Equivalent fractions

Home learning focus

In today's lesson, you will learn how to convert equivalent fractions.

This lesson includes:

  • a learning summary
  • one activity

Created in partnership with Sparx.


Key vocabulary:

  • Numerator - the number above the line in a fraction
  • Denominator - the number below the line in a fraction

What are equivalent fractions?

Equivalent fractions are fractions that have the same value as each other.

Look at the circles below. If you split the circle into two pieces and then shade one of the pieces, you have shaded one half (½).

If you split the circle into six pieces and then shade three of them, then you have shaded three sixths (³⁄₆ ).

The same amount of each circle is shaded, because these fractions are equivalent.

Fraction walls

Another way to see which fractions are equivalent is a fraction wall. Here, the width of the wall has been split into different fractions. You can see that ½ is equivalent to ³⁄₆ because they are the same width.

Why are equivalent fractions useful?

When you want to add or subtract fractions you need them to have the same denominator. You can use equivalent fractions to do this.

Also, to convert a fraction into a decimal or a percentage, you first need to find an equivalent fraction.

How to find equivalent fractions

Fractions are equivalent if you can get from one of them to the other by multiplying their numerator and denominator by the same number. For example, ⁶⁄₂₀ is equivalent to ³⁰⁄₁₀₀.


Work out the unknown value (?) in the expression below.

To work out the equivalent fraction, the numerator and denominator must be multiplied by the same number.

25 is multiplied by 4 to give 100, so you multiply 6 by 4 as well to give the unknown value.

6 × 4 = 24, so ⁶⁄₂₅ is equivalent to ²⁴⁄₁₀₀.


Activity 1

Worksheet: Equivalent fractions

Have a go at this worksheet from Sparx on equivalent fractions.

You can print it out or write your answers on a piece of paper.

Equivalent fractions

There's more to learn

Have a look at these other resources around the BBC and the web.

KS3 Maths
BBC Bitesize Daily
Play Nightfall
11 - 14 Maths
KS3 English
Britannica Digital Learning