Percentages — Grade 5 Mathematics
In Grade 5, we find any percentage of an amount using the multiplier method, calculate percentage increase and decrease, and express one number as a percentage of another.
Key Methods
Find P% of an amount
amount × P ÷ 100
17% of 300 = 300 × 17 ÷ 100 = 51
% increase / decrease
new = original × (100 ± P) ÷ 100
+20%: × 1.2 −15%: × 0.85
A as % of B
(A ÷ B) × 100
18 out of 24 = (18÷24)×100 = 75%
💡 Multiplier method: 37% of something → multiply by 0.37. Faster than finding 1% first.
Worked Examples
Example 1 — Find Any Percentage
Find 37% of 800.
- Method 1: 800 × 37 ÷ 100 = 29 600 ÷ 100 = 296
- Method 2: 10% = 80; 30% = 240; 7% = 56; 37% = 240 + 56 = 296 ✓
Example 2 — Percentage Increase
A salary of £32 000 increases by 12%. What is the new salary?
- Increase = 32 000 × 12 ÷ 100 = £3 840
- New salary = £32 000 + £3 840 = £35 840
- Or: 32 000 × 1.12 = £35 840
Example 3 — Express as Percentage 📊
A student scores 54 out of 72 in a test. What percentage is this?
- (54 ÷ 72) × 100 = 0.75 × 100 = 75%
Practice Questions
1. Find 45% of 600.
✅ 600 × 45 ÷ 100 = 270
2. A price of £480 is reduced by 15%. What is the sale price?
✅ 480 × 0.85 = £408
3. A population rises from 4 000 to 4 600. What is the percentage increase?
✅ Increase = 600; (600 ÷ 4 000) × 100 = 15%
4. Express 35 as a percentage of 140.
✅ (35 ÷ 140) × 100 = 0.25 × 100 = 25%
5. After an 8% increase, a phone costs £324. What was the original price?
✅ 1.08 × original = 324; original = 324 ÷ 1.08 = £300
Key Points to Remember
- P% of an amount: amount × P ÷ 100 (or multiply by the decimal: P ÷ 100).
- % increase: new = original × (100 + P) ÷ 100.
- % decrease: new = original × (100 − P) ÷ 100.
- A as % of B: (A ÷ B) × 100.
- Reverse percentage: divide the final value by the multiplier to find the original.