Simplifying ratios

Home learning focus

Learn how to simplify a ratio. This means using the smallest number possible on both sides of the ratio.

This lesson includes:

  • one video
  • two interactive activities

Learn

Ratios can be simplified just like fractions. To simplify a ratio, divide all of the numbers in the ratio by the same number until they cannot be divided any more.

For example:

To write the ratio 40:28 in its simplest form, look for a number that will divide into 40 and 28.

2 divides into both numbers, so 40:28 can be written as 20:14.

You can divide these by 2, so the simplified ratio is 10:7.

No number divides into 10 and 7 exactly, so 10:7 is the simplest form of the ratio.

A quick way of doing this in just one step is to divide by the highest common factor of all the numbers in the ratio. In this example, the highest common factor of 40 and 28 is 4.

Practise

Activity 1

Watch the short video below on the ink used in the printing factory, then answer the questions below to work out the ratio of inks used.

Activity 2

Ratios worksheet

Have a go at this worksheet from Twinkl and test what you know about simplifying ratios.

Working with ratio worksheet
document

Finished? Find the answers here.

There's more to learn

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

KS3 Maths
BBC Bitesize Daily
Can anyone be maths genius?
11-14 Maths
Discoveries of the Hubble Space Telescope
Coronavirus and your wellbeing