Show Working

Ratio, proportion and rates of changeFoundation and Higher

Ratio: GCSE maths practice with worked answers

Show Working has 2 kinds of ratio question for GCSE Maths, for Foundation and Higher. Every question is new each time and comes with the working, step by step.

Ratio questions ask you to simplify a ratio and to share an amount in a given ratio. Sharing starts with adding the parts to find how many shares there are in total.

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Worked example 1: simplify a ratio

Write the ratio 16 : 4 in its simplest form.

  1. Find the biggest number that goes into every number in the ratio: 4.
  2. Divide each number by 4: 16 : 4 = 4 : 1.
  3. One of the numbers is 1, so nothing else can go into all of them. That is the simplest form.

Answer 4 : 1

01 / What's covered2 kinds of question

Ratio questions in the app

Each kind makes fresh questions every time, so you can practise as often as you like.

  • Simplify a ratioBoth tiers
  • Share in a ratioBoth tiers

Worked example 2: share in a ratio

Chloe and Kira share £140 in the ratio 6 : 1. How much does each person get?

  1. Add the parts of the ratio: 6 + 1 = 7 parts altogether.
  2. Find one part: £140 ÷ 7 = £20.
  3. Multiply each share by one part: 6 × £20 = £120, 1 × £20 = £20.
  4. Check: £120 + £20 = £140.

Answer Chloe: £120, Kira: £20

A common mistake

Dividing the amount by one of the numbers in the ratio instead of the total number of parts. To share £140 in the ratio 6 : 1 there are 7 parts, so one part is £20.

02 / Practise itiPhone and iPad

Practise ratio in Show Working

In the app, open Topics and choose Ratio for ten fresh questions. Ask for a hint if you are stuck, and open the working to see the method one step at a time.

Coming soon to the App Store

More ratio, proportion and rates of change topics

PercentagesAll GCSE maths topics
The worked answer in Show Working: the answer, then numbered steps in plain words

Show WorkingComing soon to the App Store