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GCSE Maths / Edexcel

Sharing in a ratio

Split a total amount into two-part and three-part ratios by finding the value of one part first.

Ratio, Proportion and RatesFoundation and HigherGrades 3 to 5Focused skill

Curriculum path: GCSE Maths > Edexcel > Ratio, Proportion and Rates > Sharing in a ratio

Pearson Edexcel GCSE Maths ratio R5: divide a quantity in a given ratio and solve related problems.

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Revision notes

Theory, examples, and quick checks.

Keep the method short, then practise straight away. This note is written for GCSE Maths Edexcel students who need clear working and reliable method marks.

Theory

When you share in a ratio, the ratio parts tell you how many equal parts the total is split into.

First add the ratio parts. This gives the total number of equal parts.

Divide the total amount by the total number of parts to find the value of one part.

Multiply the value of one part by each ratio part to find each share.

Always check that the shares add back to the original total.

Key ruleTotal amount / total ratio parts = value of one part.

Worked examples

Two-part ratio

Share 60 pounds in the ratio 2:3.

  1. Total parts = 2 + 3 = 5.
  2. One part = 60 / 5 = 12.
  3. Shares are 2 x 12 and 3 x 12.

Answer: 24 pounds and 36 pounds

Three-part ratio

Share 72 in the ratio 1:2:3.

  1. Total parts = 1 + 2 + 3 = 6.
  2. One part = 72 / 6 = 12.
  3. Shares are 12, 24 and 36.

Answer: 12, 24 and 36

Check the total

A prize is shared in the ratio 4:5. The total is 81 pounds.

  1. Total parts = 9.
  2. One part = 81 / 9 = 9.
  3. Shares are 36 and 45.
  4. 36 + 45 = 81.

Answer: 36 pounds and 45 pounds

Common mistakes

  • Dividing by one of the ratio numbers instead of the total number of parts.
  • Finding one part but forgetting to multiply by each ratio part.
  • Giving the value of one part as the final answer.
  • Not checking that the shares add to the original total.

Quick exercise

Try these before moving to the exam-style questions.

  1. Share 40 in the ratio 3:5.
  2. Share 56 pounds in the ratio 2:5.
  3. Share 90 in the ratio 1:2:3.
  4. Share 84 in the ratio 4:3.
  5. Share 120 in the ratio 2:3:5.
Exam-style questions

Practise the same skill at three levels.

These are original GCSE-style questions with mark schemes, common wrong answers, and AI marking guidance so feedback stays close to exam expectations.

Basic GCSE styleFoundationNon-calculator3 marks

Share 45 pounds in the ratio 2:3.

sharing ratioone partfoundation ratio
Standard exam styleFoundation and HigherEither4 marks

A, B and C share 126 pounds in the ratio 2:3:4. Work out how much C receives.

three-part ratiocontextratio share
ChallengeFoundation and HigherEither5 marks

A length of ribbon is cut into three pieces in the ratio 5:7:8. The longest piece is 24 cm. Find the total length of the ribbon.

reverse ratiosharingmulti-step