Multiplying fractions

The rule for multiplying fractions

To multiply two fractions, multiply the numerators together and the denominators together. Unlike with addition, there’s no need for a common denominator!

a/b × c/d = (a × c)/(b × d)

Example

2/3 × 4/5 = (2 × 4)/(3 × 5) = 8/15

Simplify before multiplying

You can simplify by crossing out common factors before multiplying, to avoid having to work with large numbers. For example, with 3/4 × 8/9: we can see that 8 and 4 have a common factor (4), and that 3 and 9 have a common factor (3).

3/4 × 8/9 = 1/1 × 2/3 = 2/3

This gives us the simplified result straight away, without having to reduce a large fraction at the end.

Multiplying by an integer

An integer n can always be written as n/1. For example:

5 × 2/3 = 5/1 × 2/3 = 10/3

Common pitfall

Do not confuse this with addition: when multiplying fractions, you never look for a common denominator. You simply multiply the numerators together and the denominators together.