Equivalent fractions

Learning focus

Learn how to draw and discover equivalent fractions using diagrams.

This lesson includes:

  • one quiz
  • one learning summary


Test your knowledge of equivalent fractions in this quick quiz.


Equivalent fractions are the same fraction written in different ways. To find equivalent fractions, you can use:

  • Fraction walls
  • Fraction bars

Example 1

Have a look at these two fraction bars:


Our two bars have been split into different amounts.

Rectangle A has been split into 3

Rectangle B has been split into 6

These numbers would become the denominators (bottom numbers), because they represent how many the whole has been split into.


Can you see how the same amount has been shaded in each rectangle?

Rectangle A has 1 section coloured in and Rectangle B has 2 sections coloured in.

These amounts would then become the numerators (top number), because they represent how many parts are being talking about.

As a fraction, Rectangle A would have \( \frac{1}{3} \) shaded in and Rectangle B would have \( \frac{2}{6} \) shaded.

So \( \frac{1}{3} \) is equivalent to \( \frac{2}{6} \).

Example 2

Take a look at these two fraction bars.

Both identical rectangles have an equivalent amount shaded again, but they have been split up in to different amounts.

Rectangle C represents \( \frac{1}{2} \)

Rectangle D represents \( \frac{5}{10} \)

You can see that they are both equivalent.

So \( \frac{1}{2} \) = \( \frac{5}{10} \)

Example 3

You can use any identical shape that can be split easily to find equivalent fractions.

You can see how these pizzas have the same amount on each plate, but they’ve been cut into different slices. Each pizza shows an equivalent amount.

Fraction walls

Another way to see which fractions are equivalent is a fraction wall. Here, the rows of the wall have been split into different fractions.

You can see that \( \frac{1}{2} \) is equivalent to \( \frac{3}{6} \)because they are the same width.


Play Guardians: Defenders of Mathematica to learn more and sharpen your skills on this topic.

Guardians: Defenders of Mathematica
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