Fortran operators, the use of parentheses in specifying the order of evaluation, and the rules for combining operators with operands.
<MASK>
Certain Fortran operators have precedence over others when combined in an expression. The previous sections have listed the precedence among the arithmetic, logical, and expression operators. No precedence exists between the relational operators and the single character operator (//). On the highest level, the precedence among the types of expression operators, from highest to lowest, is
<MASK>
• character
• relational
<MASK>
Use parentheses to specify the order in which operators are evaluated within an expression. Expressions within parentheses are treated as an entity.
In an expression containing more than one operation, the processor first evaluates any expressions within parentheses. Subexpressions within parentheses are evaluated beginning with the innermost subexpression and proceeding sequentially to the outermost. The processor then scans the expression from left to right and performs the operations according to the operator precedence described previously.
|
## Chapter 3. Expressions
This chapter contains the following subsections:
<MASK>
• arithmetic
• character
<MASK>
• logical
<MASK>
## Arithmetic Expressions
<MASK>
• an unsigned arithmetic constant
<MASK>
• an arithmetic array element reference
• an arithmetic function reference
You can form more complicated arithmetic expressions from one or more operands together with arithmetic operators and parentheses.
An arithmetic element can include logical entities because logical data is treated as integer data when used in an arithmetic context. When both arithmetic and logical operands exist for a given operator, the logical operand is promoted to type INTEGER of the same byte length as the original logical length. For example, a LOGICAL*2 will be promoted to INTEGER*2 and a LOGICAL*4 will be promoted to INTEGER*4.
### Arithmetic Operators
Table 3-1 shows the arithmetic operators.
<MASK>
Operator
Function
**
Exponentiation
*
<MASK>
/
<MASK>
+
Subtraction or negation
<MASK>
### Interpretation of Arithmetic Expressions
Table 3-2 interprets sample arithmetic expressions.
<MASK>
Operator
Use
<MASK>
x1 ** x2
<MASK>
x1 * x2
<MASK>
/
x1 / x2
Divide x1 by x2
+
x1 + x2
<MASK>
x (identity)
x1 – x2
Subtract x1 from x2
<MASK>
An arithmetic expression containing two or more operators is interpreted based on a precedence relation among the arithmetic operators. This precedence, from highest to lowest, is
<MASK>
The following is an example of an arithmetic expression:
```A/B-C**D ```
The operators are executed in the following sequence:
<MASK>
3. The result of C**D is subtracted from the result of A/B to give the final result.
A unary operator (–) can follow another operator. Specifying the unary operator after the exponentiation operator produces a variation on the standard order of operations. The unary operator is evaluated first in that case, resulting in exponentiation taking a lower precedence in the expression.
For example, the following expression
<MASK>
is interpreted as
```A ** ( - B * C ) ```
### Arithmetic Operands
Arithmetic operands must specify values with integer, real, double-precision, complex, or double-complex data types. You can combine specific operands in an arithmetic expression. The arithmetic operands, in order of increasing complexity, are
<MASK>
• factor
<MASK>
• arithmetic expression
<MASK>
• an unsigned arithmetic constant
• a symbolic name of an arithmetic constant
• an arithmetic variable reference
<MASK>
• an arithmetic function reference
• an arithmetic expression enclosed in parentheses
<MASK>
The term incorporates the multiplicative operators into arithmetic expressions. Its forms are
<MASK>
• term * factor
The above definition indicates that factors are combined from left to right in a term containing two or more multiplication or division operators.
<MASK>
• arithmetic expression + term
• arithmetic expression – term
An arithmetic expression consists of one or more terms separated by an addition operator or a subtraction operator. The terms are combined from left to right. For example, A+B-C has the same interpretation as the expression (A+B)-C. Expressions such as A*-B and A+-B are not allowed. The correct forms are A*(–B) and A+(-B).
An arithmetic expression can begin with a plus or minus sign.
### Arithmetic Constant Expressions
An arithmetic constant expression is an arithmetic expression containing no variables. Therefore, each primary in an arithmetic constant expression must be one of the following:
<MASK>
• arithmetic constant expression enclosed in parentheses
In an arithmetic constant expression, do not specify the exponentiation operator unless the exponent is of type integer. Variable, array element, and function references are not allowed. Examples of integer constant expressions are
``` 7 –7 –7+5 3**2 x+3 (where x is the symbolic name of a constant) ```
### Integer Constant Expressions
<MASK>
### Evaluating Arithmetic Expressions
<MASK>
#### Mixed-Mode Expressions
<MASK>
Table 3-3. Data Type Ranks
<MASK>
Rank
INTEGER*1
<MASK>
REAL*4
4
REAL*8 (double precision)
5
COMPLEX*8
<MASK>
COMPLEX*16
<MASK>
Operations that combine REAL*8 (DOUBLE PRECISION) and COMPLEX*8 (COMPLEX) are not allowed. The REAL*8 operand must be explicitly converted (for example, by using the SNGL intrinsic function).
<MASK>
Exponentiation is an exception to the above rules for mixed-mode expressions. When raising a value to an integer power, the integer is not converted. The result is assigned the type of the left operand.
<MASK>
```xy = EXP (y * LOG(x)) ```
### Integer Division
One operand of type integer can be divided by another operand of type integer. The result of an integer division operation is a value of type integer, referred to as an integer quotient. The integer quotient is obtained as follows:
<MASK>
A character expression yields a character string value on evaluation. The simplest form of a character expression can be one of these types of characters:
<MASK>
• function reference
<MASK>
### Concatenate Operator
The concatenate operator (//) is the only character operator defined in Fortran. A character expression formed from the concatenation of two character operands x1 and x2 is specified as
```x1 // x2 ```
The result of this operation is a character string with a value of x1 extended on the right with the value of x2. The length of the result is the sum of the lengths of the character operands. For example,
```'HEL' // 'LO2' ```
The result of the above expression is the string HELLO2 of length six.
<MASK>
• character constant
<MASK>
• character array element reference
<MASK>
• character function reference
<MASK>
A character expression consists of one or more character primaries separated by the concatenation operator. Its forms are
• character primary
<MASK>
In a character expression containing two or more concatenation operators, the primaries are combined from left to right. Thus, the character expression
<MASK>
is interpreted the same as
```('A' // 'BCD') // 'EF' ```
The value of the above character expression is ABCDEF.
Except in a character assignment statement, concatenation of an operand with an asterisk (*) as its length specification is not allowed unless the operand is the symbolic name of a constant.
### Character Constant Expressions
<MASK>
• symbolic name of a character constant
<MASK>
A relational expression yields a logical value of either .TRUE. or .FALSE. on evaluation and comparison of two arithmetic expressions or two character expressions. A relational expression can appear only within a logical expression. Refer to “Logical Expressions” for details about logical expressions.
### Relational Operators
<MASK>
Table 3-4. Fortran Relational Operators
<MASK>
Meaning
<MASK>
Equal to
.NE.
<MASK>
.GE.
Greater than or equal to
<MASK>
.LE.
Less than or equal to
<MASK>
### Relational Operands
The operands of a relational operator can be arithmetic or character expressions. The relational expression requires exactly two operands and is written in the following form:
e1 relop e2
<MASK>
e1 and e2 are arithmetic or character expressions. relop is the relational operator.
<MASK>
### Evaluating Relational Expressions
<MASK>
### Arithmetic Relational Expressions
<MASK>
You can use complex type operands only when specifying either the .EQ. or .NE. relational operator.
<MASK>
If the two arithmetic expressions e1 and e2 differ in type, the expression is evaluated as follows:
```((e1) - (e2)) relop 0 ```
<MASK>
### Character Relational Expressions
In a character relational expression, e1 and e2 are character expressions and relop is a relational operator.
<MASK>
A character relational expression has the logical value .TRUE. only if the values of the operands satisfy the relation specified by the operator. Otherwise, the value is .FALSE.. The result of a character relational expression depends on the collating sequence as follows:
• If e1 and e2 are single characters, their relationship in the collating sequence determines the value of the operator. e1 is less than or greater than e2 if e1 is before or after e2, respectively, in the collating sequence.
• If either e1 or e2 are character strings with lengths greater than 1, corresponding individual characters are compared from left to right until a relationship other than .EQ. can be determined.
• If the operands are of unequal length, the shorter operand is extended on the right with blanks to the length of the longer operand for the comparison.
• If no other relationship can be determined after the strings are exhausted, the strings are equal.
<MASK>
• logical variable reference
• logical array element reference
• logical function reference
• relational expression
Construct complicated logical expressions from one or more logical operands together with logical operators and parentheses.
<MASK>
Table 3-5. Logical Operators
<MASK>
.NOT.
Logical negation
.AND.
Logical conjunt
.OR.
<MASK>
.EQV.
Logical equivalence
<MASK>
.XOR.
Same as .NEQV.
All logical operators require at least two operands, except the logical negation operator .NOT. , which requires only one.
A logical expression containing two or more logical operators is evaluated based on a precedence relation between the logical operators. This precedence, from highest to lowest, is
• .NOT.
<MASK>
• .OR.
• .EQV. and .NEQV.
• .XOR.
For example, in the following expression
```W .NEQV. X .OR. Y .AND. Z ```
the operators are executed in the following sequence:
<MASK>
2. X .OR. A is evaluated second (B represents the result).
<MASK>
You can use parentheses to override the precedence of the operators.
### Logical Operands
Logical operands specify values with a logical data type. The forms of a logical operands are
<MASK>
• logical term
• logical disjunct
<MASK>
#### Logical Primary
The logical primary is the basic component of a logical expression. The forms of a logical primary are
• logical constant
<MASK>
• logical array element reference
<MASK>
• integer or logical expression in parentheses
When an integer appears as an operand to a logical operator, the other operand is promoted to type integer if necessary and the operation is performed on a bit-by-bit basis producing an integer result. Whenever an arithmetic datum appears in a logical expression, the result of that expression will be of type integer because of type promotion rules. If necessary, the result can be converted back to LOGICAL.
Do not specify two logical operators consecutively and do not use implied logical operators.
#### Logical Factor
The logical factor uses the logical negation operator .NOT. to reverse the logical value to which it is applied. For example, applying .NOT. to a false relational expression makes the expression true. Therefore, if UP is true, .NOT. UP is false. The logical factor has the following forms:
• logical primary
• .NOT. logical primary
<MASK>
• Logical factor
• Logical term .AND. logical factor
In evaluating a logical term with two or more .AND. operators, the logical factors are combined from left to right. For example, X .AND. Y .AND. Z has the same interpretation as (X .AND. Y) .AND. Z.
#### Logical Disjunct
<MASK>
• Logical term
<MASK>
At the highest level of complexity is the logical expression. A logical expression is a sequence of logical disjuncts separated by the .EQV., .NEQV., or .XOR. operators. Its forms are
• logical disjunct
<MASK>
• logical expression .NEQV. logical disjunct
• logical expression .XOR. logical disjunct
<MASK>
A logical constant expression is a logical expression in which each primary is a logical constant, the symbolic name of a logical constant, a relational expression in which each primary is a constant, or a logical constant expression enclosed in parentheses. A logical constant expression can contain arithmetic and character constant expressions but not variables, array elements, or function references.
### Interpretation of Logical Expressions
<MASK>
IFA=
<MASK>
THEN
.NOT.B
<MASK>
A.OR.B
A.EQV.B
<MASK>
F
F
T
<MASK>
T
<MASK>
F
<MASK>
F
<MASK>
T
<MASK>
F
F
T
F
<MASK>
T
T
T
T
T
<MASK>
Several rules are applied to the general evaluation of Fortran expressions. This section covers the priority of the different Fortran operators, the use of parentheses in specifying the order of evaluation, and the rules for combining operators with operands.
<MASK>
Certain Fortran operators have precedence over others when combined in an expression. The previous sections have listed the precedence among the arithmetic, logical, and expression operators. No precedence exists between the relational operators and the single character operator (//). On the highest level, the precedence among the types of expression operators, from highest to lowest, is
<MASK>
• character
• relational
<MASK>
Use parentheses to specify the order in which operators are evaluated within an expression. Expressions within parentheses are treated as an entity.
In an expression containing more than one operation, the processor first evaluates any expressions within parentheses. Subexpressions within parentheses are evaluated beginning with the innermost subexpression and proceeding sequentially to the outermost. The processor then scans the expression from left to right and performs the operations according to the operator precedence described previously.
<UNMASK>
## Chapter 3. Expressions
This chapter contains the following subsections:
An expression performs a specified type of computation. It is composed of a sequence of operands, operators, and parentheses. The types of Fortran expressions are
• arithmetic
• character
<MASK>
• logical
<MASK>
## Arithmetic Expressions
<MASK>
• an unsigned arithmetic constant
<MASK>
• an arithmetic array element reference
• an arithmetic function reference
You can form more complicated arithmetic expressions from one or more operands together with arithmetic operators and parentheses.
An arithmetic element can include logical entities because logical data is treated as integer data when used in an arithmetic context. When both arithmetic and logical operands exist for a given operator, the logical operand is promoted to type INTEGER of the same byte length as the original logical length. For example, a LOGICAL*2 will be promoted to INTEGER*2 and a LOGICAL*4 will be promoted to INTEGER*4.
### Arithmetic Operators
Table 3-1 shows the arithmetic operators.
<MASK>
Operator
Function
**
Exponentiation
*
<MASK>
/
<MASK>
+
Subtraction or negation
Use the exponentiation, division, and multiplication operators between exactly two operands. You can use the addition and subtraction operators with one or two operands; in the latter case, specify the operator before the operand; for example, –TOTAL.
<MASK>
### Interpretation of Arithmetic Expressions
Table 3-2 interprets sample arithmetic expressions.
<MASK>
Operator
Use
<MASK>
x1 ** x2
<MASK>
*
x1 * x2
<MASK>
/
x1 / x2
Divide x1 by x2
+
x1 + x2
<MASK>
x (identity)
x1 – x2
Subtract x1 from x2
<MASK>
An arithmetic expression containing two or more operators is interpreted based on a precedence relation among the arithmetic operators. This precedence, from highest to lowest, is
<MASK>
The following is an example of an arithmetic expression:
```A/B-C**D ```
The operators are executed in the following sequence:
<MASK>
3. The result of C**D is subtracted from the result of A/B to give the final result.
A unary operator (–) can follow another operator. Specifying the unary operator after the exponentiation operator produces a variation on the standard order of operations. The unary operator is evaluated first in that case, resulting in exponentiation taking a lower precedence in the expression.
For example, the following expression
<MASK>
is interpreted as
```A ** ( - B * C ) ```
### Arithmetic Operands
Arithmetic operands must specify values with integer, real, double-precision, complex, or double-complex data types. You can combine specific operands in an arithmetic expression. The arithmetic operands, in order of increasing complexity, are
<MASK>
• factor
<MASK>
• arithmetic expression
<MASK>
• an unsigned arithmetic constant
• a symbolic name of an arithmetic constant
• an arithmetic variable reference
<MASK>
• an arithmetic function reference
• an arithmetic expression enclosed in parentheses
<MASK>
Factors with more than one exponentiation operator are interpreted from right to left. For example, I**J**K is interpreted as I**(J**K), and I**J**K**L is interpreted as I**(J**(K**L)).
The term incorporates the multiplicative operators into arithmetic expressions. Its forms are
<MASK>
• term * factor
The above definition indicates that factors are combined from left to right in a term containing two or more multiplication or division operators.
<MASK>
• term
<MASK>
• arithmetic expression + term
• arithmetic expression – term
An arithmetic expression consists of one or more terms separated by an addition operator or a subtraction operator. The terms are combined from left to right. For example, A+B-C has the same interpretation as the expression (A+B)-C. Expressions such as A*-B and A+-B are not allowed. The correct forms are A*(–B) and A+(-B).
An arithmetic expression can begin with a plus or minus sign.
### Arithmetic Constant Expressions
An arithmetic constant expression is an arithmetic expression containing no variables. Therefore, each primary in an arithmetic constant expression must be one of the following:
<MASK>
• arithmetic constant expression enclosed in parentheses
In an arithmetic constant expression, do not specify the exponentiation operator unless the exponent is of type integer. Variable, array element, and function references are not allowed. Examples of integer constant expressions are
``` 7 –7 –7+5 3**2 x+3 (where x is the symbolic name of a constant) ```
### Integer Constant Expressions
<MASK>
### Evaluating Arithmetic Expressions
<MASK>
#### Mixed-Mode Expressions
Mixed-mode expressions contain operands with two or more data types. The data type of the result of a mixed-mode expression depends on the rank associated with each data type, as shown in Table 3-3.
Table 3-3. Data Type Ranks
<MASK>
Rank
INTEGER*1
<MASK>
REAL*4
4
REAL*8 (double precision)
5
COMPLEX*8
<MASK>
COMPLEX*16
7 (highest)
<MASK>
Operations that combine REAL*8 (DOUBLE PRECISION) and COMPLEX*8 (COMPLEX) are not allowed. The REAL*8 operand must be explicitly converted (for example, by using the SNGL intrinsic function).
<MASK>
Exponentiation is an exception to the above rules for mixed-mode expressions. When raising a value to an integer power, the integer is not converted. The result is assigned the type of the left operand.
<MASK>
```xy = EXP (y * LOG(x)) ```
### Integer Division
One operand of type integer can be divided by another operand of type integer. The result of an integer division operation is a value of type integer, referred to as an integer quotient. The integer quotient is obtained as follows:
<MASK>
A character expression yields a character string value on evaluation. The simplest form of a character expression can be one of these types of characters:
<MASK>
• function reference
<MASK>
### Concatenate Operator
The concatenate operator (//) is the only character operator defined in Fortran. A character expression formed from the concatenation of two character operands x1 and x2 is specified as
```x1 // x2 ```
The result of this operation is a character string with a value of x1 extended on the right with the value of x2. The length of the result is the sum of the lengths of the character operands. For example,
```'HEL' // 'LO2' ```
The result of the above expression is the string HELLO2 of length six.
<MASK>
• character constant
<MASK>
• character array element reference
<MASK>
• character function reference
<MASK>
A character expression consists of one or more character primaries separated by the concatenation operator. Its forms are
• character primary
<MASK>
In a character expression containing two or more concatenation operators, the primaries are combined from left to right. Thus, the character expression
```'A' // 'BCD' // 'EF' ```
is interpreted the same as
```('A' // 'BCD') // 'EF' ```
The value of the above character expression is ABCDEF.
Except in a character assignment statement, concatenation of an operand with an asterisk (*) as its length specification is not allowed unless the operand is the symbolic name of a constant.
### Character Constant Expressions
<MASK>
• symbolic name of a character constant
<MASK>
A relational expression yields a logical value of either .TRUE. or .FALSE. on evaluation and comparison of two arithmetic expressions or two character expressions. A relational expression can appear only within a logical expression. Refer to “Logical Expressions” for details about logical expressions.
### Relational Operators
<MASK>
Table 3-4. Fortran Relational Operators
<MASK>
Meaning
<MASK>
Equal to
.NE.
<MASK>
Greater than
.GE.
Greater than or equal to
<MASK>
.LE.
Less than or equal to
<MASK>
### Relational Operands
The operands of a relational operator can be arithmetic or character expressions. The relational expression requires exactly two operands and is written in the following form:
e1 relop e2
<MASK>
e1 and e2 are arithmetic or character expressions. relop is the relational operator.
<MASK>
### Evaluating Relational Expressions
The result of a relational expression is of type logical, with a value of .TRUE. or .FALSE.. The manner in which the expression is evaluated depends on the data type of the operands.
### Arithmetic Relational Expressions
<MASK>
You can use complex type operands only when specifying either the .EQ. or .NE. relational operator.
<MASK>
If the two arithmetic expressions e1 and e2 differ in type, the expression is evaluated as follows:
```((e1) - (e2)) relop 0 ```
<MASK>
### Character Relational Expressions
In a character relational expression, e1 and e2 are character expressions and relop is a relational operator.
<MASK>
A character relational expression has the logical value .TRUE. only if the values of the operands satisfy the relation specified by the operator. Otherwise, the value is .FALSE.. The result of a character relational expression depends on the collating sequence as follows:
• If e1 and e2 are single characters, their relationship in the collating sequence determines the value of the operator. e1 is less than or greater than e2 if e1 is before or after e2, respectively, in the collating sequence.
• If either e1 or e2 are character strings with lengths greater than 1, corresponding individual characters are compared from left to right until a relationship other than .EQ. can be determined.
• If the operands are of unequal length, the shorter operand is extended on the right with blanks to the length of the longer operand for the comparison.
• If no other relationship can be determined after the strings are exhausted, the strings are equal.
<MASK>
• logical variable reference
• logical array element reference
• logical function reference
• relational expression
Construct complicated logical expressions from one or more logical operands together with logical operators and parentheses.
<MASK>
Table 3-5. Logical Operators
<MASK>
.NOT.
Logical negation
.AND.
Logical conjunt
.OR.
<MASK>
.EQV.
Logical equivalence
.NEQV.
<MASK>
.XOR.
Same as .NEQV.
All logical operators require at least two operands, except the logical negation operator .NOT. , which requires only one.
A logical expression containing two or more logical operators is evaluated based on a precedence relation between the logical operators. This precedence, from highest to lowest, is
• .NOT.
<MASK>
• .OR.
• .EQV. and .NEQV.
• .XOR.
For example, in the following expression
```W .NEQV. X .OR. Y .AND. Z ```
the operators are executed in the following sequence:
<MASK>
2. X .OR. A is evaluated second (B represents the result).
<MASK>
You can use parentheses to override the precedence of the operators.
### Logical Operands
Logical operands specify values with a logical data type. The forms of a logical operands are
<MASK>
• logical term
• logical disjunct
• logical expression
#### Logical Primary
The logical primary is the basic component of a logical expression. The forms of a logical primary are
• logical constant
<MASK>
• logical array element reference
<MASK>
• integer or logical expression in parentheses
When an integer appears as an operand to a logical operator, the other operand is promoted to type integer if necessary and the operation is performed on a bit-by-bit basis producing an integer result. Whenever an arithmetic datum appears in a logical expression, the result of that expression will be of type integer because of type promotion rules. If necessary, the result can be converted back to LOGICAL.
Do not specify two logical operators consecutively and do not use implied logical operators.
#### Logical Factor
The logical factor uses the logical negation operator .NOT. to reverse the logical value to which it is applied. For example, applying .NOT. to a false relational expression makes the expression true. Therefore, if UP is true, .NOT. UP is false. The logical factor has the following forms:
• logical primary
• .NOT. logical primary
#### Logical Term
<MASK>
• Logical factor
• Logical term .AND. logical factor
In evaluating a logical term with two or more .AND. operators, the logical factors are combined from left to right. For example, X .AND. Y .AND. Z has the same interpretation as (X .AND. Y) .AND. Z.
#### Logical Disjunct
<MASK>
• Logical term
<MASK>
At the highest level of complexity is the logical expression. A logical expression is a sequence of logical disjuncts separated by the .EQV., .NEQV., or .XOR. operators. Its forms are
• logical disjunct
<MASK>
• logical expression .NEQV. logical disjunct
• logical expression .XOR. logical disjunct
The logical disjuncts are combined from left to right when a logical expression contains two or more .EQV., .NEVQ., or .XOR. operators.
A logical constant expression is a logical expression in which each primary is a logical constant, the symbolic name of a logical constant, a relational expression in which each primary is a constant, or a logical constant expression enclosed in parentheses. A logical constant expression can contain arithmetic and character constant expressions but not variables, array elements, or function references.
### Interpretation of Logical Expressions
<MASK>
IFA=
B=
THEN
.NOT.B
<MASK>
A.OR.B
A.EQV.B
<MASK>
F
F
T
<MASK>
T
<MASK>
F
<MASK>
F
<MASK>
F
T
<MASK>
F
F
T
F
<MASK>
T
T
T
T
T
<MASK>
Several rules are applied to the general evaluation of Fortran expressions. This section covers the priority of the different Fortran operators, the use of parentheses in specifying the order of evaluation, and the rules for combining operators with operands.
<MASK>
Certain Fortran operators have precedence over others when combined in an expression. The previous sections have listed the precedence among the arithmetic, logical, and expression operators. No precedence exists between the relational operators and the single character operator (//). On the highest level, the precedence among the types of expression operators, from highest to lowest, is
<MASK>
• character
• relational
<MASK>
Use parentheses to specify the order in which operators are evaluated within an expression. Expressions within parentheses are treated as an entity.
In an expression containing more than one operation, the processor first evaluates any expressions within parentheses. Subexpressions within parentheses are evaluated beginning with the innermost subexpression and proceeding sequentially to the outermost. The processor then scans the expression from left to right and performs the operations according to the operator precedence described previously.
|
## Chapter 3. Expressions
This chapter contains the following subsections:
An expression performs a specified type of computation. It is composed of a sequence of operands, operators, and parentheses. The types of Fortran expressions are
• arithmetic
• character
<MASK>
• logical
<MASK>
## Arithmetic Expressions
<MASK>
• an unsigned arithmetic constant
<MASK>
• an arithmetic array element reference
• an arithmetic function reference
You can form more complicated arithmetic expressions from one or more operands together with arithmetic operators and parentheses.
An arithmetic element can include logical entities because logical data is treated as integer data when used in an arithmetic context. When both arithmetic and logical operands exist for a given operator, the logical operand is promoted to type INTEGER of the same byte length as the original logical length. For example, a LOGICAL*2 will be promoted to INTEGER*2 and a LOGICAL*4 will be promoted to INTEGER*4.
### Arithmetic Operators
Table 3-1 shows the arithmetic operators.
<MASK>
Operator
Function
**
Exponentiation
*
<MASK>
/
<MASK>
+
Subtraction or negation
Use the exponentiation, division, and multiplication operators between exactly two operands. You can use the addition and subtraction operators with one or two operands; in the latter case, specify the operator before the operand; for example, –TOTAL.
<MASK>
### Interpretation of Arithmetic Expressions
Table 3-2 interprets sample arithmetic expressions.
<MASK>
Operator
Use
<MASK>
x1 ** x2
<MASK>
*
x1 * x2
<MASK>
/
x1 / x2
Divide x1 by x2
+
x1 + x2
<MASK>
x (identity)
x1 – x2
Subtract x1 from x2
<MASK>
An arithmetic expression containing two or more operators is interpreted based on a precedence relation among the arithmetic operators. This precedence, from highest to lowest, is
<MASK>
The following is an example of an arithmetic expression:
```A/B-C**D ```
The operators are executed in the following sequence:
<MASK>
3. The result of C**D is subtracted from the result of A/B to give the final result.
A unary operator (–) can follow another operator. Specifying the unary operator after the exponentiation operator produces a variation on the standard order of operations. The unary operator is evaluated first in that case, resulting in exponentiation taking a lower precedence in the expression.
For example, the following expression
<MASK>
is interpreted as
```A ** ( - B * C ) ```
### Arithmetic Operands
Arithmetic operands must specify values with integer, real, double-precision, complex, or double-complex data types. You can combine specific operands in an arithmetic expression. The arithmetic operands, in order of increasing complexity, are
<MASK>
• factor
<MASK>
• arithmetic expression
<MASK>
• an unsigned arithmetic constant
• a symbolic name of an arithmetic constant
• an arithmetic variable reference
<MASK>
• an arithmetic function reference
• an arithmetic expression enclosed in parentheses
<MASK>
Factors with more than one exponentiation operator are interpreted from right to left. For example, I**J**K is interpreted as I**(J**K), and I**J**K**L is interpreted as I**(J**(K**L)).
The term incorporates the multiplicative operators into arithmetic expressions. Its forms are
<MASK>
• term * factor
The above definition indicates that factors are combined from left to right in a term containing two or more multiplication or division operators.
<MASK>
• term
<MASK>
• arithmetic expression + term
• arithmetic expression – term
An arithmetic expression consists of one or more terms separated by an addition operator or a subtraction operator. The terms are combined from left to right. For example, A+B-C has the same interpretation as the expression (A+B)-C. Expressions such as A*-B and A+-B are not allowed. The correct forms are A*(–B) and A+(-B).
An arithmetic expression can begin with a plus or minus sign.
### Arithmetic Constant Expressions
An arithmetic constant expression is an arithmetic expression containing no variables. Therefore, each primary in an arithmetic constant expression must be one of the following:
<MASK>
• arithmetic constant expression enclosed in parentheses
In an arithmetic constant expression, do not specify the exponentiation operator unless the exponent is of type integer. Variable, array element, and function references are not allowed. Examples of integer constant expressions are
``` 7 –7 –7+5 3**2 x+3 (where x is the symbolic name of a constant) ```
### Integer Constant Expressions
<MASK>
### Evaluating Arithmetic Expressions
<MASK>
#### Mixed-Mode Expressions
Mixed-mode expressions contain operands with two or more data types. The data type of the result of a mixed-mode expression depends on the rank associated with each data type, as shown in Table 3-3.
Table 3-3. Data Type Ranks
<MASK>
Rank
INTEGER*1
<MASK>
REAL*4
4
REAL*8 (double precision)
5
COMPLEX*8
<MASK>
COMPLEX*16
7 (highest)
<MASK>
Operations that combine REAL*8 (DOUBLE PRECISION) and COMPLEX*8 (COMPLEX) are not allowed. The REAL*8 operand must be explicitly converted (for example, by using the SNGL intrinsic function).
<MASK>
Exponentiation is an exception to the above rules for mixed-mode expressions. When raising a value to an integer power, the integer is not converted. The result is assigned the type of the left operand.
<MASK>
```xy = EXP (y * LOG(x)) ```
### Integer Division
One operand of type integer can be divided by another operand of type integer. The result of an integer division operation is a value of type integer, referred to as an integer quotient. The integer quotient is obtained as follows:
<MASK>
A character expression yields a character string value on evaluation. The simplest form of a character expression can be one of these types of characters:
<MASK>
• function reference
<MASK>
### Concatenate Operator
The concatenate operator (//) is the only character operator defined in Fortran. A character expression formed from the concatenation of two character operands x1 and x2 is specified as
```x1 // x2 ```
The result of this operation is a character string with a value of x1 extended on the right with the value of x2. The length of the result is the sum of the lengths of the character operands. For example,
```'HEL' // 'LO2' ```
The result of the above expression is the string HELLO2 of length six.
<MASK>
• character constant
<MASK>
• character array element reference
<MASK>
• character function reference
<MASK>
A character expression consists of one or more character primaries separated by the concatenation operator. Its forms are
• character primary
<MASK>
In a character expression containing two or more concatenation operators, the primaries are combined from left to right. Thus, the character expression
```'A' // 'BCD' // 'EF' ```
is interpreted the same as
```('A' // 'BCD') // 'EF' ```
The value of the above character expression is ABCDEF.
Except in a character assignment statement, concatenation of an operand with an asterisk (*) as its length specification is not allowed unless the operand is the symbolic name of a constant.
### Character Constant Expressions
<MASK>
• symbolic name of a character constant
<MASK>
A relational expression yields a logical value of either .TRUE. or .FALSE. on evaluation and comparison of two arithmetic expressions or two character expressions. A relational expression can appear only within a logical expression. Refer to “Logical Expressions” for details about logical expressions.
### Relational Operators
<MASK>
Table 3-4. Fortran Relational Operators
<MASK>
Meaning
<MASK>
Equal to
.NE.
<MASK>
Greater than
.GE.
Greater than or equal to
<MASK>
.LE.
Less than or equal to
<MASK>
### Relational Operands
The operands of a relational operator can be arithmetic or character expressions. The relational expression requires exactly two operands and is written in the following form:
e1 relop e2
<MASK>
e1 and e2 are arithmetic or character expressions. relop is the relational operator.
<MASK>
### Evaluating Relational Expressions
The result of a relational expression is of type logical, with a value of .TRUE. or .FALSE.. The manner in which the expression is evaluated depends on the data type of the operands.
### Arithmetic Relational Expressions
<MASK>
You can use complex type operands only when specifying either the .EQ. or .NE. relational operator.
<MASK>
If the two arithmetic expressions e1 and e2 differ in type, the expression is evaluated as follows:
```((e1) - (e2)) relop 0 ```
<MASK>
### Character Relational Expressions
In a character relational expression, e1 and e2 are character expressions and relop is a relational operator.
<MASK>
A character relational expression has the logical value .TRUE. only if the values of the operands satisfy the relation specified by the operator. Otherwise, the value is .FALSE.. The result of a character relational expression depends on the collating sequence as follows:
• If e1 and e2 are single characters, their relationship in the collating sequence determines the value of the operator. e1 is less than or greater than e2 if e1 is before or after e2, respectively, in the collating sequence.
• If either e1 or e2 are character strings with lengths greater than 1, corresponding individual characters are compared from left to right until a relationship other than .EQ. can be determined.
• If the operands are of unequal length, the shorter operand is extended on the right with blanks to the length of the longer operand for the comparison.
• If no other relationship can be determined after the strings are exhausted, the strings are equal.
<MASK>
• logical variable reference
• logical array element reference
• logical function reference
• relational expression
Construct complicated logical expressions from one or more logical operands together with logical operators and parentheses.
<MASK>
Table 3-5. Logical Operators
<MASK>
.NOT.
Logical negation
.AND.
Logical conjunt
.OR.
<MASK>
.EQV.
Logical equivalence
.NEQV.
<MASK>
.XOR.
Same as .NEQV.
All logical operators require at least two operands, except the logical negation operator .NOT. , which requires only one.
A logical expression containing two or more logical operators is evaluated based on a precedence relation between the logical operators. This precedence, from highest to lowest, is
• .NOT.
<MASK>
• .OR.
• .EQV. and .NEQV.
• .XOR.
For example, in the following expression
```W .NEQV. X .OR. Y .AND. Z ```
the operators are executed in the following sequence:
<MASK>
2. X .OR. A is evaluated second (B represents the result).
<MASK>
You can use parentheses to override the precedence of the operators.
### Logical Operands
Logical operands specify values with a logical data type. The forms of a logical operands are
<MASK>
• logical term
• logical disjunct
• logical expression
#### Logical Primary
The logical primary is the basic component of a logical expression. The forms of a logical primary are
• logical constant
<MASK>
• logical array element reference
<MASK>
• integer or logical expression in parentheses
When an integer appears as an operand to a logical operator, the other operand is promoted to type integer if necessary and the operation is performed on a bit-by-bit basis producing an integer result. Whenever an arithmetic datum appears in a logical expression, the result of that expression will be of type integer because of type promotion rules. If necessary, the result can be converted back to LOGICAL.
Do not specify two logical operators consecutively and do not use implied logical operators.
#### Logical Factor
The logical factor uses the logical negation operator .NOT. to reverse the logical value to which it is applied. For example, applying .NOT. to a false relational expression makes the expression true. Therefore, if UP is true, .NOT. UP is false. The logical factor has the following forms:
• logical primary
• .NOT. logical primary
#### Logical Term
<MASK>
• Logical factor
• Logical term .AND. logical factor
In evaluating a logical term with two or more .AND. operators, the logical factors are combined from left to right. For example, X .AND. Y .AND. Z has the same interpretation as (X .AND. Y) .AND. Z.
#### Logical Disjunct
<MASK>
• Logical term
<MASK>
At the highest level of complexity is the logical expression. A logical expression is a sequence of logical disjuncts separated by the .EQV., .NEQV., or .XOR. operators. Its forms are
• logical disjunct
<MASK>
• logical expression .NEQV. logical disjunct
• logical expression .XOR. logical disjunct
The logical disjuncts are combined from left to right when a logical expression contains two or more .EQV., .NEVQ., or .XOR. operators.
A logical constant expression is a logical expression in which each primary is a logical constant, the symbolic name of a logical constant, a relational expression in which each primary is a constant, or a logical constant expression enclosed in parentheses. A logical constant expression can contain arithmetic and character constant expressions but not variables, array elements, or function references.
### Interpretation of Logical Expressions
<MASK>
IFA=
B=
THEN
.NOT.B
<MASK>
A.OR.B
A.EQV.B
<MASK>
F
F
T
<MASK>
T
<MASK>
F
<MASK>
F
<MASK>
F
T
<MASK>
F
F
T
F
<MASK>
T
T
T
T
T
<MASK>
Several rules are applied to the general evaluation of Fortran expressions. This section covers the priority of the different Fortran operators, the use of parentheses in specifying the order of evaluation, and the rules for combining operators with operands.
<MASK>
Certain Fortran operators have precedence over others when combined in an expression. The previous sections have listed the precedence among the arithmetic, logical, and expression operators. No precedence exists between the relational operators and the single character operator (//). On the highest level, the precedence among the types of expression operators, from highest to lowest, is
<MASK>
• character
• relational
<MASK>
Use parentheses to specify the order in which operators are evaluated within an expression. Expressions within parentheses are treated as an entity.
In an expression containing more than one operation, the processor first evaluates any expressions within parentheses. Subexpressions within parentheses are evaluated beginning with the innermost subexpression and proceeding sequentially to the outermost. The processor then scans the expression from left to right and performs the operations according to the operator precedence described previously.
<UNMASK>
## Chapter 3. Expressions
This chapter contains the following subsections:
An expression performs a specified type of computation. It is composed of a sequence of operands, operators, and parentheses. The types of Fortran expressions are
• arithmetic
• character
<MASK>
• logical
This chapter describes formation, interpretation, and evaluation rules for each type of expression. This chapter also discusses mixed-mode expressions, which are Fortran 77 enhancements of Fortran 66.
## Arithmetic Expressions
<MASK>
• an unsigned arithmetic constant
<MASK>
• an arithmetic array element reference
• an arithmetic function reference
You can form more complicated arithmetic expressions from one or more operands together with arithmetic operators and parentheses.
An arithmetic element can include logical entities because logical data is treated as integer data when used in an arithmetic context. When both arithmetic and logical operands exist for a given operator, the logical operand is promoted to type INTEGER of the same byte length as the original logical length. For example, a LOGICAL*2 will be promoted to INTEGER*2 and a LOGICAL*4 will be promoted to INTEGER*4.
### Arithmetic Operators
Table 3-1 shows the arithmetic operators.
<MASK>
Operator
Function
**
Exponentiation
*
<MASK>
/
<MASK>
+
Subtraction or negation
Use the exponentiation, division, and multiplication operators between exactly two operands. You can use the addition and subtraction operators with one or two operands; in the latter case, specify the operator before the operand; for example, –TOTAL.
<MASK>
### Interpretation of Arithmetic Expressions
Table 3-2 interprets sample arithmetic expressions.
<MASK>
Operator
Use
<MASK>
x1 ** x2
<MASK>
*
x1 * x2
<MASK>
/
x1 / x2
Divide x1 by x2
+
x1 + x2
<MASK>
x (identity)
x1 – x2
Subtract x1 from x2
<MASK>
An arithmetic expression containing two or more operators is interpreted based on a precedence relation among the arithmetic operators. This precedence, from highest to lowest, is
<MASK>
The following is an example of an arithmetic expression:
```A/B-C**D ```
The operators are executed in the following sequence:
<MASK>
3. The result of C**D is subtracted from the result of A/B to give the final result.
A unary operator (–) can follow another operator. Specifying the unary operator after the exponentiation operator produces a variation on the standard order of operations. The unary operator is evaluated first in that case, resulting in exponentiation taking a lower precedence in the expression.
For example, the following expression
```A ** - B * C ```
is interpreted as
```A ** ( - B * C ) ```
### Arithmetic Operands
Arithmetic operands must specify values with integer, real, double-precision, complex, or double-complex data types. You can combine specific operands in an arithmetic expression. The arithmetic operands, in order of increasing complexity, are
<MASK>
• factor
<MASK>
• arithmetic expression
<MASK>
• an unsigned arithmetic constant
• a symbolic name of an arithmetic constant
• an arithmetic variable reference
<MASK>
• an arithmetic function reference
• an arithmetic expression enclosed in parentheses
A factor consists of one or more primaries separated by the exponentiation operator. The forms of a factor are
<MASK>
Factors with more than one exponentiation operator are interpreted from right to left. For example, I**J**K is interpreted as I**(J**K), and I**J**K**L is interpreted as I**(J**(K**L)).
The term incorporates the multiplicative operators into arithmetic expressions. Its forms are
<MASK>
• term/factor
• term * factor
The above definition indicates that factors are combined from left to right in a term containing two or more multiplication or division operators.
<MASK>
• term
<MASK>
• arithmetic expression + term
• arithmetic expression – term
An arithmetic expression consists of one or more terms separated by an addition operator or a subtraction operator. The terms are combined from left to right. For example, A+B-C has the same interpretation as the expression (A+B)-C. Expressions such as A*-B and A+-B are not allowed. The correct forms are A*(–B) and A+(-B).
An arithmetic expression can begin with a plus or minus sign.
### Arithmetic Constant Expressions
An arithmetic constant expression is an arithmetic expression containing no variables. Therefore, each primary in an arithmetic constant expression must be one of the following:
<MASK>
• arithmetic constant expression enclosed in parentheses
In an arithmetic constant expression, do not specify the exponentiation operator unless the exponent is of type integer. Variable, array element, and function references are not allowed. Examples of integer constant expressions are
``` 7 –7 –7+5 3**2 x+3 (where x is the symbolic name of a constant) ```
### Integer Constant Expressions
<MASK>
### Evaluating Arithmetic Expressions
<MASK>
#### Mixed-Mode Expressions
Mixed-mode expressions contain operands with two or more data types. The data type of the result of a mixed-mode expression depends on the rank associated with each data type, as shown in Table 3-3.
Table 3-3. Data Type Ranks
<MASK>
Rank
INTEGER*1
<MASK>
REAL*4
4
REAL*8 (double precision)
5
COMPLEX*8
<MASK>
COMPLEX*16
7 (highest)
<MASK>
Operations that combine REAL*8 (DOUBLE PRECISION) and COMPLEX*8 (COMPLEX) are not allowed. The REAL*8 operand must be explicitly converted (for example, by using the SNGL intrinsic function).
<MASK>
Exponentiation is an exception to the above rules for mixed-mode expressions. When raising a value to an integer power, the integer is not converted. The result is assigned the type of the left operand.
<MASK>
```xy = EXP (y * LOG(x)) ```
### Integer Division
One operand of type integer can be divided by another operand of type integer. The result of an integer division operation is a value of type integer, referred to as an integer quotient. The integer quotient is obtained as follows:
<MASK>
A character expression yields a character string value on evaluation. The simplest form of a character expression can be one of these types of characters:
<MASK>
• function reference
<MASK>
### Concatenate Operator
The concatenate operator (//) is the only character operator defined in Fortran. A character expression formed from the concatenation of two character operands x1 and x2 is specified as
```x1 // x2 ```
The result of this operation is a character string with a value of x1 extended on the right with the value of x2. The length of the result is the sum of the lengths of the character operands. For example,
```'HEL' // 'LO2' ```
The result of the above expression is the string HELLO2 of length six.
<MASK>
• character constant
<MASK>
• character array element reference
<MASK>
• character function reference
<MASK>
A character expression consists of one or more character primaries separated by the concatenation operator. Its forms are
• character primary
<MASK>
In a character expression containing two or more concatenation operators, the primaries are combined from left to right. Thus, the character expression
```'A' // 'BCD' // 'EF' ```
is interpreted the same as
```('A' // 'BCD') // 'EF' ```
The value of the above character expression is ABCDEF.
Except in a character assignment statement, concatenation of an operand with an asterisk (*) as its length specification is not allowed unless the operand is the symbolic name of a constant.
### Character Constant Expressions
<MASK>
• symbolic name of a character constant
<MASK>
A character constant expression cannot contain variable, array element, substring, or function references.
<MASK>
A relational expression yields a logical value of either .TRUE. or .FALSE. on evaluation and comparison of two arithmetic expressions or two character expressions. A relational expression can appear only within a logical expression. Refer to “Logical Expressions” for details about logical expressions.
### Relational Operators
<MASK>
Table 3-4. Fortran Relational Operators
Relational Operator
Meaning
<MASK>
Equal to
.NE.
<MASK>
Greater than
.GE.
Greater than or equal to
<MASK>
.LE.
Less than or equal to
Arithmetic and character operators are evaluated before relational operators.
### Relational Operands
The operands of a relational operator can be arithmetic or character expressions. The relational expression requires exactly two operands and is written in the following form:
e1 relop e2
<MASK>
e1 and e2 are arithmetic or character expressions. relop is the relational operator.
<MASK>
### Evaluating Relational Expressions
The result of a relational expression is of type logical, with a value of .TRUE. or .FALSE.. The manner in which the expression is evaluated depends on the data type of the operands.
### Arithmetic Relational Expressions
<MASK>
You can use complex type operands only when specifying either the .EQ. or .NE. relational operator.
<MASK>
If the two arithmetic expressions e1 and e2 differ in type, the expression is evaluated as follows:
```((e1) - (e2)) relop 0 ```
<MASK>
### Character Relational Expressions
In a character relational expression, e1 and e2 are character expressions and relop is a relational operator.
<MASK>
A character relational expression has the logical value .TRUE. only if the values of the operands satisfy the relation specified by the operator. Otherwise, the value is .FALSE.. The result of a character relational expression depends on the collating sequence as follows:
• If e1 and e2 are single characters, their relationship in the collating sequence determines the value of the operator. e1 is less than or greater than e2 if e1 is before or after e2, respectively, in the collating sequence.
• If either e1 or e2 are character strings with lengths greater than 1, corresponding individual characters are compared from left to right until a relationship other than .EQ. can be determined.
• If the operands are of unequal length, the shorter operand is extended on the right with blanks to the length of the longer operand for the comparison.
• If no other relationship can be determined after the strings are exhausted, the strings are equal.
<MASK>
• logical variable reference
• logical array element reference
• logical function reference
• relational expression
Construct complicated logical expressions from one or more logical operands together with logical operators and parentheses.
<MASK>
Table 3-5. Logical Operators
<MASK>
.NOT.
Logical negation
.AND.
Logical conjunt
.OR.
<MASK>
.EQV.
Logical equivalence
.NEQV.
<MASK>
.XOR.
Same as .NEQV.
All logical operators require at least two operands, except the logical negation operator .NOT. , which requires only one.
A logical expression containing two or more logical operators is evaluated based on a precedence relation between the logical operators. This precedence, from highest to lowest, is
• .NOT.
<MASK>
• .OR.
• .EQV. and .NEQV.
• .XOR.
For example, in the following expression
```W .NEQV. X .OR. Y .AND. Z ```
the operators are executed in the following sequence:
<MASK>
2. X .OR. A is evaluated second (B represents the result).
<MASK>
You can use parentheses to override the precedence of the operators.
### Logical Operands
Logical operands specify values with a logical data type. The forms of a logical operands are
• logical primary
<MASK>
• logical term
• logical disjunct
• logical expression
#### Logical Primary
The logical primary is the basic component of a logical expression. The forms of a logical primary are
• logical constant
<MASK>
• logical array element reference
<MASK>
• integer or logical expression in parentheses
When an integer appears as an operand to a logical operator, the other operand is promoted to type integer if necessary and the operation is performed on a bit-by-bit basis producing an integer result. Whenever an arithmetic datum appears in a logical expression, the result of that expression will be of type integer because of type promotion rules. If necessary, the result can be converted back to LOGICAL.
Do not specify two logical operators consecutively and do not use implied logical operators.
#### Logical Factor
The logical factor uses the logical negation operator .NOT. to reverse the logical value to which it is applied. For example, applying .NOT. to a false relational expression makes the expression true. Therefore, if UP is true, .NOT. UP is false. The logical factor has the following forms:
• logical primary
• .NOT. logical primary
#### Logical Term
<MASK>
• Logical factor
• Logical term .AND. logical factor
In evaluating a logical term with two or more .AND. operators, the logical factors are combined from left to right. For example, X .AND. Y .AND. Z has the same interpretation as (X .AND. Y) .AND. Z.
#### Logical Disjunct
<MASK>
• Logical term
<MASK>
At the highest level of complexity is the logical expression. A logical expression is a sequence of logical disjuncts separated by the .EQV., .NEQV., or .XOR. operators. Its forms are
• logical disjunct
<MASK>
• logical expression .NEQV. logical disjunct
• logical expression .XOR. logical disjunct
The logical disjuncts are combined from left to right when a logical expression contains two or more .EQV., .NEVQ., or .XOR. operators.
A logical constant expression is a logical expression in which each primary is a logical constant, the symbolic name of a logical constant, a relational expression in which each primary is a constant, or a logical constant expression enclosed in parentheses. A logical constant expression can contain arithmetic and character constant expressions but not variables, array elements, or function references.
### Interpretation of Logical Expressions
<MASK>
IFA=
B=
THEN
.NOT.B
<MASK>
A.OR.B
A.EQV.B
<MASK>
F
F
T
F
<MASK>
T
<MASK>
F
<MASK>
F
<MASK>
F
T
<MASK>
F
F
T
F
<MASK>
T
T
T
T
T
F
<MASK>
Several rules are applied to the general evaluation of Fortran expressions. This section covers the priority of the different Fortran operators, the use of parentheses in specifying the order of evaluation, and the rules for combining operators with operands.
<MASK>
### Precedence of Operators
Certain Fortran operators have precedence over others when combined in an expression. The previous sections have listed the precedence among the arithmetic, logical, and expression operators. No precedence exists between the relational operators and the single character operator (//). On the highest level, the precedence among the types of expression operators, from highest to lowest, is
<MASK>
• character
• relational
• logical
<MASK>
Use parentheses to specify the order in which operators are evaluated within an expression. Expressions within parentheses are treated as an entity.
In an expression containing more than one operation, the processor first evaluates any expressions within parentheses. Subexpressions within parentheses are evaluated beginning with the innermost subexpression and proceeding sequentially to the outermost. The processor then scans the expression from left to right and performs the operations according to the operator precedence described previously.
|
## Chapter 3. Expressions
This chapter contains the following subsections:
An expression performs a specified type of computation. It is composed of a sequence of operands, operators, and parentheses. The types of Fortran expressions are
• arithmetic
• character
<MASK>
• logical
This chapter describes formation, interpretation, and evaluation rules for each type of expression. This chapter also discusses mixed-mode expressions, which are Fortran 77 enhancements of Fortran 66.
## Arithmetic Expressions
<MASK>
• an unsigned arithmetic constant
<MASK>
• an arithmetic array element reference
• an arithmetic function reference
You can form more complicated arithmetic expressions from one or more operands together with arithmetic operators and parentheses.
An arithmetic element can include logical entities because logical data is treated as integer data when used in an arithmetic context. When both arithmetic and logical operands exist for a given operator, the logical operand is promoted to type INTEGER of the same byte length as the original logical length. For example, a LOGICAL*2 will be promoted to INTEGER*2 and a LOGICAL*4 will be promoted to INTEGER*4.
### Arithmetic Operators
Table 3-1 shows the arithmetic operators.
<MASK>
Operator
Function
**
Exponentiation
*
<MASK>
/
<MASK>
+
Subtraction or negation
Use the exponentiation, division, and multiplication operators between exactly two operands. You can use the addition and subtraction operators with one or two operands; in the latter case, specify the operator before the operand; for example, –TOTAL.
<MASK>
### Interpretation of Arithmetic Expressions
Table 3-2 interprets sample arithmetic expressions.
<MASK>
Operator
Use
<MASK>
x1 ** x2
<MASK>
*
x1 * x2
<MASK>
/
x1 / x2
Divide x1 by x2
+
x1 + x2
<MASK>
x (identity)
x1 – x2
Subtract x1 from x2
<MASK>
An arithmetic expression containing two or more operators is interpreted based on a precedence relation among the arithmetic operators. This precedence, from highest to lowest, is
<MASK>
The following is an example of an arithmetic expression:
```A/B-C**D ```
The operators are executed in the following sequence:
<MASK>
3. The result of C**D is subtracted from the result of A/B to give the final result.
A unary operator (–) can follow another operator. Specifying the unary operator after the exponentiation operator produces a variation on the standard order of operations. The unary operator is evaluated first in that case, resulting in exponentiation taking a lower precedence in the expression.
For example, the following expression
```A ** - B * C ```
is interpreted as
```A ** ( - B * C ) ```
### Arithmetic Operands
Arithmetic operands must specify values with integer, real, double-precision, complex, or double-complex data types. You can combine specific operands in an arithmetic expression. The arithmetic operands, in order of increasing complexity, are
<MASK>
• factor
<MASK>
• arithmetic expression
<MASK>
• an unsigned arithmetic constant
• a symbolic name of an arithmetic constant
• an arithmetic variable reference
<MASK>
• an arithmetic function reference
• an arithmetic expression enclosed in parentheses
A factor consists of one or more primaries separated by the exponentiation operator. The forms of a factor are
<MASK>
Factors with more than one exponentiation operator are interpreted from right to left. For example, I**J**K is interpreted as I**(J**K), and I**J**K**L is interpreted as I**(J**(K**L)).
The term incorporates the multiplicative operators into arithmetic expressions. Its forms are
<MASK>
• term/factor
• term * factor
The above definition indicates that factors are combined from left to right in a term containing two or more multiplication or division operators.
<MASK>
• term
<MASK>
• arithmetic expression + term
• arithmetic expression – term
An arithmetic expression consists of one or more terms separated by an addition operator or a subtraction operator. The terms are combined from left to right. For example, A+B-C has the same interpretation as the expression (A+B)-C. Expressions such as A*-B and A+-B are not allowed. The correct forms are A*(–B) and A+(-B).
An arithmetic expression can begin with a plus or minus sign.
### Arithmetic Constant Expressions
An arithmetic constant expression is an arithmetic expression containing no variables. Therefore, each primary in an arithmetic constant expression must be one of the following:
<MASK>
• arithmetic constant expression enclosed in parentheses
In an arithmetic constant expression, do not specify the exponentiation operator unless the exponent is of type integer. Variable, array element, and function references are not allowed. Examples of integer constant expressions are
``` 7 –7 –7+5 3**2 x+3 (where x is the symbolic name of a constant) ```
### Integer Constant Expressions
<MASK>
### Evaluating Arithmetic Expressions
<MASK>
#### Mixed-Mode Expressions
Mixed-mode expressions contain operands with two or more data types. The data type of the result of a mixed-mode expression depends on the rank associated with each data type, as shown in Table 3-3.
Table 3-3. Data Type Ranks
<MASK>
Rank
INTEGER*1
<MASK>
REAL*4
4
REAL*8 (double precision)
5
COMPLEX*8
<MASK>
COMPLEX*16
7 (highest)
<MASK>
Operations that combine REAL*8 (DOUBLE PRECISION) and COMPLEX*8 (COMPLEX) are not allowed. The REAL*8 operand must be explicitly converted (for example, by using the SNGL intrinsic function).
<MASK>
Exponentiation is an exception to the above rules for mixed-mode expressions. When raising a value to an integer power, the integer is not converted. The result is assigned the type of the left operand.
<MASK>
```xy = EXP (y * LOG(x)) ```
### Integer Division
One operand of type integer can be divided by another operand of type integer. The result of an integer division operation is a value of type integer, referred to as an integer quotient. The integer quotient is obtained as follows:
<MASK>
A character expression yields a character string value on evaluation. The simplest form of a character expression can be one of these types of characters:
<MASK>
• function reference
<MASK>
### Concatenate Operator
The concatenate operator (//) is the only character operator defined in Fortran. A character expression formed from the concatenation of two character operands x1 and x2 is specified as
```x1 // x2 ```
The result of this operation is a character string with a value of x1 extended on the right with the value of x2. The length of the result is the sum of the lengths of the character operands. For example,
```'HEL' // 'LO2' ```
The result of the above expression is the string HELLO2 of length six.
<MASK>
• character constant
<MASK>
• character array element reference
<MASK>
• character function reference
<MASK>
A character expression consists of one or more character primaries separated by the concatenation operator. Its forms are
• character primary
<MASK>
In a character expression containing two or more concatenation operators, the primaries are combined from left to right. Thus, the character expression
```'A' // 'BCD' // 'EF' ```
is interpreted the same as
```('A' // 'BCD') // 'EF' ```
The value of the above character expression is ABCDEF.
Except in a character assignment statement, concatenation of an operand with an asterisk (*) as its length specification is not allowed unless the operand is the symbolic name of a constant.
### Character Constant Expressions
<MASK>
• symbolic name of a character constant
<MASK>
A character constant expression cannot contain variable, array element, substring, or function references.
<MASK>
A relational expression yields a logical value of either .TRUE. or .FALSE. on evaluation and comparison of two arithmetic expressions or two character expressions. A relational expression can appear only within a logical expression. Refer to “Logical Expressions” for details about logical expressions.
### Relational Operators
<MASK>
Table 3-4. Fortran Relational Operators
Relational Operator
Meaning
<MASK>
Equal to
.NE.
<MASK>
Greater than
.GE.
Greater than or equal to
<MASK>
.LE.
Less than or equal to
Arithmetic and character operators are evaluated before relational operators.
### Relational Operands
The operands of a relational operator can be arithmetic or character expressions. The relational expression requires exactly two operands and is written in the following form:
e1 relop e2
<MASK>
e1 and e2 are arithmetic or character expressions. relop is the relational operator.
<MASK>
### Evaluating Relational Expressions
The result of a relational expression is of type logical, with a value of .TRUE. or .FALSE.. The manner in which the expression is evaluated depends on the data type of the operands.
### Arithmetic Relational Expressions
<MASK>
You can use complex type operands only when specifying either the .EQ. or .NE. relational operator.
<MASK>
If the two arithmetic expressions e1 and e2 differ in type, the expression is evaluated as follows:
```((e1) - (e2)) relop 0 ```
<MASK>
### Character Relational Expressions
In a character relational expression, e1 and e2 are character expressions and relop is a relational operator.
<MASK>
A character relational expression has the logical value .TRUE. only if the values of the operands satisfy the relation specified by the operator. Otherwise, the value is .FALSE.. The result of a character relational expression depends on the collating sequence as follows:
• If e1 and e2 are single characters, their relationship in the collating sequence determines the value of the operator. e1 is less than or greater than e2 if e1 is before or after e2, respectively, in the collating sequence.
• If either e1 or e2 are character strings with lengths greater than 1, corresponding individual characters are compared from left to right until a relationship other than .EQ. can be determined.
• If the operands are of unequal length, the shorter operand is extended on the right with blanks to the length of the longer operand for the comparison.
• If no other relationship can be determined after the strings are exhausted, the strings are equal.
<MASK>
• logical variable reference
• logical array element reference
• logical function reference
• relational expression
Construct complicated logical expressions from one or more logical operands together with logical operators and parentheses.
<MASK>
Table 3-5. Logical Operators
<MASK>
.NOT.
Logical negation
.AND.
Logical conjunt
.OR.
<MASK>
.EQV.
Logical equivalence
.NEQV.
<MASK>
.XOR.
Same as .NEQV.
All logical operators require at least two operands, except the logical negation operator .NOT. , which requires only one.
A logical expression containing two or more logical operators is evaluated based on a precedence relation between the logical operators. This precedence, from highest to lowest, is
• .NOT.
<MASK>
• .OR.
• .EQV. and .NEQV.
• .XOR.
For example, in the following expression
```W .NEQV. X .OR. Y .AND. Z ```
the operators are executed in the following sequence:
<MASK>
2. X .OR. A is evaluated second (B represents the result).
<MASK>
You can use parentheses to override the precedence of the operators.
### Logical Operands
Logical operands specify values with a logical data type. The forms of a logical operands are
• logical primary
<MASK>
• logical term
• logical disjunct
• logical expression
#### Logical Primary
The logical primary is the basic component of a logical expression. The forms of a logical primary are
• logical constant
<MASK>
• logical array element reference
<MASK>
• integer or logical expression in parentheses
When an integer appears as an operand to a logical operator, the other operand is promoted to type integer if necessary and the operation is performed on a bit-by-bit basis producing an integer result. Whenever an arithmetic datum appears in a logical expression, the result of that expression will be of type integer because of type promotion rules. If necessary, the result can be converted back to LOGICAL.
Do not specify two logical operators consecutively and do not use implied logical operators.
#### Logical Factor
The logical factor uses the logical negation operator .NOT. to reverse the logical value to which it is applied. For example, applying .NOT. to a false relational expression makes the expression true. Therefore, if UP is true, .NOT. UP is false. The logical factor has the following forms:
• logical primary
• .NOT. logical primary
#### Logical Term
<MASK>
• Logical factor
• Logical term .AND. logical factor
In evaluating a logical term with two or more .AND. operators, the logical factors are combined from left to right. For example, X .AND. Y .AND. Z has the same interpretation as (X .AND. Y) .AND. Z.
#### Logical Disjunct
<MASK>
• Logical term
<MASK>
At the highest level of complexity is the logical expression. A logical expression is a sequence of logical disjuncts separated by the .EQV., .NEQV., or .XOR. operators. Its forms are
• logical disjunct
<MASK>
• logical expression .NEQV. logical disjunct
• logical expression .XOR. logical disjunct
The logical disjuncts are combined from left to right when a logical expression contains two or more .EQV., .NEVQ., or .XOR. operators.
A logical constant expression is a logical expression in which each primary is a logical constant, the symbolic name of a logical constant, a relational expression in which each primary is a constant, or a logical constant expression enclosed in parentheses. A logical constant expression can contain arithmetic and character constant expressions but not variables, array elements, or function references.
### Interpretation of Logical Expressions
<MASK>
IFA=
B=
THEN
.NOT.B
<MASK>
A.OR.B
A.EQV.B
<MASK>
F
F
T
F
<MASK>
T
<MASK>
F
<MASK>
F
<MASK>
F
T
<MASK>
F
F
T
F
<MASK>
T
T
T
T
T
F
<MASK>
Several rules are applied to the general evaluation of Fortran expressions. This section covers the priority of the different Fortran operators, the use of parentheses in specifying the order of evaluation, and the rules for combining operators with operands.
<MASK>
### Precedence of Operators
Certain Fortran operators have precedence over others when combined in an expression. The previous sections have listed the precedence among the arithmetic, logical, and expression operators. No precedence exists between the relational operators and the single character operator (//). On the highest level, the precedence among the types of expression operators, from highest to lowest, is
<MASK>
• character
• relational
• logical
<MASK>
Use parentheses to specify the order in which operators are evaluated within an expression. Expressions within parentheses are treated as an entity.
In an expression containing more than one operation, the processor first evaluates any expressions within parentheses. Subexpressions within parentheses are evaluated beginning with the innermost subexpression and proceeding sequentially to the outermost. The processor then scans the expression from left to right and performs the operations according to the operator precedence described previously.
<UNMASK>
## Chapter 3. Expressions
This chapter contains the following subsections:
An expression performs a specified type of computation. It is composed of a sequence of operands, operators, and parentheses. The types of Fortran expressions are
• arithmetic
• character
• relational
• logical
This chapter describes formation, interpretation, and evaluation rules for each type of expression. This chapter also discusses mixed-mode expressions, which are Fortran 77 enhancements of Fortran 66.
## Arithmetic Expressions
An arithmetic expression specifies a numeric computation that yields a numeric value on evaluation. The simplest form of an arithmetic expression can be:
• an unsigned arithmetic constant
• a symbolic name of an arithmetic constant
• an arithmetic variable reference
• an arithmetic array element reference
• an arithmetic function reference
You can form more complicated arithmetic expressions from one or more operands together with arithmetic operators and parentheses.
An arithmetic element can include logical entities because logical data is treated as integer data when used in an arithmetic context. When both arithmetic and logical operands exist for a given operator, the logical operand is promoted to type INTEGER of the same byte length as the original logical length. For example, a LOGICAL*2 will be promoted to INTEGER*2 and a LOGICAL*4 will be promoted to INTEGER*4.
### Arithmetic Operators
Table 3-1 shows the arithmetic operators.
Table 3-1. Arithmetic Operators
Operator
Function
**
Exponentiation
*
Multiplication
/
Division
+
Subtraction or negation
Use the exponentiation, division, and multiplication operators between exactly two operands. You can use the addition and subtraction operators with one or two operands; in the latter case, specify the operator before the operand; for example, –TOTAL.
Do not specify two operators in succession. (Note that the exponentiation operator consists of the two characters (**), but is a single operator.) Implied operators, as in implied multiplication, are not allowed.
### Interpretation of Arithmetic Expressions
Table 3-2 interprets sample arithmetic expressions.
Table 3-2. Interpretation of Arithmetic Expressions
Operator
Use
Interpretation
**
x1 ** x2
Exponentiate x1 to the power of x2
*
x1 * x2
Multiply x1 and x2
/
x1 / x2
Divide x1 by x2
+
x1 + x2
+ x
x (identity)
x1 – x2
Subtract x1 from x2
-x
Negate x
An arithmetic expression containing two or more operators is interpreted based on a precedence relation among the arithmetic operators. This precedence, from highest to lowest, is
• ( )
• **
• * and /
• + and –
Use parentheses to override the order of precedence.
The following is an example of an arithmetic expression:
```A/B-C**D ```
The operators are executed in the following sequence:
1. C**D is evaluated first.
2. A/B is evaluated next.
3. The result of C**D is subtracted from the result of A/B to give the final result.
A unary operator (–) can follow another operator. Specifying the unary operator after the exponentiation operator produces a variation on the standard order of operations. The unary operator is evaluated first in that case, resulting in exponentiation taking a lower precedence in the expression.
For example, the following expression
```A ** - B * C ```
is interpreted as
```A ** ( - B * C ) ```
### Arithmetic Operands
Arithmetic operands must specify values with integer, real, double-precision, complex, or double-complex data types. You can combine specific operands in an arithmetic expression. The arithmetic operands, in order of increasing complexity, are
• primary
• factor
• term
• arithmetic expression
A primary is the basic component in an arithmetic expression. The forms of a primary are
• an unsigned arithmetic constant
• a symbolic name of an arithmetic constant
• an arithmetic variable reference
• an arithmetic array element reference
• an arithmetic function reference
• an arithmetic expression enclosed in parentheses
A factor consists of one or more primaries separated by the exponentiation operator. The forms of a factor are
• primary
• primary ** factor
Factors with more than one exponentiation operator are interpreted from right to left. For example, I**J**K is interpreted as I**(J**K), and I**J**K**L is interpreted as I**(J**(K**L)).
The term incorporates the multiplicative operators into arithmetic expressions. Its forms are
• factor
• term/factor
• term * factor
The above definition indicates that factors are combined from left to right in a term containing two or more multiplication or division operators.
Finally, at the highest level of the hierarchy, are the arithmetic expressions. The forms of an arithmetic expression are
• term
• + term
• – term
• arithmetic expression + term
• arithmetic expression – term
An arithmetic expression consists of one or more terms separated by an addition operator or a subtraction operator. The terms are combined from left to right. For example, A+B-C has the same interpretation as the expression (A+B)-C. Expressions such as A*-B and A+-B are not allowed. The correct forms are A*(–B) and A+(-B).
An arithmetic expression can begin with a plus or minus sign.
### Arithmetic Constant Expressions
An arithmetic constant expression is an arithmetic expression containing no variables. Therefore, each primary in an arithmetic constant expression must be one of the following:
• arithmetic constant
• symbolic name of an arithmetic constant
• arithmetic constant expression enclosed in parentheses
In an arithmetic constant expression, do not specify the exponentiation operator unless the exponent is of type integer. Variable, array element, and function references are not allowed. Examples of integer constant expressions are
``` 7 –7 –7+5 3**2 x+3 (where x is the symbolic name of a constant) ```
### Integer Constant Expressions
An integer constant expression is an arithmetic constant expression containing only integers. It can contain constants or symbolic names of constants, provided they are of type integer. As with all constant expressions, no variables, array elements, or function references are allowed.
### Evaluating Arithmetic Expressions
The data type of an expression is determined by the data types of the operands and functions that are referenced. Thus, integer expressions, real expressions, double-precision expressions, complex expressions, and double expressions have values of type integer, real, double-precision, complex, and double-complex, respectively.
#### Single-Mode Expressions
Single-mode expressions are arithmetic expressions in which all operands have the same data type. The data type of the value of a single-mode expression is thus the same as the data type of the operands. When the addition operator or the subtraction operator is used with a single operand, the data type of the resulting expression is the same as the data type of the operand.
#### Mixed-Mode Expressions
Mixed-mode expressions contain operands with two or more data types. The data type of the result of a mixed-mode expression depends on the rank associated with each data type, as shown in Table 3-3.
Table 3-3. Data Type Ranks
Data Type
Rank
INTEGER*1
1 (lowest)
INTEGER*2
2
INTEGER*4
3
REAL*4
4
REAL*8 (double precision)
5
COMPLEX*8
6
COMPLEX*16
7 (highest)
Except for exponentiation (discussed below), the result of a mixed-mode expression is assigned the data type of the highest-ranked element in the expression. The lower-ranked operand is converted to the type of the higher-ranked operand so that the operation is performed on values with equivalent data types. For example, an operation on an integer operand and a real operand produces a result of type real.
Operations that combine REAL*8 (DOUBLE PRECISION) and COMPLEX*8 (COMPLEX) are not allowed. The REAL*8 operand must be explicitly converted (for example, by using the SNGL intrinsic function).
### Exponentiation
Exponentiation is an exception to the above rules for mixed-mode expressions. When raising a value to an integer power, the integer is not converted. The result is assigned the type of the left operand.
When a complex value is raised to a complex power, the value of the expression is defined as follows:
```xy = EXP (y * LOG(x)) ```
### Integer Division
One operand of type integer can be divided by another operand of type integer. The result of an integer division operation is a value of type integer, referred to as an integer quotient. The integer quotient is obtained as follows:
• If the magnitude of the mathematical quotient is less than one, then the integer quotient is zero. For example, the value of the expression (18/30) is zero.
• If the magnitude of the mathematical quotient is greater than or equal to one, then the integer quotient is the largest integer that does not exceed the magnitude of the mathematical quotient and whose sign is the same as that of the mathematical quotient. For example, the value of the expression (–9/2) is –4.
## Character Expressions
A character expression yields a character string value on evaluation. The simplest form of a character expression can be one of these types of characters:
• constant
• variable reference
• array element reference
• substring reference
• function reference
Construct complicated character expressions from one or more operands together with the concatenate operator and parentheses.
### Concatenate Operator
The concatenate operator (//) is the only character operator defined in Fortran. A character expression formed from the concatenation of two character operands x1 and x2 is specified as
```x1 // x2 ```
The result of this operation is a character string with a value of x1 extended on the right with the value of x2. The length of the result is the sum of the lengths of the character operands. For example,
```'HEL' // 'LO2' ```
The result of the above expression is the string HELLO2 of length six.
### Character Operands
A character operand must identify a value of type character and must be a character expression. The basic component in a character expression is the character primary. The forms of a character primary are
• character constant
• symbolic name of a character constant
• character variable reference
• character array element reference
• character substring reference
• character function reference
• character expression enclosed in parentheses
A character expression consists of one or more character primaries separated by the concatenation operator. Its forms are
• character primary
• character expression // character primary
In a character expression containing two or more concatenation operators, the primaries are combined from left to right. Thus, the character expression
```'A' // 'BCD' // 'EF' ```
is interpreted the same as
```('A' // 'BCD') // 'EF' ```
The value of the above character expression is ABCDEF.
Except in a character assignment statement, concatenation of an operand with an asterisk (*) as its length specification is not allowed unless the operand is the symbolic name of a constant.
### Character Constant Expressions
A character constant expression is made up of operands that cannot vary. Each primary in a character constant expression must be a
• character constant
• symbolic name of a character constant
• character constant expression enclosed in parentheses
A character constant expression cannot contain variable, array element, substring, or function references.
## Relational Expressions
A relational expression yields a logical value of either .TRUE. or .FALSE. on evaluation and comparison of two arithmetic expressions or two character expressions. A relational expression can appear only within a logical expression. Refer to “Logical Expressions” for details about logical expressions.
### Relational Operators
Table 3-4 lists the Fortran relational operators.
Table 3-4. Fortran Relational Operators
Relational Operator
Meaning
.EQ.
Equal to
.NE.
Not equal to
.GT.
Greater than
.GE.
Greater than or equal to
.LT.
Less than
.LE.
Less than or equal to
Arithmetic and character operators are evaluated before relational operators.
### Relational Operands
The operands of a relational operator can be arithmetic or character expressions. The relational expression requires exactly two operands and is written in the following form:
e1 relop e2
where
e1 and e2 are arithmetic or character expressions. relop is the relational operator.
Note: Both e1 and e2 must be the same type of expression, either arithmetic or character.
### Evaluating Relational Expressions
The result of a relational expression is of type logical, with a value of .TRUE. or .FALSE.. The manner in which the expression is evaluated depends on the data type of the operands.
### Arithmetic Relational Expressions
In an arithmetic relational expression, e1 and e2 must each be an integer, real, double precision, complex, or double complex expression. relop must be a relational operator.
The following are examples of arithmetic relational expressions:
```(a + b) .EQ. (c + 1) HOURS .LE. 40 ```
You can use complex type operands only when specifying either the .EQ. or .NE. relational operator.
An arithmetic relational expression has the logical value .TRUE. only if the values of the operands satisfy the relation specified by the operator. Otherwise, the value is .FALSE..
If the two arithmetic expressions e1 and e2 differ in type, the expression is evaluated as follows:
```((e1) - (e2)) relop 0 ```
where the value 0 (zero) is of the same type as the expression ((e1)- (e2)) and the type conversion rules apply to the expression. Do not compare a double precision value with a complex value.
### Character Relational Expressions
In a character relational expression, e1 and e2 are character expressions and relop is a relational operator.
The following is an example of a character relational expression:
```NAME .EQ. 'HOMER' ```
A character relational expression has the logical value .TRUE. only if the values of the operands satisfy the relation specified by the operator. Otherwise, the value is .FALSE.. The result of a character relational expression depends on the collating sequence as follows:
• If e1 and e2 are single characters, their relationship in the collating sequence determines the value of the operator. e1 is less than or greater than e2 if e1 is before or after e2, respectively, in the collating sequence.
• If either e1 or e2 are character strings with lengths greater than 1, corresponding individual characters are compared from left to right until a relationship other than .EQ. can be determined.
• If the operands are of unequal length, the shorter operand is extended on the right with blanks to the length of the longer operand for the comparison.
• If no other relationship can be determined after the strings are exhausted, the strings are equal.
The collating sequence depends partially on the processor; however, equality tests .EQ. and .NE. do not depend on the processor collating sequence and can be used on any processor.
## Logical Expressions
A logical expression specifies a logical computation that yields a logical value. The simplest form of a logical expression is one of the following:
• logical constant
• logical variable reference
• logical array element reference
• logical function reference
• relational expression
Construct complicated logical expressions from one or more logical operands together with logical operators and parentheses.
### Logical Operators
Table 3-5 defines the Fortran logical operators.
Table 3-5. Logical Operators
Logical Operator
Meaning
.NOT.
Logical negation
.AND.
Logical conjunt
.OR.
Logical disjunct
.EQV.
Logical equivalence
.NEQV.
Logical exclusive or
.XOR.
Same as .NEQV.
All logical operators require at least two operands, except the logical negation operator .NOT. , which requires only one.
A logical expression containing two or more logical operators is evaluated based on a precedence relation between the logical operators. This precedence, from highest to lowest, is
• .NOT.
• .AND.
• .OR.
• .EQV. and .NEQV.
• .XOR.
For example, in the following expression
```W .NEQV. X .OR. Y .AND. Z ```
the operators are executed in the following sequence:
1. Y .AND. Z is evaluated first (A represents the result).
2. X .OR. A is evaluated second (B represents the result).
3. W .NEQV. B is evaluated to produce the final result.
You can use parentheses to override the precedence of the operators.
### Logical Operands
Logical operands specify values with a logical data type. The forms of a logical operands are
• logical primary
• logical factor
• logical term
• logical disjunct
• logical expression
#### Logical Primary
The logical primary is the basic component of a logical expression. The forms of a logical primary are
• logical constant
• symbolic name of a logical constant
• integer or logical variable reference
• logical array element reference
• integer or logical function reference
• relational expression
• integer or logical expression in parentheses
When an integer appears as an operand to a logical operator, the other operand is promoted to type integer if necessary and the operation is performed on a bit-by-bit basis producing an integer result. Whenever an arithmetic datum appears in a logical expression, the result of that expression will be of type integer because of type promotion rules. If necessary, the result can be converted back to LOGICAL.
Do not specify two logical operators consecutively and do not use implied logical operators.
#### Logical Factor
The logical factor uses the logical negation operator .NOT. to reverse the logical value to which it is applied. For example, applying .NOT. to a false relational expression makes the expression true. Therefore, if UP is true, .NOT. UP is false. The logical factor has the following forms:
• logical primary
• .NOT. logical primary
#### Logical Term
The logical term uses the logical conjunct operator .AND. to combine logical factors. It takes the forms
• Logical factor
• Logical term .AND. logical factor
In evaluating a logical term with two or more .AND. operators, the logical factors are combined from left to right. For example, X .AND. Y .AND. Z has the same interpretation as (X .AND. Y) .AND. Z.
#### Logical Disjunct
The logical disjunct is a sequence of logical terms separated by the .OR. operator and has the following two forms:
• Logical term
• Logical disjunct .OR. logical term
In an expression containing two or more .OR. operators, the logical terms are combined from left to right in succession. For example, the expression X .OR. Y .OR. Z has the same interpretation as (X .OR. Y) .OR. Z.
#### Logical Expression
At the highest level of complexity is the logical expression. A logical expression is a sequence of logical disjuncts separated by the .EQV., .NEQV., or .XOR. operators. Its forms are
• logical disjunct
• logical expression .EQV. logical disjunct
• logical expression .NEQV. logical disjunct
• logical expression .XOR. logical disjunct
The logical disjuncts are combined from left to right when a logical expression contains two or more .EQV., .NEVQ., or .XOR. operators.
A logical constant expression is a logical expression in which each primary is a logical constant, the symbolic name of a logical constant, a relational expression in which each primary is a constant, or a logical constant expression enclosed in parentheses. A logical constant expression can contain arithmetic and character constant expressions but not variables, array elements, or function references.
### Interpretation of Logical Expressions
In general, logical expressions containing two or more logical operators are executed according to the hierarchy of operators described previously, unless the order has been overridden by the use of parentheses. Table 3-6 defines the form and interpretation of the logical expressions.
Table 3-6. Logical Expressions
IFA=
B=
THEN
.NOT.B
A.AND.B
A.OR.B
A.EQV.B
A.XOR.B
A.NEQV.B
F
F
T
F
F
T
F
F
T
F
F
T
F
T
T
F
F
T
F
T
T
T
T
T
T
F
## Evaluating Expressions in General
Several rules are applied to the general evaluation of Fortran expressions. This section covers the priority of the different Fortran operators, the use of parentheses in specifying the order of evaluation, and the rules for combining operators with operands.
Note: Any variable, array element, function, or character substring in an expression must be defined with a value of the correct type at the time it is referenced.
### Precedence of Operators
Certain Fortran operators have precedence over others when combined in an expression. The previous sections have listed the precedence among the arithmetic, logical, and expression operators. No precedence exists between the relational operators and the single character operator (//). On the highest level, the precedence among the types of expression operators, from highest to lowest, is
• arithmetic
• character
• relational
• logical
### Integrity of Parentheses and Interpretation Rules
Use parentheses to specify the order in which operators are evaluated within an expression. Expressions within parentheses are treated as an entity.
In an expression containing more than one operation, the processor first evaluates any expressions within parentheses. Subexpressions within parentheses are evaluated beginning with the innermost subexpression and proceeding sequentially to the outermost. The processor then scans the expression from left to right and performs the operations according to the operator precedence described previously.
|
<MASK>
# 2 cars are 120 miles apart.If both cars go at a constant
Author Message
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a. 35
b. 40
c. 70
d. 85
e. 90
SVP
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Posts: 1582
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<MASK>
they will drive for 50 miles but the difference is 120 so there is still 70 miles to cover
<MASK>
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
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According to that hypothesis;
in an hour one moves 40 miles and the other 30, initial distance gets dropped to 110 miles, so every hour on the hour one car closes the gap by 10 miles.
From the meeting point the distance between them an hour before would be 10 miles (by the same logic)
since this is not a choice, they probably are going towards each other, either the author of the quesiton missed something or the question is badly phrased
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<MASK>
Kudos [?]: 13 [0], given: 0
Rupstar wrote:
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
<MASK>
Kudos [?]: 87 [0], given: 0
let n be the time taken for both cars to meet.
<MASK>
Kudos [?]: 13 [0], given: 0
<MASK>
i agree with you. definitely a GMAT DS thinking.
<MASK>
<UNMASK>
<MASK>
# 2 cars are 120 miles apart.If both cars go at a constant
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2 cars are 120 miles apart.If both cars go at a constant [#permalink] 06 Mar 2005, 18:46
2 cars are 120 miles apart.If both cars go at a constant speed with one of them going at 30/mph and the other 40/mph - how far apart will the 2 cars be in exactly 1 hour before they meet?
a. 35
b. 40
c. 70
d. 85
e. 90
SVP
Joined: 25 Nov 2004
Posts: 1582
Followers: 4
<MASK>
c.70
<MASK>
for 40mp/h car -> 40*5/7 = 200/7
for 30mp/h car -> 30*5/7 = 150/7
they will drive for 50 miles but the difference is 120 so there is still 70 miles to cover
<MASK>
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
Senior Manager
Joined: 15 Feb 2005
Posts: 258
Location: Rockville
Followers: 1
Kudos [?]: 5 [0], given: 0
<MASK>
According to that hypothesis;
in an hour one moves 40 miles and the other 30, initial distance gets dropped to 110 miles, so every hour on the hour one car closes the gap by 10 miles.
From the meeting point the distance between them an hour before would be 10 miles (by the same logic)
since this is not a choice, they probably are going towards each other, either the author of the quesiton missed something or the question is badly phrased
SVP
Joined: 03 Jan 2005
Posts: 2322
Followers: 9
<MASK>
Rupstar wrote:
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
<MASK>
Kudos [?]: 13 [0], given: 0
Rupstar wrote:
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
i agree with you. definitely a GMAT DS thinking.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5134
Location: Singapore
Followers: 9
Kudos [?]: 87 [0], given: 0
let n be the time taken for both cars to meet.
<MASK>
For the car travelling at 40km/h - would have covered 28 4/7 km
For the car travelling at 30km/h - would have covered 21 3/7 km
In total they cover 50km
<MASK>
Kudos [?]: 13 [0], given: 0
MA wrote:
Rupstar wrote:
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
i agree with you. definitely a GMAT DS thinking.
<MASK>
|
<MASK>
# 2 cars are 120 miles apart.If both cars go at a constant
Author Message
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2 cars are 120 miles apart.If both cars go at a constant [#permalink] 06 Mar 2005, 18:46
2 cars are 120 miles apart.If both cars go at a constant speed with one of them going at 30/mph and the other 40/mph - how far apart will the 2 cars be in exactly 1 hour before they meet?
a. 35
b. 40
c. 70
d. 85
e. 90
SVP
Joined: 25 Nov 2004
Posts: 1582
Followers: 4
<MASK>
c.70
<MASK>
for 40mp/h car -> 40*5/7 = 200/7
for 30mp/h car -> 30*5/7 = 150/7
they will drive for 50 miles but the difference is 120 so there is still 70 miles to cover
<MASK>
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
Senior Manager
Joined: 15 Feb 2005
Posts: 258
Location: Rockville
Followers: 1
Kudos [?]: 5 [0], given: 0
<MASK>
According to that hypothesis;
in an hour one moves 40 miles and the other 30, initial distance gets dropped to 110 miles, so every hour on the hour one car closes the gap by 10 miles.
From the meeting point the distance between them an hour before would be 10 miles (by the same logic)
since this is not a choice, they probably are going towards each other, either the author of the quesiton missed something or the question is badly phrased
SVP
Joined: 03 Jan 2005
Posts: 2322
Followers: 9
<MASK>
Rupstar wrote:
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
<MASK>
Kudos [?]: 13 [0], given: 0
Rupstar wrote:
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
i agree with you. definitely a GMAT DS thinking.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5134
Location: Singapore
Followers: 9
Kudos [?]: 87 [0], given: 0
let n be the time taken for both cars to meet.
<MASK>
For the car travelling at 40km/h - would have covered 28 4/7 km
For the car travelling at 30km/h - would have covered 21 3/7 km
In total they cover 50km
<MASK>
Kudos [?]: 13 [0], given: 0
MA wrote:
Rupstar wrote:
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
i agree with you. definitely a GMAT DS thinking.
<MASK>
<UNMASK>
<MASK>
# 2 cars are 120 miles apart.If both cars go at a constant
Author Message
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2 cars are 120 miles apart.If both cars go at a constant [#permalink] 06 Mar 2005, 18:46
2 cars are 120 miles apart.If both cars go at a constant speed with one of them going at 30/mph and the other 40/mph - how far apart will the 2 cars be in exactly 1 hour before they meet?
a. 35
b. 40
c. 70
d. 85
e. 90
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Joined: 25 Nov 2004
Posts: 1582
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Kudos [?]: 13 [0], given: 0
<MASK>
c.70
first, both cars will meet :
40x + 30x = 120 ; x = 12/7h
means that 1h before they meet both cars would have driven 12/7-7/7 = 5/7h
for 40mp/h car -> 40*5/7 = 200/7
for 30mp/h car -> 30*5/7 = 150/7
they will drive for 50 miles but the difference is 120 so there is still 70 miles to cover
<MASK>
Kudos [?]: 5 [0], given: 0
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
Senior Manager
Joined: 15 Feb 2005
Posts: 258
Location: Rockville
Followers: 1
Kudos [?]: 5 [0], given: 0
Two choices...
since this question doesnt clearly state whether they are heading in opposite directions towards each other or away from each other or in the same direction, its difficult to decide.
Since it isnt stated that they are going in opposite directions, and that is usually rare/less common in the speed problems
we have ption 1 in which they head towards each other...as Antmavel chose...this is usually what you see alot of on the
GMAT speed/distance/time problems.
Using the same process as Antmavel i too got 70 but now considering that NOTHING IS SAID about direction
the first inclination is that they are 120 miles apart heading in the same direction.
According to that hypothesis;
in an hour one moves 40 miles and the other 30, initial distance gets dropped to 110 miles, so every hour on the hour one car closes the gap by 10 miles.
From the meeting point the distance between them an hour before would be 10 miles (by the same logic)
since this is not a choice, they probably are going towards each other, either the author of the quesiton missed something or the question is badly phrased
SVP
Joined: 03 Jan 2005
Posts: 2322
Followers: 9
<MASK>
Rupstar wrote:
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
Good thinking. And there's the chance that they never meet if they both go the other direction. Although this means the question is not well defined, if you met a question like this in the test, you would have to work in the range that is given, in other words since 10 and infinite are not included in the choices you pick the only possible correct answer 70.
SVP
Joined: 25 Nov 2004
Posts: 1582
Followers: 4
Kudos [?]: 13 [0], given: 0
Rupstar wrote:
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
i agree with you. definitely a GMAT DS thinking.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5134
Location: Singapore
Followers: 9
Kudos [?]: 87 [0], given: 0
let n be the time taken for both cars to meet.
<MASK>
For the car travelling at 40km/h - would have covered 28 4/7 km
For the car travelling at 30km/h - would have covered 21 3/7 km
In total they cover 50km
<MASK>
Kudos [?]: 13 [0], given: 0
MA wrote:
Rupstar wrote:
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
i agree with you. definitely a GMAT DS thinking.
<MASK>
|
<MASK>
# 2 cars are 120 miles apart.If both cars go at a constant
Author Message
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2 cars are 120 miles apart.If both cars go at a constant [#permalink] 06 Mar 2005, 18:46
2 cars are 120 miles apart.If both cars go at a constant speed with one of them going at 30/mph and the other 40/mph - how far apart will the 2 cars be in exactly 1 hour before they meet?
a. 35
b. 40
c. 70
d. 85
e. 90
SVP
Joined: 25 Nov 2004
Posts: 1582
Followers: 4
Kudos [?]: 13 [0], given: 0
<MASK>
c.70
first, both cars will meet :
40x + 30x = 120 ; x = 12/7h
means that 1h before they meet both cars would have driven 12/7-7/7 = 5/7h
for 40mp/h car -> 40*5/7 = 200/7
for 30mp/h car -> 30*5/7 = 150/7
they will drive for 50 miles but the difference is 120 so there is still 70 miles to cover
<MASK>
Kudos [?]: 5 [0], given: 0
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
Senior Manager
Joined: 15 Feb 2005
Posts: 258
Location: Rockville
Followers: 1
Kudos [?]: 5 [0], given: 0
Two choices...
since this question doesnt clearly state whether they are heading in opposite directions towards each other or away from each other or in the same direction, its difficult to decide.
Since it isnt stated that they are going in opposite directions, and that is usually rare/less common in the speed problems
we have ption 1 in which they head towards each other...as Antmavel chose...this is usually what you see alot of on the
GMAT speed/distance/time problems.
Using the same process as Antmavel i too got 70 but now considering that NOTHING IS SAID about direction
the first inclination is that they are 120 miles apart heading in the same direction.
According to that hypothesis;
in an hour one moves 40 miles and the other 30, initial distance gets dropped to 110 miles, so every hour on the hour one car closes the gap by 10 miles.
From the meeting point the distance between them an hour before would be 10 miles (by the same logic)
since this is not a choice, they probably are going towards each other, either the author of the quesiton missed something or the question is badly phrased
SVP
Joined: 03 Jan 2005
Posts: 2322
Followers: 9
<MASK>
Rupstar wrote:
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
Good thinking. And there's the chance that they never meet if they both go the other direction. Although this means the question is not well defined, if you met a question like this in the test, you would have to work in the range that is given, in other words since 10 and infinite are not included in the choices you pick the only possible correct answer 70.
SVP
Joined: 25 Nov 2004
Posts: 1582
Followers: 4
Kudos [?]: 13 [0], given: 0
Rupstar wrote:
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
i agree with you. definitely a GMAT DS thinking.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5134
Location: Singapore
Followers: 9
Kudos [?]: 87 [0], given: 0
let n be the time taken for both cars to meet.
<MASK>
For the car travelling at 40km/h - would have covered 28 4/7 km
For the car travelling at 30km/h - would have covered 21 3/7 km
In total they cover 50km
<MASK>
Kudos [?]: 13 [0], given: 0
MA wrote:
Rupstar wrote:
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
i agree with you. definitely a GMAT DS thinking.
<MASK>
<UNMASK>
<MASK>
It is currently 21 May 2013, 17:28
# 2 cars are 120 miles apart.If both cars go at a constant
Author Message
TAGS:
Manager
Joined: 14 Dec 2004
Posts: 119
Followers: 1
Kudos [?]: 0 [0], given: 0
2 cars are 120 miles apart.If both cars go at a constant [#permalink] 06 Mar 2005, 18:46
2 cars are 120 miles apart.If both cars go at a constant speed with one of them going at 30/mph and the other 40/mph - how far apart will the 2 cars be in exactly 1 hour before they meet?
a. 35
b. 40
c. 70
d. 85
e. 90
SVP
Joined: 25 Nov 2004
Posts: 1582
Followers: 4
Kudos [?]: 13 [0], given: 0
Re: cars [#permalink] 06 Mar 2005, 19:11
do we need to calculate? because these cars go 70 miles/hour.
VP
Joined: 13 Jun 2004
Posts: 1135
Location: London, UK
Schools: Tuck'08
Followers: 5
<MASK>
c.70
first, both cars will meet :
40x + 30x = 120 ; x = 12/7h
means that 1h before they meet both cars would have driven 12/7-7/7 = 5/7h
for 40mp/h car -> 40*5/7 = 200/7
for 30mp/h car -> 30*5/7 = 150/7
they will drive for 50 miles but the difference is 120 so there is still 70 miles to cover
however, if you ignore the fact that there are 120 miles apart, you can find 70 considering that both cars begins at the same location, how far both cars will be from each other after 1h ? 30+40 = 70. I really assume it is a lucky number and that's pure coincidence. I can't see any other reason. I doubt this problem would be given on Gmat, or at least the lucky number would'nt be the real OA, they would have given 20 mph and 80mph driving 2hrs for exemple...they don't want you pick the easiest stupid number (1h and 30+40) an answer correctly to a more complex problem
Senior Manager
Joined: 15 Feb 2005
Posts: 258
Location: Rockville
Followers: 1
Kudos [?]: 5 [0], given: 0
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
Senior Manager
Joined: 15 Feb 2005
Posts: 258
Location: Rockville
Followers: 1
Kudos [?]: 5 [0], given: 0
Two choices...
since this question doesnt clearly state whether they are heading in opposite directions towards each other or away from each other or in the same direction, its difficult to decide.
Since it isnt stated that they are going in opposite directions, and that is usually rare/less common in the speed problems
we have ption 1 in which they head towards each other...as Antmavel chose...this is usually what you see alot of on the
GMAT speed/distance/time problems.
Using the same process as Antmavel i too got 70 but now considering that NOTHING IS SAID about direction
the first inclination is that they are 120 miles apart heading in the same direction.
According to that hypothesis;
in an hour one moves 40 miles and the other 30, initial distance gets dropped to 110 miles, so every hour on the hour one car closes the gap by 10 miles.
From the meeting point the distance between them an hour before would be 10 miles (by the same logic)
since this is not a choice, they probably are going towards each other, either the author of the quesiton missed something or the question is badly phrased
SVP
Joined: 03 Jan 2005
Posts: 2322
Followers: 9
<MASK>
Rupstar wrote:
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
Good thinking. And there's the chance that they never meet if they both go the other direction. Although this means the question is not well defined, if you met a question like this in the test, you would have to work in the range that is given, in other words since 10 and infinite are not included in the choices you pick the only possible correct answer 70.
SVP
Joined: 25 Nov 2004
Posts: 1582
Followers: 4
Kudos [?]: 13 [0], given: 0
Rupstar wrote:
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
i agree with you. definitely a GMAT DS thinking.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5134
Location: Singapore
Followers: 9
Kudos [?]: 87 [0], given: 0
let n be the time taken for both cars to meet.
<MASK>
For the car travelling at 40km/h - would have covered 28 4/7 km
For the car travelling at 30km/h - would have covered 21 3/7 km
In total they cover 50km
<MASK>
Kudos [?]: 13 [0], given: 0
MA wrote:
Rupstar wrote:
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
i agree with you. definitely a GMAT DS thinking.
I am withdrawing my previous statement because the question mentioned "MEET". if these cars are meeting after 1 hour they must be travelling towards each other because their speeds do not allow them to travel in the same direction.
Similar topics Replies Last post
Similar
Topics:
A car traveling at a certain constant speed takes 2 seconds 13 02 Feb 2005, 22:41
A car traveling at a certain constant speed takes 2 seconds 4 25 Apr 2006, 12:38
Q28: A car traveling at a certain constant speed takes 2 3 05 Jun 2007, 20:40
A car traveling at a certain constant speed takes 2 seconds 6 19 Jan 2008, 07:11
A car traveling at a certain constant speed takes 2 seconds 2 23 Sep 2008, 07:00
Display posts from previous: Sort by
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<MASK>
It is currently 21 May 2013, 17:28
# 2 cars are 120 miles apart.If both cars go at a constant
Author Message
TAGS:
Manager
Joined: 14 Dec 2004
Posts: 119
Followers: 1
Kudos [?]: 0 [0], given: 0
2 cars are 120 miles apart.If both cars go at a constant [#permalink] 06 Mar 2005, 18:46
2 cars are 120 miles apart.If both cars go at a constant speed with one of them going at 30/mph and the other 40/mph - how far apart will the 2 cars be in exactly 1 hour before they meet?
a. 35
b. 40
c. 70
d. 85
e. 90
SVP
Joined: 25 Nov 2004
Posts: 1582
Followers: 4
Kudos [?]: 13 [0], given: 0
Re: cars [#permalink] 06 Mar 2005, 19:11
do we need to calculate? because these cars go 70 miles/hour.
VP
Joined: 13 Jun 2004
Posts: 1135
Location: London, UK
Schools: Tuck'08
Followers: 5
<MASK>
c.70
first, both cars will meet :
40x + 30x = 120 ; x = 12/7h
means that 1h before they meet both cars would have driven 12/7-7/7 = 5/7h
for 40mp/h car -> 40*5/7 = 200/7
for 30mp/h car -> 30*5/7 = 150/7
they will drive for 50 miles but the difference is 120 so there is still 70 miles to cover
however, if you ignore the fact that there are 120 miles apart, you can find 70 considering that both cars begins at the same location, how far both cars will be from each other after 1h ? 30+40 = 70. I really assume it is a lucky number and that's pure coincidence. I can't see any other reason. I doubt this problem would be given on Gmat, or at least the lucky number would'nt be the real OA, they would have given 20 mph and 80mph driving 2hrs for exemple...they don't want you pick the easiest stupid number (1h and 30+40) an answer correctly to a more complex problem
Senior Manager
Joined: 15 Feb 2005
Posts: 258
Location: Rockville
Followers: 1
Kudos [?]: 5 [0], given: 0
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
Senior Manager
Joined: 15 Feb 2005
Posts: 258
Location: Rockville
Followers: 1
Kudos [?]: 5 [0], given: 0
Two choices...
since this question doesnt clearly state whether they are heading in opposite directions towards each other or away from each other or in the same direction, its difficult to decide.
Since it isnt stated that they are going in opposite directions, and that is usually rare/less common in the speed problems
we have ption 1 in which they head towards each other...as Antmavel chose...this is usually what you see alot of on the
GMAT speed/distance/time problems.
Using the same process as Antmavel i too got 70 but now considering that NOTHING IS SAID about direction
the first inclination is that they are 120 miles apart heading in the same direction.
According to that hypothesis;
in an hour one moves 40 miles and the other 30, initial distance gets dropped to 110 miles, so every hour on the hour one car closes the gap by 10 miles.
From the meeting point the distance between them an hour before would be 10 miles (by the same logic)
since this is not a choice, they probably are going towards each other, either the author of the quesiton missed something or the question is badly phrased
SVP
Joined: 03 Jan 2005
Posts: 2322
Followers: 9
<MASK>
Rupstar wrote:
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
Good thinking. And there's the chance that they never meet if they both go the other direction. Although this means the question is not well defined, if you met a question like this in the test, you would have to work in the range that is given, in other words since 10 and infinite are not included in the choices you pick the only possible correct answer 70.
SVP
Joined: 25 Nov 2004
Posts: 1582
Followers: 4
Kudos [?]: 13 [0], given: 0
Rupstar wrote:
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
i agree with you. definitely a GMAT DS thinking.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5134
Location: Singapore
Followers: 9
Kudos [?]: 87 [0], given: 0
let n be the time taken for both cars to meet.
<MASK>
For the car travelling at 40km/h - would have covered 28 4/7 km
For the car travelling at 30km/h - would have covered 21 3/7 km
In total they cover 50km
<MASK>
Kudos [?]: 13 [0], given: 0
MA wrote:
Rupstar wrote:
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
i agree with you. definitely a GMAT DS thinking.
I am withdrawing my previous statement because the question mentioned "MEET". if these cars are meeting after 1 hour they must be travelling towards each other because their speeds do not allow them to travel in the same direction.
Similar topics Replies Last post
Similar
Topics:
A car traveling at a certain constant speed takes 2 seconds 13 02 Feb 2005, 22:41
A car traveling at a certain constant speed takes 2 seconds 4 25 Apr 2006, 12:38
Q28: A car traveling at a certain constant speed takes 2 3 05 Jun 2007, 20:40
A car traveling at a certain constant speed takes 2 seconds 6 19 Jan 2008, 07:11
A car traveling at a certain constant speed takes 2 seconds 2 23 Sep 2008, 07:00
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It is currently 21 May 2013, 17:28
# 2 cars are 120 miles apart.If both cars go at a constant
Author Message
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Manager
Joined: 14 Dec 2004
Posts: 119
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2 cars are 120 miles apart.If both cars go at a constant [#permalink] 06 Mar 2005, 18:46
2 cars are 120 miles apart.If both cars go at a constant speed with one of them going at 30/mph and the other 40/mph - how far apart will the 2 cars be in exactly 1 hour before they meet?
a. 35
b. 40
c. 70
d. 85
e. 90
SVP
Joined: 25 Nov 2004
Posts: 1582
Followers: 4
Kudos [?]: 13 [0], given: 0
Re: cars [#permalink] 06 Mar 2005, 19:11
do we need to calculate? because these cars go 70 miles/hour.
VP
Joined: 13 Jun 2004
Posts: 1135
Location: London, UK
Schools: Tuck'08
Followers: 5
Kudos [?]: 14 [0], given: 0
c.70
first, both cars will meet :
40x + 30x = 120 ; x = 12/7h
means that 1h before they meet both cars would have driven 12/7-7/7 = 5/7h
for 40mp/h car -> 40*5/7 = 200/7
for 30mp/h car -> 30*5/7 = 150/7
they will drive for 50 miles but the difference is 120 so there is still 70 miles to cover
however, if you ignore the fact that there are 120 miles apart, you can find 70 considering that both cars begins at the same location, how far both cars will be from each other after 1h ? 30+40 = 70. I really assume it is a lucky number and that's pure coincidence. I can't see any other reason. I doubt this problem would be given on Gmat, or at least the lucky number would'nt be the real OA, they would have given 20 mph and 80mph driving 2hrs for exemple...they don't want you pick the easiest stupid number (1h and 30+40) an answer correctly to a more complex problem
Senior Manager
Joined: 15 Feb 2005
Posts: 258
Location: Rockville
Followers: 1
Kudos [?]: 5 [0], given: 0
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
Senior Manager
Joined: 15 Feb 2005
Posts: 258
Location: Rockville
Followers: 1
Kudos [?]: 5 [0], given: 0
Two choices...
since this question doesnt clearly state whether they are heading in opposite directions towards each other or away from each other or in the same direction, its difficult to decide.
Since it isnt stated that they are going in opposite directions, and that is usually rare/less common in the speed problems
we have ption 1 in which they head towards each other...as Antmavel chose...this is usually what you see alot of on the
GMAT speed/distance/time problems.
Using the same process as Antmavel i too got 70 but now considering that NOTHING IS SAID about direction
the first inclination is that they are 120 miles apart heading in the same direction.
According to that hypothesis;
in an hour one moves 40 miles and the other 30, initial distance gets dropped to 110 miles, so every hour on the hour one car closes the gap by 10 miles.
From the meeting point the distance between them an hour before would be 10 miles (by the same logic)
since this is not a choice, they probably are going towards each other, either the author of the quesiton missed something or the question is badly phrased
SVP
Joined: 03 Jan 2005
Posts: 2322
Followers: 9
Kudos [?]: 157 [0], given: 0
Rupstar wrote:
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
Good thinking. And there's the chance that they never meet if they both go the other direction. Although this means the question is not well defined, if you met a question like this in the test, you would have to work in the range that is given, in other words since 10 and infinite are not included in the choices you pick the only possible correct answer 70.
SVP
Joined: 25 Nov 2004
Posts: 1582
Followers: 4
Kudos [?]: 13 [0], given: 0
Rupstar wrote:
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
i agree with you. definitely a GMAT DS thinking.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5134
Location: Singapore
Followers: 9
Kudos [?]: 87 [0], given: 0
let n be the time taken for both cars to meet.
Then 40n + 30n = 120
n = 12/7
Since we want the distance 1 hr before they meet, the cars must have travelled for 5/7 hour
For the car travelling at 40km/h - would have covered 28 4/7 km
For the car travelling at 30km/h - would have covered 21 3/7 km
In total they cover 50km
So they are now 120-50 = 70km apart.
SVP
Joined: 25 Nov 2004
Posts: 1582
Followers: 4
Kudos [?]: 13 [0], given: 0
MA wrote:
Rupstar wrote:
Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer
i agree with you. definitely a GMAT DS thinking.
I am withdrawing my previous statement because the question mentioned "MEET". if these cars are meeting after 1 hour they must be travelling towards each other because their speeds do not allow them to travel in the same direction.
Similar topics Replies Last post
Similar
Topics:
A car traveling at a certain constant speed takes 2 seconds 13 02 Feb 2005, 22:41
A car traveling at a certain constant speed takes 2 seconds 4 25 Apr 2006, 12:38
Q28: A car traveling at a certain constant speed takes 2 3 05 Jun 2007, 20:40
A car traveling at a certain constant speed takes 2 seconds 6 19 Jan 2008, 07:11
A car traveling at a certain constant speed takes 2 seconds 2 23 Sep 2008, 07:00
Display posts from previous: Sort by
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<MASK>
## Is 50 a perfect square?
<MASK>
18 is not a perfect square.
<MASK>
Definition of Perfect Squares: The product of a whole number multiplied by itself. square because it can be written as 52 • Perfect Squares – 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, . . .
<MASK>
<UNMASK>
<MASK>
## Is 50 a perfect square?
<MASK>
18 is not a perfect square.
<MASK>
Definition of Perfect Squares: The product of a whole number multiplied by itself. square because it can be written as 52 • Perfect Squares – 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, . . .
<MASK>
## What are 5 perfect squares?
<MASK>
|
<MASK>
## Is 50 a perfect square?
<MASK>
18 is not a perfect square.
<MASK>
Definition of Perfect Squares: The product of a whole number multiplied by itself. square because it can be written as 52 • Perfect Squares – 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, . . .
<MASK>
## What are 5 perfect squares?
<MASK>
<UNMASK>
# Question: What Does A Perfect Square Mean?
## Is 50 a perfect square?
<MASK>
## Which items are perfect square?
<MASK>
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, … 2, 5, 8, 10, 13, 17, 18, 20, 25, 26, 29, 32, … 50, 65, 85, 125, 130, 145, 170, 185, 200, … 3, 6, 9, 11, 12, 14, 17, 18, 19, 21, 22, 24, …
## IS 300 a perfect square?
<MASK>
## Is 18 a perfect square?
18 is not a perfect square.
<MASK>
500 is not a perfect square.
<MASK>
Definition of Perfect Squares: The product of a whole number multiplied by itself. square because it can be written as 52 • Perfect Squares – 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, . . .
<MASK>
## What number is a perfect square?
<MASK>
## What are 5 perfect squares?
<MASK>
A number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. Here, the square root of 400 is 20. Therefore, the square root of 400 is an integer, and as a consequence 400 is a perfect square.
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