Maths · Ratio & Proportion
Share in a ratio
Split an amount into parts by ratio.
Practice & Master are locked until you try:
What does sharing in a ratio mean?
A ratio tells you how to divide a total into parts. For example, 2:3 means split into 2 parts and 3 parts. The parts must be equal in size. Together they make the whole amount.
Finding the total number of parts
Add all the numbers in the ratio together to find how many equal parts you have. In the ratio 2:3, you have 2 + 3 = 5 parts in total. Each part is the same size.
Working out each share
Divide the total amount by the number of parts to find one part. Then multiply by each number in the ratio. If 5 parts share £20, one part = £4. Two parts = £8 and three parts = £12.
Checking your answer
Always add your shares together. They must equal the original total. This helps you spot mistakes. For example, £8 + £12 = £20, which matches our starting amount.
Worked examples
1. Share £30 in the ratio 1:2.
- Find total parts: 1 + 2 = 3 parts
- Find one part: £30 ÷ 3 = £10
- First share: 1 × £10 = £10
- Second share: 2 × £10 = £20
- Check: £10 + £20 = £30 ✓
2. Divide 45 sweets between Ali and Ben in the ratio 2:3.
- Total parts: 2 + 3 = 5
- One part: 45 ÷ 5 = 9 sweets
- Ali gets: 2 × 9 = 18 sweets
- Ben gets: 3 × 9 = 27 sweets
- Check: 18 + 27 = 45 ✓
3. Share £56 in the ratio 3:4:1.
- Total parts: 3 + 4 + 1 = 8
- One part: £56 ÷ 8 = £7
- Shares: 3 × £7 = £21, 4 × £7 = £28, 1 × £7 = £7
- Check: £21 + £28 + £7 = £56 ✓
Try it yourself
Share 40 marbles in the ratio 3:5. How many marbles does the larger share get?
Ready to test yourself?
Take a short topic test — every question maps to a syllabus point so you’ll see exactly which parts you’ve mastered.