To find a percentage of an amount, either convert the percentage to a decimal and multiply, or build it from simple percentages you already know (10%, 5%, 1%). Both methods work without a calculator and appear on every KS3 maths paper, from Year 7 through to GCSE.
Method 1 — decimal multiplier (fastest with a calculator)
Convert the percentage to a decimal by dividing by 100, then multiply by the amount.
Percentage of amount = (percentage ÷ 100) × amount
Worked example 1 — 35% of 240
35 ÷ 100 = 0.35
0.35 × 240 = 84
Answer: 84
Worked example 2 — 17.5% of 360
17.5 ÷ 100 = 0.175
0.175 × 360 = 63
Answer: 63
The decimal multiplier is the preferred method in calculator papers. It works for any percentage, including decimals.
Method 2 — build from 10% (best without a calculator)
Find 10% by dividing by 10. Use that to build other percentages.
| Percentage | How to find it |
|---|---|
| 50% | Halve the amount |
| 25% | Halve, then halve again (or ÷ 4) |
| 10% | Divide by 10 |
| 5% | Find 10%, then halve it |
| 1% | Divide by 100 |
| 20% | Find 10%, then double it |
Worked example 3 — 35% of 80 without a calculator
10% of 80 = 8
30% = 3 × 8 = 24
5% = half of 10% = 8 ÷ 2 = 4
35% = 30% + 5% = 24 + 4 = 28
Answer: 28
Worked example 4 — 15% of 260 without a calculator
10% of 260 = 26
5% = 26 ÷ 2 = 13
15% = 26 + 13 = 39
Answer: 39
Percentage increase and decrease
To increase or decrease an amount by a percentage, there are two approaches.
Two-step method
- Find the percentage of the amount.
- Add it (increase) or subtract it (decrease).
Worked example 5 — 20% increase on £85
20% of £85: 0.20 × 85 = £17
New price: £85 + £17 = £102
Answer: £102
Worked example 6 — 15% decrease on £60
15% of £60: 0.15 × 60 = £9
New price: £60 − £9 = £51
Answer: £51
Multiplier method (Year 9 / GCSE)
For a percentage increase of p%, multiply by (1 + p/100). For a decrease, multiply by (1 − p/100).
- 20% increase: multiply by
1.20 - 15% decrease: multiply by
0.85
Worked example 6 using multiplier: £60 × 0.85 = £51 ✓
The multiplier method is quicker and essential for compound percentage questions at GCSE (e.g. compound interest).
Writing one quantity as a percentage of another
Sometimes a question asks: "What percentage is 36 of 150?"
Formula: (part ÷ whole) × 100
(36 ÷ 150) × 100 = 0.24 × 100 = 24%
Answer: 36 is 24% of 150.
Worked example 7 — percentage mark
A student scores 54 out of 75 in a test. What is their percentage score?
(54 ÷ 75) × 100 = 0.72 × 100 = 72%
Answer: 72%
Reverse percentage
A reverse percentage question gives you the final amount after a percentage change and asks for the original.
Key rule: never take a percentage of the changed amount. Always work with the multiplier.
Worked example 8 — find the original price after a 30% increase
A jacket now costs £91 after a 30% increase. What was the original price?
After a 30% increase, the new price = 130% of the original = 1.30 × original.
Original = £91 ÷ 1.30 = £70
Answer: the original price was £70.
Check: £70 × 1.30 = £91 ✓
Worked example 9 — find the original price after a 20% reduction
A television costs £320 after a 20% reduction. What was the original price?
After a 20% reduction, the new price = 80% of the original = 0.80 × original.
Original = £320 ÷ 0.80 = £400
Answer: the original price was £400.
Check: £400 × 0.80 = £320 ✓
Percentages in the national curriculum
The DfE's KS3 mathematics programme of study (Department for Education) requires pupils to interpret percentages and percentage changes as a fraction or decimal, and to solve problems involving percentage change, including percentage increase and decrease and original value problems. According to BBC Bitesize's KS3 maths resources, percentages are among the most frequently tested number topics across both calculator and non-calculator GCSE papers.
Common mistakes at KS3
| Mistake | Example of error | Correct approach |
|---|---|---|
| Dividing by the wrong number for 10% | 10% of 240 = 240 ÷ 100 = 2.4 (correct) but then doubling to get 20% and getting 4.8 | 20% = 2 × 2.4 = 48 (not 4.8 — do not move the decimal again) |
| Taking a % of the wrong amount in reverse % | "30% off £91 = £27.30, original = £91 + £27.30 = £118.30" | Divide by the correct multiplier: £91 ÷ 0.70 = £130 |
| Confusing % increase with final amount | Adding 25% to £80 and writing £20 as the answer | £20 is the increase; the new amount is £80 + £20 = £100 |
| Rounding mid-calculation | Finding 17.5% step by step and rounding at each step | Keep full decimal values until the final answer |
Frequently asked questions
How do I find 10% of any number?
Divide the number by 10. Move the decimal point one place to the left. For example, 10% of 350 = 35; 10% of 4.6 = 0.46. This is the foundation of the build-up method for non-calculator percentage questions.
What is the decimal multiplier for a percentage increase or decrease?
For an increase of p%, the multiplier is 1 + p/100. For a decrease of p%, it is 1 − p/100. Examples: 25% increase → multiply by 1.25; 40% decrease → multiply by 0.60. Memorising this pattern makes both percentage change and reverse percentage questions much faster.
How do I solve a reverse percentage question?
Identify the multiplier that was applied (e.g. a 30% increase means the multiplier is 1.30). Then divide the final amount by that multiplier to get the original. Never take the percentage of the changed amount — that gives the wrong answer.
What is the difference between percentage change and percentage point change?
A percentage change is calculated as (change ÷ original) × 100. A percentage point change is the arithmetic difference between two percentages. For example, if a tax rate rises from 20% to 25%, that is a 5 percentage-point increase but a (5 ÷ 20) × 100 = 25% percentage increase. The distinction matters at GCSE and beyond.
For Socratic maths tutoring that works through percentage problems step by step — without giving away the answer — visit aitutors.me.