Fractions
Adding and subtracting fractions with unlike denominators
None
Subtracting fractions: different denominators
If you conquered adding fractions with different denominators, then subtracting fractions will be a snap. Don't worry...we'll take it slow and explain every step.
Discussion and questions for this video
 Let's figure out 7/12 minus 6/13.
 And in order to be able to do this,
 we need to find a common denominator.
 We notice that they're not common right over here.
 Here, the denominator is 12.
 Here, it is 13.
 And the common denominator is going
 to be the least common multiple of 12 and 13.
 And 12 and 13 share no common factors other than 1,
 so their least common multiple is actually
 just going to be 12 times 13.
 Actually, I'm just going to leave
 it written as 12 times 13.
 So let's first try to rewrite this right over here.
 And I'll do the denominator first.
 So 7/12.
 Instead of the denominator being 12,
 I'm going to write it as 12 times 13.
 Well, if we multiply the denominator by 13 in order
 to not change the value of the fraction,
 we need to multiply the numerator times 13.
 So notice, all I did is I multiplied
 the numerator and the denominator
 by the same number that's equivalent to just multiplying
 it by 13/13, or 1.
 And so this is still equivalent to 7/12.
 Similarly let me do this one in blue right over here
 the common denominator, we want is 12 times 13.
 So here in the denominator, we multiply
 let me now write it as 13 times 12.
 13 times 12.
 Well, if we multiply the denominator by 12,
 we have to multiply the numerator by 12 as well.
 So I'll write the numerator as 6 times 12.
 Notice, here we multiplied the numerator and the denominator
 by 13.
 Here, we multiplied the numerator and the denominator
 by 12.
 How did I know to multiply this by 12?
 Well, the common denominator is 13 times 12.
 So here, I multiplied the denominator by 12
 so I have do the numerator by 12.
 The common denominator here is 13 times 12.
 But here, I had to multiply it by 13 to get it,
 so I have to multiply the numerator by 13 as well.
 But now we are ready to subtract.
 You might say, hey, Sal.
 Hold on.
 Wait, what do these actually evaluate to?
 Well, maybe that's a good idea.
 Let's figure that out first .
 So this is equal to 7 times 13.
 Let's see, 7 times 13 is 70 plus 21.
 It's 91 over 12 times 13.
 Let's see, I haven't memorized my 13 times tables.
 So we know that 12 times 12 is 144.
 You put on one more 12, you get to 156.
 156.
 So 91/156 is the exact same thing as 7/12.
 I just multiplied the numerator and denominator by 13.
 And from that we are going to subtract 6 times 12.
 6 times 12 is 72.
 72 over.
 Well, we already figured out what 12 times 13 is
 or what 13 times 12 is.
 It is 156.
 And now that we have a common denominator,
 we can rewrite this as being equal to 91 minus 72 over 156.
 I'll just write that in a neutral color, over 156.
 Let's see, if it was 92 minus 72, it would be 20.
 That's 1 less, so it's going to be 19/156.
 So this is going to be equal to 19/156.
 And as far as I can tell, let's see.
 19 does not go into 156.
 Let me just make sure of that, that somehow, magically, 156
 isn't a multiple of 19 so I could simplify this.
 So let's see, 19 is almost 20.
 So maybe, let's see if it will go 7 times.
 7 times 9 is 63.
 7 times 1 is 7.
 Plus 6 is 13.
 Let's see the difference here.
 Actually, I could have gone in one more time.
 So let's do it eight times.
 8 times 9 is 72.
 8 times 1 is 8.
 Plus 7 is 15.
 Yeah, you have a remainder here.
 So this doesn't go evenly.
 This isn't divisible by 19.
 And they don't share any other common factors,
 so we've simplified it about as much as we can.
 This is equal to 19/156.
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?

Have something that's not a question about this content? 
This discussion area is not meant for answering homework questions.
Does the method that Sal used to add fractions work for subtracting fractions?
Yes, but know that either way, the denominator has to be the same!
yeah, but I have found adding to be much easier.
you cant bwahaha
yes.but I have found adding to be much easier.
yes but either way it works
yes but when the denominators are the same its a different story.when the denominators are the same u dont add them u leave them
Yes at 0:24 it is the same method
How would I subtract a number with a larger numerator from a number with a smaller numerator if they have unlike denominators? I was at work and somehow the subject of doing this came up, and it's been bugging me. 8/9  11/7? Would I have to first make the improper fraction into a mixed number? If so, where would I go from there? The last time I had to do this kind of stuff was in 5th grade, and it didn't exactly stick with me.
You do not have to convert 11/7 into a mixed number, however you still must find the common denominator.
Excuse me I have a question
i kind of get it
Good for you :)
But Kind of isn't good enough. Need help?
But Kind of isn't good enough. Need help?
buiawrio;sdgtrjio;
where did he get the 21 from on 2:10?
That's just him adding breaking up the thirteen and multiplying them separately. He then added them to get that answer.
my name is jeff and im 21
I dont understand
What do you not understand? :)
Try watching the video again slowly, taking notes (if that helps you). As your parents for help, and you can ask more specific questions here.
How do you multiply with different denominators?
you just multiply them like 2/5 x 3/6= 6/30
unless ur in 5 grade
1 1/2  5/8 =
i really don't get this stuff ... Can anyone and Anyway somebody could help me , and i need a coach..... ?
7/8 is the answer to 1 1/2  5/8
i think it needs more points at the end of the video because it wastes peoples time of there day to watch the video
when is the real math going to start
The video will not start why?
or refresh the page :)
can't you simiplify
this is really confusing me, can somebody help?
When you are subtracting (or adding) fractions with different denominators, you must first get them to a common denominator. You change the denominator for a fraction by multiplying by some number over itself (for example 5/5).
Let's consider an example
3/4  5/8
First step is to find a common denominator to use. In this case, it's pretty easy because 2*4=8. To change 3/4 into some number of 8ths, we multiply by 2/2. (You can always multiply by 1 and 2/2 is a special way of writing 1.)
2/2*3/4  5/8
Now you can distribute and multiply to get a difference of two fractions with the same denominator:
(2*3) / (2*4)  5/8 = 6/8  5/8
And solve:
6/8  5/8 = (65)/8 = 1/8
It gets harder when you have things like 5/123/8. If you are stuck finding a common denominator, you can always multiply the first fraction by the second denominator over itself and vice versa:
5/123/8= 8/8 * 5/12  3/8 * 12/12 = (8*5)/(12*8)  (3*12)/(8*12) = 40/96  36/96=4/96
4/96 simplifies down to 1/24
You could also solve the above problem using 24 as the denominator throughout by multiplying by 2/2*5/12 and 3/3*3/8.
I hope this helps make it less confusing. [If so, vote :). If not, please ask a clarifying question]
Let's consider an example
3/4  5/8
First step is to find a common denominator to use. In this case, it's pretty easy because 2*4=8. To change 3/4 into some number of 8ths, we multiply by 2/2. (You can always multiply by 1 and 2/2 is a special way of writing 1.)
2/2*3/4  5/8
Now you can distribute and multiply to get a difference of two fractions with the same denominator:
(2*3) / (2*4)  5/8 = 6/8  5/8
And solve:
6/8  5/8 = (65)/8 = 1/8
It gets harder when you have things like 5/123/8. If you are stuck finding a common denominator, you can always multiply the first fraction by the second denominator over itself and vice versa:
5/123/8= 8/8 * 5/12  3/8 * 12/12 = (8*5)/(12*8)  (3*12)/(8*12) = 40/96  36/96=4/96
4/96 simplifies down to 1/24
You could also solve the above problem using 24 as the denominator throughout by multiplying by 2/2*5/12 and 3/3*3/8.
I hope this helps make it less confusing. [If so, vote :). If not, please ask a clarifying question]
what do you mean
At 0:44 why does Sal use a dot instead of the multiplication sign? We aren't doing algebra , are we?
When you get into algebra, and you use "x", it is confusing to use the multiplication symbol, so they turn it into a dot. Or sometimes we even leave it out!
The dot is a multiplication sign
A dot is the same thing as a multiplication symbol, but a lot of people use that instead so that way they don't confuse themselves.You may not want to use it, but he does it so he doesn't confuse himself.
5/2  3/4 = ?
First, use common denominators. 5/2 is 10/4, and we change it.
Now, 10/43/4. Subtract the numerators and keep the denominators to get 7/4.
Hope this helps!
Now, 10/43/4. Subtract the numerators and keep the denominators to get 7/4.
Hope this helps!
this is very easy if you are
Is this helpful if you want to be a engineer?
madison.tippett, yes it will be helpful if you want to be an engineer.
How to subtract mixed numbers
You can just scroll down on your dashboard and add "adding and subtracting mixed numbers" there is also a video on it
Why do you have to make the denominators the same? Can't you just subtract the numerators and the denominators?
You can't subtract fractions that have different denominators because the fractions are different so you have to make the denominators same.
do you have to multiply by 12?
yes you have to because if the denominators are not the same number it will be difficult to do the problem
Why do you have to make the denominaters the same
u have to do that in order to answer the question.If u dont find the LCD or the common denominator then ur answer would be wrong
You do that so you can add/subtract. You can't add/subtract if it isn't the same denominator. You'd get a pretty messed up answer if you didn't.
is it a must to change improper fraction to a mix fraction?
I guess the answer depends on what you mean by must. Mathematically speaking, you do not need to, improper numbers are no different than the equivalent mixed fraction. Ex 5/2 = 2 1/2 For the purpose of working through problems, improper fractions usually make work easier. So for this reason you will often have answers expressed in improper fractions. Unless your teacher or Khan academy asks you to change it to a mixed fraction, there is no need to take this extra step (but it is still useful to know how sense in daily life we use mixed fractions to express quantities more frequently).
it depends!if the question is asking u to change an improper to a mixed then yes u probably have to change it
Pls suggest to subtract 7/10 from 11/12
do you do this method Sal to the addition,subtraction and,multiplication?
for subtraction and addition.. yes but in multiplication its a different story.U have to multiply the numerators instead and u have to change the denominators sometimes
That's a good method, but it takes too long, I mean you have to solve many problems in order to solve one, is there another way?
i dont rlly think there is another way to answer it
What if one of the numerators are equal to each and make zero what would happen then?
how do I get like a 100 on all my math teas then
tis is REALLY confusing
no it isent. it is helpful
i Agree this i s avery complicated video
yes, very very confusing!
Can you use the up and down way while subtracting fractions? 9
Also can you do it an easier way? + 8
______
17
Also can you do it an easier way? + 8
______
17
For your 1st question, yes, and the 2nd one..well in my opinion long way is easier.
So all you have to do is multiply then subtract? Would that be mathmatically correct or still wrong?
it would be mathematically correct
do we always have to do it that way?.
yes.this is the only way to do it!!
Is there an easier, less complicated way to do this?
Yes.
example: 1/21/4=?
Explanation: do this
2X2=4 1X2=2
Easier way: 2/41/4
Hope i Helped you
example: 1/21/4=?
Explanation: do this
2X2=4 1X2=2
Easier way: 2/41/4
Hope i Helped you
That's really complicated. Is there by any chance an easier/simpler way to do this?
At 2:44, where did he get 72 from?
He does it so visual learners can understand better
6 * 12.
Watch his colors. He has broken the different pieces up by color.
Watch his colors. He has broken the different pieces up by color.
I really still don't get it...
http://www.mathsisfun.com/fractions_subtraction.html
It explains how to subtract unlike and like denominator fractions.
It explains how to subtract unlike and like denominator fractions.
whats 9 plus 10
21. NO! 19. 21 if ur stopid and 19 if ur a nerd
are you the owner on KHAN!
The person talking in the video (which is Sal Khan) is the owner of Khan Academy
Can't you just check if the numerator is prime? that way you wouldn't have to divide 19 into 156.
Of course you can! But most people don't know prime numbers after 101 . . . and it's usually a factorable number anyway.
i was doing my homework and i got all of them doing that tecneek
it is kind of confusing for me
nevermind i get it now
at 0:43 why did he put the dots as multiplication signs if there is no algebra?
It doesn't have to be algebra when you are using dots as multiplication signs. You can sue a dot as the sign anywhere in a multiplication problem, its just that most people use an x as the multiplication sign before they reach algebra.
this is every thing I new I thot you were better.
how come when i was doing the question with him i got a repating dectimal
could you explain the whole prossess of this and vote on it
thank you and sorry for bad spelling
The way it compares cause it is all math and it is fractions just sith diffrend botton numbers
What if the numerator is lower than what you are subtracting by like 5/10  8/17? Please help!
20140213T16:18:05Z
by
Anonymous
Well, in this example you will need to find a common denominator. For simplicity we will use 170. So the problem you gave really comes out to 85/170  80/170. The answer becomes 5/170 or 1/34.
If you mean what happens when the fraction that you are subtracting by is lower than the other fraction, well, then you would have a negative answer.
If you mean what happens when the fraction that you are subtracting by is lower than the other fraction, well, then you would have a negative answer.
do you add the top number of the fraction first or the bottom first
yeah its confusing if u don't do one with an lcm
you probably dont know the answer
And what if a fraction has a numerator bigger than the denominator. For example. 6/2  7/4?
You would do that in pretty much the same way.
What if the number is improper?
If the fraction is improper you turn it into a mixed number
I still don't understand it.
Basically, you just need to make this problem that you don't know how to solve into one that you do know how to solve. You just need to make the denominators (the bottom numbers) the same.
EX: 1/2  2/4
STEP 1) We know that 2 is half of 4, so 2/4 is actually just 1/2.
STEP 2) 1/2  1/2 = 0
I hope this helps!
EX: 1/2  2/4
STEP 1) We know that 2 is half of 4, so 2/4 is actually just 1/2.
STEP 2) 1/2  1/2 = 0
I hope this helps!
6 3/12  3 9/36
you have to make the denominators "like" before you can do anything else. you have to find the LCM (Lowest Common Multiple) which makes the denominators equal. hope this is of any help to you :)
How do you solve a fraction with one whole number and the other number another fraction Ex: 1 and 3/20 9/10?
1 3/20 is same as 20/20 + 3/20 which makes 23/20, now substracting 9/10 can be by giving the same nominator, so 9/10 is same as 18/20, 23/20  18/20 = 5/20 = 1/4
If at an election 6/9 of the members voted and there are 171 members how many people actually voted? Not sure how to work this problem.
I don't get it can someone explain it?
Shure be glad too say we need to subtract 1/2 1/4 first we need to get them to the same denominator by multiplying the numerator and the denominator by 2 to get 2/41/4 which is now a very simple fraction problem.
Hope this helped.
and good luck.
Hope this helped.
and good luck.
How do you earn a testla badge
check this out for how to earn the black hole badges
https://www.khanacademy.org/cs/whatintheworldareblackholebadges/5449570030977024
https://www.khanacademy.org/cs/whatintheworldareblackholebadges/5449570030977024
I believe you have to earn 10,000,000 energy points to get a Tesla badge. Obviously, that requires a whole load of effort and constant learning, and so not many people on Khan Academy have the badge. As for the other black hole badges, I have no idea.
well for thelove off pizza, of course you need to get the lowest common denominator, it says it in the title
*of*
Yeah, he's *explaining* it to others.
Yeah, he's *explaining* it to others.
How do you add and subtract positive and negative fractions with different denominators
thank you so much
Hi Justin,
Anytime you are adding or subtracting fractions, you first have to come up with a common denominator. So if you have something like:
1/2 + 3/5
you first have to figure out a common denominator for both fractions. In this case, 10 would be a good common denominator so we would have:
(5/5)(1/2) + (2/2)(3/5)
5/10 + 6/10
At this point, we could combine the numerators over a single denominator
(5 + 6)/10
Then add or subtract the numerators: 5 + 6 = 1
So our answer would be 1/10
Hope that helps!
Anytime you are adding or subtracting fractions, you first have to come up with a common denominator. So if you have something like:
1/2 + 3/5
you first have to figure out a common denominator for both fractions. In this case, 10 would be a good common denominator so we would have:
(5/5)(1/2) + (2/2)(3/5)
5/10 + 6/10
At this point, we could combine the numerators over a single denominator
(5 + 6)/10
Then add or subtract the numerators: 5 + 6 = 1
So our answer would be 1/10
Hope that helps!
why is it that big of a number, when ur just subtracting those little number... it's like your adding instead of subtracting!
don't know bro
If you are having trouble with this, you may want to go back and review the factors and multiples section as all of that content is key to understanding how and why things are done this way.
https://www.khanacademy.org/math/arithmetic/factorsmultiples
https://www.khanacademy.org/math/arithmetic/factorsmultiples
I don't understand this at all can some one please explain this to me?
Hello Hannah, if you find yourself frustrated or confused by a topic or what Sal says in the video, you may try either:
1) rewatching the video, pausing and repeating confusing parts
2) reading through the questions and answers in here (some might contain the little bit you're missing)
3) asking specific questions about what you don't understand
Good luck!
1) rewatching the video, pausing and repeating confusing parts
2) reading through the questions and answers in here (some might contain the little bit you're missing)
3) asking specific questions about what you don't understand
Good luck!
How do you figure out 4 cups of flour and you need to use 1 3/4 cups for a recipe. How much do you have left?
We can make that problem easier by estimating a bit to get the whole number portion of the question out of the way. We know you are using 1 whole cup and part of another, so lets round up to 2 cups being used and subtract them from the initial 4 cups, which means that we know for sure there are at least 2 whole cups remaining.
After taking those off the question is now how much is left of the remaining 2 cups if we take 1 3/4 cup away. We can subtract out that whole cup used from both values leaving us with 1 cup  3/4 cup which is a much easier problem to figure out.
We then take the answer to that and add it back in with the other 2 whole cups we had already determined would be left over.
After taking those off the question is now how much is left of the remaining 2 cups if we take 1 3/4 cup away. We can subtract out that whole cup used from both values leaving us with 1 cup  3/4 cup which is a much easier problem to figure out.
We then take the answer to that and add it back in with the other 2 whole cups we had already determined would be left over.
Can you talk a little bit more happy
i still do not get it like 9/123/24
Make sure the denominators are equal. What times 12 equals 24?
Is there any simpler way to do this?
is there a easier way to multiply the denominator?
i don't think so
😲what happens if the denominator?do you need to add/subtract both of the denominator?😵
the denominator is something you do not change you only do the top number?
yep. the denominator and the other ones too
That is correct :)
it is depend all on multiplication ,division,subtraction and addition
What if the numerator for the first fraction has a greater number than the second fraction? 21>5
Saying 21 is the first fraction over whatever it could be, and it's subtracting.
Saying 21 is the first fraction over whatever it could be, and it's subtracting.
If i find the common numerator and do it, do I get the same answer?
No, you do not get the same answer.
thank you now I understand!
is there any shorter ways to find the common denominator
i dont get anything about this concept. :(
Try watching the video more carefully.
what if you want to subtract a number like 1/41/3 where they have a LCM but the first number is smaller than the second number is it just a negative, thx
How? im confused
first we should multiply the numerator of first fraction to the denominator of second fraction.then multiply second fraction's numerator to the first fraction's denominator.then multiply both fractions denominator.
for example : 2/5  6/3 = 6/15 30/15 = 24/15
for example : 2/5  6/3 = 6/15 30/15 = 24/15
I still don't know whats going on
why do we make the steps that we make
its not that complicated
at 1:00 he says that the denominator is 12x13. How/why?
I liked this video but on I was wondering if you could show me subtracting fractions with different denominators vertically
how do you subtract a fraction like this 3 5/6  1 6/7 ?
Change 16/7 to a mixed number which is 2 2/7, then find an equal denominator and finally subtract.
Your really good at math
Why do we need to do to numerator that you did in the denominator? ( multiplication)
Isn't there a easier way of doing this? Because I thought all we have to do is find the least common denominator then multiply that with the numerator, finally we add them and then we have the answer. I s that not correct?
why do you figure out the number relating to both 13 and 12 in multiplication
Ok, basically in order to subtract the fractions they have to have identical denominators. In order to do that he is multiplying the numerator and denominator of one fraction by the denominator of the other. You can keep a fraction as having the same value as long as it is multiplied by 1. Any number divided by itself is 1, so 12/12 = 1 and 13/13 is 1. He doesn't simplify it into that of course just so he can actually perform the subtraction
```
7 6
  
12 13
Multiply both of the fractions by 1
7 1 6 1
 X    X 
12 1 13 1
I'm just going to do each one individually for the moment
7 7 1 7 13 7 X 13 91
 =  X  =  X  =  = , I did the 13/13 as that's the denominator of the other fraction
12 12 1 12 13 12 X 13 156
6 6 1 6 12 6 X 12 72
 =  X  =  X  =  = , I did the 13/13 as that's the denominator of the other fraction
13 13 1 13 12 13 X 12 156
Going back to the problem
7 6 7 X 13 6 X 12 91 72 91  72 19
   =    =    =  = 
12 13 12 X 13 13 X 12 156 156 156 156
```
```
7 6
  
12 13
Multiply both of the fractions by 1
7 1 6 1
 X    X 
12 1 13 1
I'm just going to do each one individually for the moment
7 7 1 7 13 7 X 13 91
 =  X  =  X  =  = , I did the 13/13 as that's the denominator of the other fraction
12 12 1 12 13 12 X 13 156
6 6 1 6 12 6 X 12 72
 =  X  =  X  =  = , I did the 13/13 as that's the denominator of the other fraction
13 13 1 13 12 13 X 12 156
Going back to the problem
7 6 7 X 13 6 X 12 91 72 91  72 19
   =    =    =  = 
12 13 12 X 13 13 X 12 156 156 156 156
```
Wouldn't it just be easier to do to find the LCD first??
How did you get the 13
Just a question, if the answer is like 44/28 what do you do?
If the answer is 44/28 you will need to think, how many times does 44 go into 28? the answer is 1 remainder 16 so now you have two fractions, 28/28 and 16/28. now we can change 28/28 into 1, making the number 1&16/28
First, you divide 44/28 on both sides by their GCF, which is 4. 44/4 is 11 and 28/4 is 7.
So, the simplified fraction is 11/7, or 1 4/7.
So, the simplified fraction is 11/7, or 1 4/7.
You have to simplify. Khan Academy will accept an improper fraction if it is in simplest form. Divide both the top and bottom by a common factor  try 4 and you get 11/7.
You can also change to a mixed number 1 4/7.
Hope this helps.
You can also change to a mixed number 1 4/7.
Hope this helps.
Is it that odd and even numbers don't share a common denominator? Or I am wrong
Some do share a common denominator for instance 2&5 do share a common denominator 10 sorry again 4 the confusion.
I don't really get how to simplify a fraction how do you do it?
find the lowest common factor
you have to find the lcm (lowest common factor) of the dinominator and numerator. now divide numerator and dinominator with the lcm.
example 5/10
lcm of 5 and 10 is 5
so 5/5=1
10/5=2
the answer is 1/2
example 5/10
lcm of 5 and 10 is 5
so 5/5=1
10/5=2
the answer is 1/2
you could see what number goes into both numerator and denominator and see how many times each number goes into it .
here is an example;
6/103/4= k
k= _
10 & 4 have common multiples and one is 40.
so it is something over 40
ok so since you multiplied the denominator of 6/10 by 4 you have to multiply the numerator by 10! o it would be 24/40_
i think you get it now, don't you?
6/103/4= k
k= _
10 & 4 have common multiples and one is 40.
so it is something over 40
ok so since you multiplied the denominator of 6/10 by 4 you have to multiply the numerator by 10! o it would be 24/40_
i think you get it now, don't you?
why did people make khan acedemy
Are you trolling/joking? To help people learn...
I still don't get it. How do you do it? We are learning about it at school! Help!
i don't get it
if one or two of the denominators are odd do you just multiply the two?