Ratio — Grade 5 Mathematics
A ratio compares two or more quantities. In Grade 5, we write and simplify ratios, share amounts in a given ratio, and connect ratios to fractions and percentages.
Writing and Simplifying Ratios
A ratio is written with a colon: 2 : 3 (read "2 to 3").
Simplify by dividing both parts by their HCF.
Example: 12 : 18 → HCF = 6 → 2 : 3
The ratio 2 : 3 means: for every 2 of the first quantity there are 3 of the second.
Simplify by dividing both parts by their HCF.
Example: 12 : 18 → HCF = 6 → 2 : 3
The ratio 2 : 3 means: for every 2 of the first quantity there are 3 of the second.
Visual: ratio 2 : 3 — orange (2 parts) and gold (3 parts) of a total 5 parts
Sharing in a Given Ratio
Method:
1. Add the parts of the ratio to find the total number of parts.
2. Divide the total amount by the total parts to find the value of 1 part.
3. Multiply by each ratio number.
1. Add the parts of the ratio to find the total number of parts.
2. Divide the total amount by the total parts to find the value of 1 part.
3. Multiply by each ratio number.
| Example: Share £60 in ratio 2 : 3 | Amount |
|---|---|
| Total parts = 2 + 3 = 5; 1 part = £60 ÷ 5 = £12 | |
| Part A: 2 × £12 | £24 |
| Part B: 3 × £12 | £36 |
| Check: £24 + £36 | = £60 ✓ |
Worked Examples
Example 1 — Simplify a Ratio
Simplify 36 : 24.
- HCF(36, 24) = 12
- 36 ÷ 12 = 3; 24 ÷ 12 = 2
- Simplified ratio: 3 : 2
Example 2 — Share in Ratio 3 : 5
Share 240 ml in ratio 3 : 5.
- Total parts = 8; 1 part = 240 ÷ 8 = 30 ml
- Part A: 3 × 30 = 90 ml
- Part B: 5 × 30 = 150 ml
- Check: 90 + 150 = 240 ✓ → 90 ml : 150 ml
Example 3 — Recipe Scaling 🍰
A recipe uses flour and sugar in ratio 4 : 1. If 200 g of sugar is used, how much flour?
- 1 part = 200 g (sugar)
- Flour = 4 parts = 4 × 200 = 800 g
Practice Questions
1. Simplify 15 : 25.
✅ HCF = 5; 15÷5 : 25÷5 = 3 : 5
2. Share £90 in ratio 2 : 7.
✅ 9 parts; 1 part = £10; 2 parts = £20; 7 parts = £70 → £20 : £70
3. Share 120 sweets between Ali and Beth in ratio 3 : 2.
✅ 5 parts; 1 part = 24; Ali = 72; Beth = 48 → 72 : 48
4. In a class the ratio of boys to girls is 3 : 4. There are 12 boys. How many girls?
✅ 1 part = 12 ÷ 3 = 4; girls = 4 × 4 = 16 girls
5. Write 45 cm to 1.2 m as a ratio in simplest form.
✅ Convert to same unit: 45 cm : 120 cm; HCF = 15 → 3 : 8
Key Points to Remember
- Simplify ratios by dividing all parts by their HCF.
- Before writing a ratio, convert both quantities to the same unit.
- Sharing: find 1 part (total ÷ sum of ratio), then multiply for each share.
- Check: all shares should add back to the total.
- Ratio a : b → fraction of total for a = a/(a+b).