Finding a percentage of an amount is one of the most useful maths skills you will use in everyday life. You can calculate any percentage using either the fraction method or the multiplier method. From working out VAT on a purchase to finding a mark-up on a product, percentages are everywhere in the real world.
How do I find a percentage of an amount?
There are two reliable methods for finding a percentage of an amount. Both always give the same answer — choose whichever feels more natural to you.
Method 1 — The fraction method
Write the percentage as a fraction over 100, then multiply by the amount:
x% of an amount = (x ÷ 100) × amount
Worked Example 1 — Find 35% of 280
35% of 280 = (35 ÷ 100) × 280 = 0.35 × 280
0.35 × 280 = (0.3 × 280) + (0.05 × 280) = 84 + 14 = 98
Method 2 — Build up from 10%
For percentages that are easy multiples of 10, use the building-block approach:
- 10% of 280 = 28
- 30% = 3 × 28 = 84
- 5% = 28 ÷ 2 = 14
- 35% = 84 + 14 = 98 ✓
Both methods agree, so the answer is confirmed.
What is the multiplier method?
The multiplier method is the most efficient approach once you understand it. You convert the percentage directly into a decimal and multiply:
- 20% → multiplier 0.20
- 15% → multiplier 0.15
- 7.5% → multiplier 0.075
Worked Example 2 — Find 15% of £240
15% of £240 = 0.15 × £240 = £36
Check: 10% of 240 = £24; 5% of 240 = £12; 15% = £24 + £12 = £36 ✓
The table below shows the most commonly needed multipliers, applied to an amount of £120:
| Percentage | Multiplier | Amount | Result |
|---|---|---|---|
| 5% | 0.05 | £120 | £6 |
| 10% | 0.10 | £120 | £12 |
| 15% | 0.15 | £120 | £18 |
| 17.5% | 0.175 | £120 | £21 |
| 20% | 0.20 | £120 | £24 |
| 25% | 0.25 | £120 | £30 |
Memorising the multipliers for 10%, 20%, and 25% will cover the vast majority of KS3 percentage questions.
How does VAT work in the UK?
VAT (Value Added Tax) is a tax added to the sale price of most goods and services in the UK. There are three standard rates:
- Standard rate: 20% — applies to most goods and services.
- Reduced rate: 5% — applies to items such as domestic fuel and children's car seats.
- Zero rate: 0% — applies to items such as most food and children's clothing.
At KS3 the standard 20% rate is the one you will almost always work with. The key idea is that the buyer pays the pre-VAT price plus the tax on top.
How do I calculate the price including VAT?
Price including VAT = pre-VAT price × 1.20 (for the 20% standard rate)
This works because you are keeping 100% of the original price and adding 20%, giving a total of 120% = 1.20 as a multiplier.
Worked Example 3 — A jacket has a pre-VAT price of £90. What is the total price including 20% VAT?
Total = £90 × 1.20 = £108
Check: 20% of £90 = 0.20 × £90 = £18; £90 + £18 = £108 ✓
Worked Example 4 — A laptop has a pre-VAT price of £85. What is the total price including 20% VAT?
Total = £85 × 1.20 = £102
Check: 20% of £85 = £17; £85 + £17 = £102 ✓
How do I find the original price before VAT?
If a price already includes VAT, you need to reverse the process. Dividing by 1.20 undoes the 20% addition:
Pre-VAT price = price including VAT ÷ 1.20
A common mistake is to subtract 20% of the inclusive price instead — this is incorrect because the 20% was calculated on the pre-VAT price, not on the total.
Worked Example 5 — A laptop costs £360 including 20% VAT. Find the price before VAT.
Pre-VAT price = £360 ÷ 1.20 = £300
Check: £300 × 1.20 = £360 ✓
Note: £360 × 0.80 = £288 — this is the wrong answer because it removes 20% of the VAT-inclusive price, which overcorrects.
How do I solve real-life percentage problems?
The same multiplier method applies to tips, discounts, and mark-ups. The key is to identify whether you are finding a percentage of the original, or finding the result after the change.
Worked Example 6 — A restaurant bill is £75. A 12.5% service charge is added. What is the total bill?
Service charge = 0.125 × £75 = £9.375, rounded to £9.38. Total = £75 + £9.38 = £84.38
Alternatively, using the multiplier for the total: £75 × 1.125 = £84.375 ≈ £84.38 ✓
Worked Example 7 — A shop buys trainers for £60 and adds a 25% mark-up to find the selling price.
Selling price = £60 × 1.25 = £75
Check: 25% of £60 = £15; £60 + £15 = £75 ✓
Tip: when you see "mark-up of x%", add x% to 100% and use that as your multiplier (e.g. 25% mark-up → 1.25). When you see "discount of x%", subtract x% from 100% (e.g. 30% discount → 0.70).
Frequently Asked Questions
What is the difference between the fraction method and the multiplier method?
They are mathematically identical — the multiplier method is simply a shorthand version of the fraction method, because writing "÷ 100 × amount" is the same as "× (percentage/100)". Once you are comfortable with decimals, the multiplier method is faster and less prone to errors in a written exam. Use whichever method your teacher has introduced first.
Why do I divide by 1.20 to reverse VAT, not subtract 20%?
The 20% VAT was calculated on the original (pre-VAT) price, not on the VAT-inclusive total. If you subtract 20% of the inclusive price, you are removing a larger amount than was actually added, so the result is too low. Dividing by 1.20 exactly reverses the multiplication that was used to add the VAT in the first place.
Do all goods in the UK have 20% VAT?
No. The standard rate of 20% applies to most goods and services, but a reduced rate of 5% applies to some items (such as domestic energy), and a zero rate of 0% applies to essentials such as most food, children's clothing, and books. At KS3 you will almost always be told which rate to use — if in doubt, assume 20% unless the question states otherwise.
Can I use the multiplier method for percentages greater than 100%?
Yes. For example, increasing an amount by 130% means the final value is 230% of the original, so the multiplier is 2.30. This situation arises in growth and percentage increase questions but follows exactly the same logic as the examples above.
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