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

Updated on March 6, 2012 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

working