Multiplying and dividing fractions
To multiply fractions, you need to multiply the top numbers together, and multiply the bottom numbers together. Remember that you cannot cancel numbers that are both on the top of a fraction. Have a look at the example below.
4/5 × 5/6
Multiply then cancel:
OR cancel between the top and the bottom then multiply:
- Question
Calculate: 5/6 × 5/8
- Answer
5/6 × 5/8 = 25/48
The 5s do not cancel because they are both on the top of the fraction.
Dividing a fraction by a whole number
3/4 divided by 3 should be 1/3 of the original fraction, which would make the answer 1/4.
So 3/4 ÷ 3
= 3/4 ÷ 3/1 (writing 3 as 3/1)
= 1/4.
Dividing by a fraction
The rule to remember when dividing fractions is that you turn the fraction you are dividing by upside down, and multiply.
So going back to the previous example we can work this out by turning the 3/1 upside down.
3/4 ÷ 3/1 = 3/4 × 1/3 = 1/4
Dividing by 3 is the same as multiplying by 1/3.
It works with all fractions. For example dividing by 3/4 is the same as multiplying by 4/3.
- Question
Calculate: 3/8 ÷ 3/4
- Answer
3/8 ÷ 3/4
= 3/8 × 4/3
= 1/2
Now try a Test Bite
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