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Ages 11-13

Multiplying fractions

The easiest operation of them all

What is this about?

Multiplying fractions is surprisingly easier than adding them. There's no common denominator to find and nothing to match. Multiplying by a fraction means taking a part of something: 1/2 of 1/3 is half of a third.

The rule to remember

Multiply the numerators together and the denominators together. Then simplify if you can. That's it.

Example 1

2/3 × 4/5

  1. 1Multiply the top numbers: 2 × 4 = 8.
  2. 2Multiply the bottom numbers: 3 × 5 = 15.
  3. 3The result is 8/15 and it can't be simplified any further.

Result: 8/15

Example 2

3/4 × 2/9

  1. 1Top: 3 × 2 = 6. Bottom: 4 × 9 = 36.
  2. 2That gives 6/36, which can be simplified.
  3. 3Divide top and bottom by 6: 1/6.

Result: 1/6

The most common mistake

Many people write

Looking for a common denominator before multiplying

Why it's wrong

It's wasted effort: the common denominator is only needed for adding and subtracting. In multiplication you multiply straight away and save half the work.

Did it click?

The best way to find out is to try. These exercises are exactly on this topic.

Practise this topic