GCSE MATHS • HIGHER TIER
Sharing in a Ratio Made Simple
Divide amounts accurately using ratio parts, the value of one part, and a final check.
Clear method
Exam practice
Worked proofs
Sharing in a Ratio in Four Moves
1
Add
Add all parts of the ratio .
2
Divide
Divide the total amount by the total number of parts .
3
Multiply
Multiply the value of one part by each ratio number .
4
Check
Add the shares to confirm they equal the original total.
What You’ll Learn
Understand Ratio Sharing
Know what it means to split a total according to a ratio.
Find Total Parts
Add all ratio parts correctly, including three-part ratios.
Find One Part
Divide the original amount by the total number of parts.
Calculate Each Share
Multiply the value of one part by each ratio value.
Check Your Answer
Confirm that all shares add back to the original total.
Key Rules
Add Every Ratio Part
Add all the numbers in the ratio to find the total number of parts.
Find One Part First
Divide the total amount by the total number of ratio parts.
Calculate Each Share
Multiply the value of one part by each number in the ratio.
Include Every Part
For three-part ratios, calculate all three shares separately.
Worked Proof: Sharing in a Ratio
Step-by-Step Method
- 1. Add the parts of the ratio together.
- 2. Divide the total amount by the number of parts.
- 3. Multiply by each ratio value.
- 4. Check that the shares add up to the original total.
More Worked Examples
1
Question : Share £50 in the ratio 2:3
2 + 3 = 5
50 ÷ 5 = 10
2 × 10 = £20
3 × 10 = £30
2 × 10 = £20
3 × 10 = £30
2
Question : Share £72 in the ratio 1:3
1 + 3 = 4
72 ÷ 4 = 18
1 × 18 = £18
3 × 18 = £54
1 × 18 = £18
3 × 18 = £54
3
Question : Share £84 in the ratio 2:5
2 + 5 = 7
84 ÷ 7 = 12
2 × 12 = £24
5 × 12 = £60
2 × 12 = £24
5 × 12 = £60
4
Question : Share 120 sweets in the ratio 3:5
3 + 5 = 8
120 ÷ 8 = 15
3 × 15 = 45
5 × 15 = 75
3 × 15 = 45
5 × 15 = 75
- Common GCSE Mistakes
- • Total parts: Do not forget to add every part of the ratio first.
- • Division: Divide by the total number of parts, not by one ratio value.
- • Three-part ratios: Include all three parts before finding one part.
- • Arithmetic: Check multiplication and addition carefully.
- Exam Tips
- Write the total number of ratio parts before dividing.
- Find the value of one part clearly before calculating each share.
- Keep the units with your answers, such as pounds, sweets or marbles.
- For three-part ratios, calculate all three shares separately.
- Add the final shares to check they equal the original total.
- Show your working because method marks may be available.
Skills Used in Sharing in a Ratio
Ratio
Proportion
Fractions
Percentages
Arithmetic
Division
Multiplication
Problem Solving
Checking Answers
Ready to Practise?
Printable Worksheet
Download and print practice questions with answers.
Interactive Quiz
Test your knowledge with instant feedback and hints.
Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Sharing in a Ratio Tutorial
Step-by-step walkthroughs of Sharing in a Ratio with clear methods and exam tips.
Frequently Asked Questions
It means dividing a total amount into parts according to a given relationship.
Add all the parts of the ratio together.
Divide the total amount by the total number of ratio parts.
Multiply the value of one part by each number in the ratio.
Add all the shares together and confirm they equal the original total.
Yes. The source includes several three-part ratio examples.