Multiplying Fractions

Multiplying Fractions

GCSE(F),

To multiply fractions, multiply the two numerators together and multiply the two denominators together.  After multiplication, simplify.

Sometimes the calculation can be made a lot easier by cancelling first.  Cancelling makes the size of the numbers in the fractions smaller before the multiplication takes place. This will result in easier arithmetic.

An integer can be written as a fraction by setting 1 as the denominator: 12 = `frac(12)(1)`.

Examples

1. Multiply `frac(2)(3)` by `frac(1)(4)`.

Answer: `frac(1)(6)`

Cancel down the fractions then multiply: 

`frac(2)(3)xxfrac(1)(4)`

`=frac(2^(÷2)xx1)(3xx4_(÷2))`

`= frac(1xx1)(3xx2)`

`=frac(1)(6)`

The calculation is made easier by simplifying first. Make sure that the answer is in its simplest form.

2. A bar of chocolate has 20 squares.  I eat `frac(2)(5)` of the bar.  How many squares are left?

Answer: 12

`20xxfrac(2)(5)`

`=frac(20^(÷5)xx2)(1xx5_(÷5))`

`= frac(4xx2)(1xx1)`

`= frac(8)(1) = 8`

This calculation gives the number of squares eaten; the question asks for the number of squares remaining: 20 - 8 = 12.