What is an equivalent fraction and how to work out an equivalent fraction (2/4 = 4/8)

Equivalent fractions are fractions that are the same size. The numbers on the numerator and denominator may be different, but if you draw out the fractions on a circle they will cover exactly the same amount of space. So for example, 4/8 and 2/4 are equivalent to each other, as they cover exactly half of a shape.

To find a fraction which is equivalent to another fraction, all you need to do is multiply the numerator and denominator of the fraction by the same number.

Example 1

Write down an equivalent fraction to 2/3.

All you need to do is pick a times-table and multiply the numerator and denominator by this times table.

Let’s go with the 6 times table.

2 × 6 = 12

3 × 6 = 18

So 2/3 = 12/18

Example 2

Write down an equivalent fraction to 6/11.

Like example 1, all you need to do is pick a times-table and multiply the numerator and denominator by this times-table.

This time, let’s pick the 7 times table.

6 × 7 = 42

11 × 7 = 77

Therefore, 6/11 = 42/77

Example 3

Write down an equivalent fraction to 5/8.

This time, let’s pick the 3 times-table.

5 × 3 = 15

8 × 3 = 24

Therefore, 5/8 = 15/24

Example 4

Write down an equivalent fraction to 3/4.

This time, let’s pick the 9 times-table.

3 × 9 = 27

4 × 9 = 36

Therefore, 3/4 = 27/36

Example 5

Find the missing numerator of these equivalent fractions 2/5 = ?/35.

Here, you need to find the times-table that the first fraction has been multiplied by to give the second fraction.

Do this by dividing the two denominators.

35 ÷ 5 = 7

So all you need to do now is multiply the numerator by 7.

2 × 7 = 14.

So 2/5 = 14/35.

Example 6

Find the missing denominator of these equivalent fractions 5/6 = 20/?

Again, you need to find the times-table that the first fraction has been multiplied by to give the second fraction.

Do this by dividing the two numerators.

20 ÷ 5 = 4

So all you need to do now is multiply the numerator by 4.

6 × 4 = 24.

So 5/6 = 20/24