Fractions
Adding and subtracting fractions with unlike denominators
None
Example of subtracting fractions with unlike 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?

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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.
Actually, you don't! This method works for both adding and subtracting fractions without changing the denominators. It's called the BOWTIE.
Step 1: Multiply the denominator of the second fraction by the numerator of the first one.
A / B  C / D > D * A
Step 2: Multiply the denominator of the fist fraction by the numerator of the second one.
A / B  C / D > C * B
Step 3: Multiply the 2 denominators. This is your denominator.
To add, add the product of step 1 and the product of step 2. This is your numerator.
To subtract, subtract the product of step 1 and the product of step 2. This is your numerator.
I hope you understand this.
Step 1: Multiply the denominator of the second fraction by the numerator of the first one.
A / B  C / D > D * A
Step 2: Multiply the denominator of the fist fraction by the numerator of the second one.
A / B  C / D > C * B
Step 3: Multiply the 2 denominators. This is your denominator.
To add, add the product of step 1 and the product of step 2. This is your numerator.
To subtract, subtract the product of step 1 and the product of step 2. This is your numerator.
I hope you understand this.
he already knows his facts if you know your multipulcatoin facts good you will know straight away
Its just maths and the way you do it.
well most of the time if you do not make them equal it will be in the decimals and it gets much harder in the decimals
you do or the will have unlike denamnators and it is reasonable
U have 2 make the denominators the same 2 add/subtract them together & solve the problem.
You Always need a LCD too be able to add or subtract. but if you have a common denominator you can add or subtract straight across. That's why common denominators are supper important!
you don't have to find the LCD, but it is way easier to add and subtract.
Pls suggest to subtract 7/10 from 11/12
```11/12  7/10 = 13/60```
your all wrong!
and im just telling the truth!
and im just telling the truth!
its produce in the lowest term
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?
same. also don't think there is another way to answer it.
i dont rlly think there is another way to answer it
hey sumaiyah r. you spelled realy wrong!
there is no way other than this hard one
4 my facts, I think it's just the way u saw it
thank you for helping me this is really useful
Thank you for helping me, this is really uesful!
videos dont help
Why do you have to make the denominators the same? Can't you just subtract the numerators and the denominators?
8967=78
6786=89
76 89=86
6786=89
76 89=86
In the video, you saw that you cannot subtract 13 from 12 because 12 (as a denominator) comes first in the problem. This is why it's just easier to do this method in order to avoid being dumbfounded by impossible questions (impossible while not running into the negative numbers.)
You can't subtract fractions that have different denominators because the fractions are different so you have to make the denominators same.
I Dont Know ?
thats wat the video was basiclly talking about
i need more help on fractions
maybe you should watch more videos! lol
no it is not hard at all I have it for homework.
How learn the multiplication
By listeing dedicated subjects
how do you multiply with diffrent denominator?
The denominators stay the same. It also goes with division.
hey akira.morris you spelled different wrong
are my games very fun? i made new ones!
thanks helped a lot
love math alot
I hate math but ever since I got on khan academy I loved it!
math is too hard i get frustrated
Don't worry, eventually you'll get the answer, and you'll feel so great because you're so smart! Don't feel down because math is hard, because if you try enough, you will get it and it will be the best thing in the world! Good luck! :D
hey cookiedough313 I like your avatar! its cute!
that is very nice
but 76 is 1 so it should be 1/156
you make these vids so complicated
you make these vids so complicated
But you forgot that you need to multiply 13 to 7 and 12 to 6 in order for the fraction to stay the same and not ruin the equation, that's why its 9172 which is equals to 19. If its still vague i can give an example
I don't get the part at the end dividing it because on my sum I divided and I got an answer and now I have know idea what to do and I have to sign it in toady at 2 pm
and cookiedough313 my mom says keep practicing and you'll get better at it!
He did it to make shure 19 fight into 156 if it did fight he would have simplified it
Is it the same as addition just subtracting instead?
manmanolseki you spelled today wrong!
Nope, totally not worth my time. That's my opinion. That guy makes no sense!
Yes, everything else is the same
Yes i think so
Why do you have to make the denominators the same? Can't you just subtract the numerators and the denominators?
No, you can't, because you can't subtract unlike fractions
No you can't!
tis is REALLY confusing
no it isent. it is helpful
hey greta svendsen you spelled this wrong! and hey concodroid you spelled isn't wrong!
its extremely easy...
one way to understand it is that there is a cross section:
the left denominator x right denominator
then the right numerator x left denominator
and vice versa.
then you just subtract the two numerators you get ( you should simplify afterwards)
the left denominator x right denominator
then the right numerator x left denominator
and vice versa.
then you just subtract the two numerators you get ( you should simplify afterwards)
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.
what 1 whole and 2/4 minus 3/4
1 2/4 = 6/4
6/4  3/4 = 3/4
6/4  3/4 = 3/4
good explanation
Why are you suppose to make the denominater the same?
when adding or subtracting fractions, you need to have a like denominator, or the same denominator, because that way, the answer won't have a completely different denominator. example: 2/51/3
you shouldn't just leave the denominators the way they are and subtract them from each other, because then you will have the answer 1/2
you shouldn't just leave the denominators the way they are and subtract them from each other, because then you will have the answer 1/2
what is a fraction
it is when the denominator is greater than the numerator
can an answer be simplyfied
Yes, just like 20/80 equals 1/4. When the numerator is 1, (like 1.2,) it cannot be simplified anymore. If, for example, 5/6 is your fraction you simplified, it cannot be simplified anymore either, because the numerator is one away from the denominator. I hope this helps!!
How do i subtract 7 3/10 from 2 3/4
First of all, we would convert the mixed numbers to improper fractions:
11/4  73/10
Then we would find a like multiple of the denominators, 4 and 10, such as 20. 20/4 is 5, so we'd multiply the numerator and denominator by 5, to get 55/20. 20/10 is 2, so we'd multiply the numerator and denominator of 73/10 by 2, to get 146/20. Our final problem:
55/20  146/20 = 91/20
11/4  73/10
Then we would find a like multiple of the denominators, 4 and 10, such as 20. 20/4 is 5, so we'd multiply the numerator and denominator by 5, to get 55/20. 20/10 is 2, so we'd multiply the numerator and denominator of 73/10 by 2, to get 146/20. Our final problem:
55/20  146/20 = 91/20
This guy is so confusing!
do you have a specific question that I could answer for you?
do u need help with anything ?
What is 9 over 10 take away 1 over 2
2/5 which is two over five.
I don't get about the thing in the end..
So what he did near the end was combine the two fractions into a fraction with a like denominator and the two different numerators that are being subtracted., because only numerators can be subtracted.
Sorry this is late but hope this helps
Sorry this is late but hope this helps
do you do this method Sal to the addition,subtraction and,multiplication?
Ya what they said
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
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
Study! study! study!
Studying hard.
how do i find the comon denominator in 15/16 +1/6 please help me figure this out please i begging you
So all you have to do is multiply then subtract? Would that be mathmatically correct or still wrong?
it would be mathematically correct
Thank you for the video it was very helpful.
Aviona Hoskins
Aviona Hoskins
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
20140603T04:06:19Z
by
Anonymous
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
are you the owner on KHAN!
The person talking in the video (which is Sal Khan) is the owner of Khan Academy
So can you talk a little bit slower
look at this it might help u https://www.mathsisfun.com/fractions_subtraction.html
i was doing my homework and i got all of them doing that tecneek
That's good because you practiced really hard. Practice makes perfect.
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.
can you please explain more because i don't get it at all. like how to divide
Oh it is easy. First take any fraction(9/13) and divide it by(3/4). All you need to do is take the reciprocal of the second no.(3/4)and multiply both of them. If you can simplify do it.
Hope this was helpful
Hope this was helpful
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.
well for thelove off pizza, of course you need to get the lowest common denominator, it says it in the title
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 :)
20150224T23:40:20Z
by
Anonymous
it is depend all on multiplication ,division,subtraction and addition