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)`.

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

Cancel down the fractions then multiply:

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

`=frac(2xx1)(3xx4)`

`=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.

Answer: `frac(1)(6)`

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

`20xxfrac(2)(5)`

`=frac(20xx2)(1xx5)`

`=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.

Answer: 12

See also Calculating Exactly with Fractions

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