AI generatedRatio, proportion and rates of changeKS3 / GCSE

Finding shares from the difference between them

Subtract the ratio numbers to find how many parts represent the difference.

  • Subtract the ratio numbers to find how many parts represent the difference.
  • Divide the stated difference by this part difference to find one part.
  • Multiply by each ratio number. Check that the difference between the shares is correct.

Example 1

Ali : Bea = 2 : 3. Bea receives £3 more than Ali. Find both shares.

Subtract the ratio parts.The known difference represents these parts.Multiply each part by the same value.Multiply each part by the same value.
£6.00, £9.00

Example 2

Ali : Bea = 3 : 4. Bea receives £4 more than Ali. Find both shares.

Subtract the ratio parts.The known difference represents these parts.Multiply each part by the same value.Multiply each part by the same value.
£12.00, £16.00

Remember
Use the worked steps to check your method, not just the final answer.

Your turn

Question 1

Ali : Bea = 4 : 5. Bea receives £5 more than Ali. Find both shares.

Check answer
Subtract the ratio parts.The known difference represents these parts.Multiply each part by the same value.Multiply each part by the same value.
£20.00, £25.00

Check: the shares add to £45.

Question 2

Ali : Bea = 5 : 6. Bea receives £6 more than Ali. Find both shares.

Check answer
Subtract the ratio parts.The known difference represents these parts.Multiply each part by the same value.Multiply each part by the same value.
£30.00, £36.00

Check: the shares add to £66.

Question 3

Ali : Bea = 6 : 7. Bea receives £7 more than Ali. Find both shares.

Check answer
Subtract the ratio parts.The known difference represents these parts.Multiply each part by the same value.Multiply each part by the same value.
£42.00, £49.00

Check: the shares add to £91.

Question 4

Ali : Bea = 7 : 8. Bea receives £3 more than Ali. Find both shares.

Check answer
Subtract the ratio parts.The known difference represents these parts.Multiply each part by the same value.Multiply each part by the same value.
£21.00, £24.00

Check: the shares add to £45.

Question 5

Ali : Bea = 8 : 9. Bea receives £4 more than Ali. Find both shares.

Check answer
Subtract the ratio parts.The known difference represents these parts.Multiply each part by the same value.Multiply each part by the same value.
£32.00, £36.00

Check: the shares add to £68.

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