NUMBAT OER - Open Educational Resources

3.2 Dividing fractions

Whilst multiplying fractions looks very much like adding or subtracting, it is not quite so easy to see how you can divide one fraction by another:

( 5 )  ÷  ( 3 )  =  ( 5 )  /  ( 3 )
8 4 8 4

This expression is a fraction itself, with the numerator equal to:

5
8

And the denominator equal to:

3
4

By analogy with multiplication, the answer should look like this:

( 5 )  ÷  ( 3 )  =  (5 ÷ 3)
8 4 (8 ÷ 4)

However, it is quite likely that either the numerator or denominator will not be a whole number - in this case the numerator is equal to:

1  2
3

The way to solve this is to turn the sum into a multiplication, and this is done by inverting the denominator:

( 5 )  ÷  ( 3 )  =  ( 5 )  ×  ( 4 )  =  (5 × 4)  =  20  =  5
8 4 8 3 (8 × 3) 24 6

For the purists, we can write this expression as:

( 5 )  ÷  ( 3 )  =  ( 5 )  ×  ( 3 ) -1  =  ( 5 )  ×  ( 4 )
8 4 8 4 8 3