YOU ARE LEARNING:
Multiplying Fractions
Multiplying Fractions
You can multiply fractions following a particular rule.
How much of this pizza is left? Give your answer as a fraction.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/0ZAT3H6pRP2bDx191b3Y.png)
If you wanted to split the left-over pizza evenly between two people they would each get _______ of the remaining pizza.
A) half B) a third C) all
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/vAKaG4M5TlKi7BPuKwWH.png)
So two people split the left-over pizza so they each get half of the remaining pizza
You can express that with fractions like this 32×21
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/vAKaG4M5TlKi7BPuKwWH.png)
How much of the original whole pizza does each of the two people get? Give your answer as a fraction.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/oCf6cNq2S4WORweGuGYn.png)
Each of the two people will get 31 of the original pizza
So 32×21=31
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/vCpSO547RYyldC2dsYxL.png)
What if you didn't want to split the remaining 32 between 2 people?
What if you wanted to split it between 3 people?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/vAKaG4M5TlKi7BPuKwWH.png)
When you split between 2 people, you multiplied by 21. If you split between 3 people, you multiply by...
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/vAKaG4M5TlKi7BPuKwWH.png)
In order to split the left-over pizza evenly, you can split up each of the slices into thirds
This is the same as if the pizza had originally been divided into 9 slices.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/nMjMzqd4TrW5mDGC4Kky.png)
How many slices are left of this pizza now after it has been divided into 9ths?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/nMjMzqd4TrW5mDGC4Kky.png)
There are 6 remaining slices and 3 people - if each person gets the same number of slices, how many slices does each person get?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/1AWavA6kTMO4fTXGKpyo.png)
So each of the 3 people get 2 out of the 9 slices in the original pizza. How do you write that as a fraction?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/sE4ZVU3mT9uaHZL1lyC9.png)
So!
32×31=92
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/7eD2gvWBQAS4cGZr2oev.png)
Now, look only at the maths in this example
How did you actually get from 32×31 to 92?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/x3jt8oHVQFKLlPOkS7MC.png)
You got to the denominator 9 by ______________ the denominators in the other fractions.
A) adding B) multiplying
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/x3jt8oHVQFKLlPOkS7MC.png)
You also got to the numerator 2 in the result by ______________ the numerators in the other fractions.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/x3jt8oHVQFKLlPOkS7MC.png)
So you multiply two fractions by multiplying the numerators and the denominators. How do you write that in a generalised form?
A) ca×db=c+da+b B) ca×db=c×da×b
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/x3jt8oHVQFKLlPOkS7MC.png)
So you multiply two fractions like this
ca×db=c×da×b
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/x3jt8oHVQFKLlPOkS7MC.png)
What is 54×32? Give your answer as a fraction.
What is 63×34? Give your answer as a fully simplified fraction.
Sometimes you end up having to multiply numbers that aren't super easy to multiply
For example, here you are meant to multiply 21 and 25
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/BILgzkstTgCai96CBcSy.png)
There is a trick!
If you can find a number that both the numerator of one fraction and the denominator of the other fraction can be divided by, you can make the problem easier.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/BILgzkstTgCai96CBcSy.png)
What is the highest number that both 10 and 25 can be divided by (their highest common factor)?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/mqMKasyT7muzME9NlNAk.png)
So you can now simplify by dividing that numerator and that denominator by 5
2110÷5×25÷57=212×57
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/mqMKasyT7muzME9NlNAk.png)
What is the highest common factor between 7 and 21?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/GZybbMTdQumIgnmGlTru.png)
So you can now simplify further by dividing that numerator and that denominator by 7
21÷72×57÷7=32×51
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/pgvTggHGR6KOLk5vYETS.png)
So now you have simplified 2110×257 to 32×51. What is the result as a fraction?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/pgvTggHGR6KOLk5vYETS.png)
It would also be good to simplify this problem
You need to find the highest common factor between the numerator of one fraction and the denominator of the other fraction.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/J0w6J9lbTbanTrrG6TXC.png)
What is the highest common factor between 14 and 35?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/vK2U5ZtTSYK8RDbgTD8P.png)
What is the highest common factor between 18 and 12?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/TbdsRNKSUSV1WsFmpbX6.png)
So now you have simplified 1814×3512 to 32×52. What is the result as a fraction?
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/ZQJKGr8EQoSSbAtUnp24.png)
So you could simplify 1814×3512 to 32×52
That made it easier to work out that 1814×3512=154
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/nNiF951JQbjWuNRLELYQ.png)
Simplify 2416×324 and give your answer as a fully simplified fraction.
Summary! You can multiply a fraction with another fraction
You multiply the numerators in the two fractions and then the denominators.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/djcBeMaVQvWS4fHloj5s.png)
If the multiplication is complicated, you can try to simplify the problem
You find the highest common factor between the numerator in one fraction and the denominator in the other fraction.
![](https://cdn.hejalbert.se/teen/blocks-images/en_GB/nNiF951JQbjWuNRLELYQ.png)