Share £12 in the ratio 1 : 2.
Total parts = 1 + 2.
Total parts = 3. Each part = 12 ÷ 3 = 4. So amounts are £4 and £8.
Sharing in a Ratio
Sharing in a ratio means dividing a quantity into parts based on a given ratio. It uses ideas from direct proportion and is commonly tested in real-life GCSE Maths problems.
Overview
Sharing in a ratio means splitting a total amount according to the parts in the ratio.
The numbers in the ratio tell you how many parts each person or group should receive.
Share 20 in the ratio \( 2:3 \)
This does not mean split 20 into 2 and 3.
It means split 20 into 5 equal parts, then give 2 parts to one share and 3 parts to the other.
What you should understand after this topic
- Find total parts in a ratio
- Work out the value of one part
- Calculate each share correctly
- Check final answers
- Handle 2-part and 3-part sharing questions
Key Definitions
Share in a Ratio
Split a total amount according to the ratio parts.
Total Parts
The sum of all the numbers in the ratio.
One Part
The value of one equal share after dividing the total.
Ratio Part
One of the numbers in the ratio, such as \(2\) in \(2:3\).
Amount Shared
The total quantity to be divided.
Check Total
Add the final shares to ensure they equal the original amount.
Key Rules
Add the parts first
For \(2:3\), total parts = \(5\).
Find one part
Divide the total amount by the total number of parts.
Multiply for each share
Multiply one part by each ratio number.
Check the total
Your final shares should add back to the original amount.
Quick Pattern Check
\(1:2\)
Total parts = 3
\(2:3\)
Total parts = 5
\(3:4:5\)
Total parts = 12
Always check
Add all the shares at the end.
How to Solve
What does sharing in a ratio mean?
Sharing in a ratio means dividing a total into parts that follow a given ratio.
\( 2:3 \)
This means 2 parts to 3 parts.
The total is split into equal-sized parts (units), then grouped according to the ratio.
Step-by-step method
- Add the parts in the ratio.
- Divide the total by the number of parts.
- Multiply by each ratio number.
- Check the shares add to the total.
Visual understanding
Think of the total as being split into equal blocks.
For \(2:3\), the total is split into 5 equal parts.
2 parts go to one share, 3 parts to the other.
Exam thinking
Always find the total number of parts first.
Do not multiply the total directly by the ratio numbers.
Exam tip: Always check your answers add back to the original total.
Example Questions
Edexcel
Exam-style questions inspired by Edexcel GCSE Mathematics, focusing on sharing quantities in a given ratio.
Edexcel
Share £60 in the ratio \( 2:3 \).
Edexcel
Divide 48 sweets in the ratio \( 5:3 \).
Edexcel
Share 84 cm in the ratio \( 3:4 \).
Edexcel
A prize of £72 is shared between Tom and Sam in the ratio \( 5:7 \). How much does each receive?
Edexcel
Divide 150 in the ratio \( 2:3:5 \).
AQA
Exam-style questions based on the AQA GCSE Mathematics specification, emphasising real-life contexts and multi-step ratio problems.
AQA
£90 is shared between Ali and Ben in the ratio \( 4:5 \). Find how much each receives.
AQA
Three friends share £120 in the ratio \( 2:3:7 \). Calculate each person's share.
AQA
A sum of money is shared in the ratio \( 3:5 \). One share is £45. Find the total amount.
AQA
The ratio of boys to girls in a class is \( 4:3 \). There are 28 students in total. Find the number of boys and girls.
AQA
£84 is shared between Anna and Leo in the ratio \( 2:5 \). How much more does Leo receive than Anna?
OCR
Exam-style questions aligned with OCR GCSE Mathematics, focusing on reasoning, reverse problems, and algebraic applications of ratios.
OCR
£96 is shared between Jack and Mia in the ratio \( 7:5 \). Find each share.
OCR
A quantity is shared in the ratio \( 3:8 \). The larger share is 64. Find the total amount.
OCR
Two numbers are in the ratio \( 5:9 \). Their sum is 98. Find the two numbers.
OCR
A sum of money is shared between three people in the ratio \( 1:2:3 \). The smallest share is £15. Find the total amount.
OCR
Explain how to share an amount in a given ratio.
Exam Checklist
Step 1
Add all the ratio parts together.
Step 2
Divide the total amount by that number.
Step 3
Multiply by each part of the ratio.
Step 4
Check the shares add back to the total.
Most common exam mistakes
Total parts mistake
Using one part instead of the total number of parts.
Division mistake
Finding one part incorrectly.
Multiplication mistake
Not multiplying the value of one part correctly.
No check
Forgetting to add the final answers to confirm the total.
Common Mistakes
These are common mistakes students make when sharing quantities in a ratio in GCSE Maths.
Not finding the total number of parts
Incorrect
A student uses only one part of the ratio instead of adding them.
Correct
Always add all parts of the ratio first to find the total number of parts before dividing.
Splitting directly into ratio numbers
Incorrect
A student tries to split the total into the ratio values themselves.
Correct
The ratio shows proportions, not actual amounts. First find the value of one part, then scale up.
Forgetting to scale up from one part
Incorrect
A student finds one part but does not multiply to get each share.
Correct
After finding one part, multiply it by each number in the ratio to get the final shares.
Arithmetic errors when dividing
Incorrect
A student makes mistakes when dividing the total by the number of parts.
Correct
Take care when dividing, as errors here affect all final answers. Check your calculation carefully.
Not checking the final total
Incorrect
A student does not verify their answer.
Correct
Add the final shares together to ensure they equal the original total.
Try It Yourself
Practise sharing quantities in a given ratio.
Foundation
Foundation Practice
Share amounts using simple ratios.
Share 15 sweets in the ratio 1 : 2. Give your answers separated by a comma.
Find total parts first.
Total parts = 3. Each part = 15 ÷ 3 = 5. So 5 and 10.
Share 20 in the ratio 3 : 1.
Total parts = 4.
20 ÷ 4 = 5 per part. So 3 parts = 15 and 1 part = 5.
Share £18 in the ratio 2 : 1. Give your answers separated by a comma.
Total parts = 3.
Each part = 18 ÷ 3 = 6. So 2 parts = 12 and 1 part = 6.
Three people share £24 in the ratio 1 : 1 : 2. What do they get?
Total parts = 4.
Each part = 24 ÷ 4 = 6. So amounts are £6, £6 and £12.
Share 30 in the ratio 2 : 3. Give your answers separated by a comma.
Total parts = 5.
Each part = 30 ÷ 5 = 6. So 12 and 18.
A student shares 20 in the ratio 1 : 4 and gets 10 and 10. What is the mistake?
Total parts is not 2.
1 + 4 = 5 parts. They incorrectly used 2 parts instead of 5.
Share 28 in the ratio 3 : 4. Give your answers separated by a comma.
Total parts = 7.
Each part = 28 ÷ 7 = 4. So 12 and 16.
Share £40 in the ratio 1 : 3.
Total parts = 4.
Each part = 40 ÷ 4 = 10. So 10 and 30.
Share 21 in the ratio 2 : 5. Give your answers separated by a comma.
Total parts = 7.
Each part = 21 ÷ 7 = 3. So 6 and 15.
Higher
Higher Practice
Solve multi-step ratio sharing problems and reverse questions.
£60 is shared between A and B in the ratio 2 : 3. How much does B get?
Find value of one part first.
Total parts = 5. Each part = 60 ÷ 5 = 12. B gets 3 parts = £36.
£72 is shared in the ratio 5 : 3. How much does the larger share get?
Find value of one part.
Total parts = 8. Each part = 9. Larger share = 5 × 9 = 45.
A and B share money in the ratio 3 : 2. A gets £45. How much does B get?
Find the value of one part from A.
A = 3 parts = 45 → 1 part = 15. B = 2 parts = £30.
Two people share money in the ratio 4 : 1. The smaller share is £10. What is the total amount?
1 part = 10.
Total parts = 5. Each part = 10 → total = 50.
Three people share £90 in the ratio 2 : 3 : 4. How much does the largest share get?
Total parts = 9.
Each part = 10. Largest share = 4 × 10 = £40.
£84 is shared between A and B in the ratio 5 : 2. How much does A get?
Total parts = 7.
Each part = 12. A gets 5 × 12 = £60.
A student shares £48 in the ratio 2 : 2 and says the answers are £16 and £32. What is wrong?
2 : 2 means equal shares.
2 : 2 means equal shares → both should be £24.
Two numbers are in the ratio 3 : 7. Their total is 80. Find the larger number.
Total parts = 10.
Each part = 8. Larger = 7 × 8 = 56.
A and B share £100 in the ratio 1 : 4. How much more does B get than A?
Find both shares first.
Each part = 20. A = 20, B = 80 → difference = 60.
Three numbers are in the ratio 2 : 3 : 5 and their total is 100. Find the smallest number.
Total parts = 10.
Each part = 10. Smallest = 2 × 10 = 20.
Games
Practise this topic with interactive games.
Games coming soon.