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### Course: MAP Recommended Practice>Unit 34

Lesson 15: Adding and subtracting fractions with unlike denominators

# Subtracting fractions with unlike denominators

To subtract fractions with different denominators, you need to find a common denominator. This can be done by identifying the least common multiple of the two denominators. After rewriting the fractions so they both have the common denominator, you can subtract the numerators as you would with any two fractions.

## Want to join the conversation?

• what if they are the same denominaters
• If the denominators are the same , you leave the denominators the same and add or subtract the numerators. Make sure you don't add or subtract the denominators.
• What do i do when i have this?
14/6
The numerator is bigger than the denominator.
• The answer would be 2 2/6 because 6 goes into 14 2 times and 2 would be left and that turns into the numerator, and the denominator would stay the same
• how do you subtract 8/2 - 7/12
• create common denominators so set 8/2 to 48/12 (6 x 2=12, 8 x 6=48) then subtract 48 by 7 to get 41 and place that back over 12 to get 41/12
• how do you multiply or divide with unlike denominators
• what if there is 2 diffrent denomanonater
• You will have to find a multiple that both denominators have. Then, multiply the numerator by the number you multiplied the denominator to get the common multiple.

For example: 5/9 - 6/5
You will need to find a common multiple that 9 and 5 both have.

9: 9, 18, 27, 36, 45, 54...
5: 5, 10, 15, 20, 25, 30, 35, 45, 50...

In this case 45 is the common multiple. Then, you would have to multiply the numerators by the number you multiplied their denominator to get the common multiple. Since 9 times 5 equals 45, the 5 in 5/9 needs to be multiplied by 5 and the 6 in 6/5 would need to be multiplied by 9.

So, 5/9 becomes 25/45 and 6/5 becomes 54/45.

Therefore, 25/45 - 54/45 = -29/45

Hope this helped :)
• what if there numerators are bigger than there denominators
• then you turn the fraction into a mixed number
• I was given the question 2/x+4=3/x
I'm not sure how to work this out... how wold i make the denominates common?
• Your denominator would be either x or what x stands for.
(1 vote)
• how do I subtract mixed fraction where only one fraction is mixed
• You turn both fractions into improper fractions, next you find a like denominator, then you subtract.
• what if the numerater is bigger than the denominator
• It is an improper fraction. It better to keep it that way when solving but if it is the answer you can change it into an mixed fraction or keep it the same to lessen the work.
• What do i do when i have this?
14/6
The numerator is bigger than the denominator.
• You need to put it into a mixed fraction, 14/6. 6 goes into 14 twice so that would be 2 and then the left over would be 2/6 put it together and you get 2 2/6 = 2 1/3

## Video transcript

- [VOICEOVER] Let's see if we can figure out what 4/3 minus 1/5 is, and if you think you know how to do it, I encourage you to pause the video and give it a go. So, when you first look at this, the thing that might jump out at you is we have different denominators here. So, it's not obvious how to subtract 1/5 from 4/3 when you have these different denominators and the key is, is to rewrite each of these fractions so that they have the same denominator. And how do we figure out what that same denominator is? Well, it's going to be a common multiple of three and five, and, ideally, it's going to be the least common multiple of three and five. So, how can we calculate that? Well, we can start with the larger of the two numbers, say five, and let's go through it's multiples and see when we get to one that's divisible perfectly by three. So, five is not divisible by three, 10 is not divisible by three, 15 is divisible by three. In fact, 15 is three times five. So, I can rewrite both of these fractions as something over 15. So, what's 4/3 if I were to rewrite it as something over 15? Well, to get from three to 15 in the denominator, we have to multiply by five. So, if you multiply the denominator by five, if you don't want to change the value of the fraction, you have to multiply the numerator by five as well. So, you have to multiply the numerator by five as well, four times five is going to be 20. So, 4/3 is the same thing as 20/15. Alright. Now, how would we rewrite 1/5 and something over 15? So, we're going to have 15 in the denominator. Well, to go from five to 15, we had to multiply by three. So, if we multiply the denominator by three, we have to multiply the numerator by three as well. So, times three. One times three is just three. So, 4/3 minus 1/5, we can rewrite that as 20/15 minus 3/15. Now, this becomes a lot more straight forward. What is this going to be? Well, this is going to be a certain number of fifteenths. We have 20/15 and we're taking away three of those fifteenths. So, we are going to have, if you have 20 of something and you take away three of them, you're going to have 17 of those things. In this case, we're talking about fifteenths. So, this is going to be 17/15. And if we wanted to write it as a mixed number, we could say 15 goes into 17 one time with a remainder of two. So, it's one and 2/15. Let's do another example. Let's see if we can figure out what 7/10 minus 5/8 is. Five over eight. And I encourage you to pause this video and see if you can calculate it yourself. Well, just like we saw before, we have different denominators but we need to rewrite them so they have a common denominator, that way, we can subtract. And so, what's a common multiple of 10 and eight and, ideally, the least common multiple. It doesn't have to be but it keeps things a little bit simpler. Well, let's start with the larger of the two numbers and then keep finding in their multiples and find one that is perfectly divisible by the other one, by eight. So, ten isn't perfectly divisible by eight, 20 isn't, 30 isn't, 40 is. 40 is a multiple of 10 and it's a multiple of eight. In fact, it's the least common multiple of 10 and eight. So, we can rewrite both of these fractions as something over 40. So, that's going to be something over 40 minus something over 40. Minus something over 40 is equal to something. So, 7/10 is what over 40? Well, to go from 10 to 40 in the denominator, we multiplied by four. So, we have to do the same thing in the numerator, multiply the numerator by four. Seven times four is 28. So, 7/10 is the same thing as 28/40. Now, let's do the same thing with the other fraction. To go from eight to 40 in the denominator, we had to multiply the denominator by five. Eight times five is 40. So, if we multiply the denominator by five, we have to multiply the numerator by five as well. Five times five is 25. So, 7/10 minus 5/8 is the exact same things as 28/40 minus 25/40 and now this makes a lot of sense. It's going to be a certain number of fortieths. If I have 28/40 and I take away 25 of those fortieths, how many fortieths am I going to have left? Well, I'm going to 3/40 left. 28/40 minus 25/40. So, I'm going to have 3/40. 28 minus 25 is three and we are done. 7/10 minus 5/8 is 3/40.