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.

Subtracting fractions: different denominators

Discussion and questions for this video
Does the method that Sal used to add fractions work for subtracting fractions?
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.
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 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 = (6-5)/8 = 1/8

It gets harder when you have things like 5/12-3/8. If you are stuck finding a common denominator, you can always multiply the first fraction by the second denominator over itself and vice versa:

5/12-3/8= 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]
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!
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.
yes you have to because if the denominators are not the same number it will be difficult to do the problem
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
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).
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?
What if one of the numerators are equal to each and make zero what would happen then?
Can you use the up and down way while subtracting fractions? 9
Also can you do it an easier way? + 8
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?
example: 1/2-1/4=?
Explanation: do this
2X2=4 1X2=2
Easier way: 2/4-1/4
Hope i Helped you
That's really complicated. Is there by any chance an easier/simpler way to do this?
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.
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.
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
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!
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.
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.
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!
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.
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 2/4-1/4 which is now a very simple fraction problem.
Hope this helped.
and good luck.
How do you add and subtract positive and negative fractions with different denominators
why is it that big of a number, when ur just subtracting those little number... it's like your adding instead of subtracting!
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!
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.
😲what happens if the denominator?do you need to add/subtract both of the denominator?😵
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.
what if you want to subtract a number like 1/4-1/3 where they have a LCM but the first number is smaller than the second number is it just a negative, thx
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
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
Change 16/7 to a mixed number which is 2 2/7, then find an equal denominator and finally subtract.
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
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
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 still don't get it. How do you do it? We are learning about it at school! Help!
if one or two of the denominators are odd do you just multiply the two?