Percentages crop up in almost every GCSE Maths paper and in everyday life — discounts, tax, interest rates, and data analysis all rely on them. Both Foundation and Higher tier students must handle percentage of an amount, percentage change, and converting between fractions, decimals, and percentages. Higher tier adds reverse percentages and repeated percentage change (compound interest and depreciation). This guide covers every skill with worked examples, common pitfalls, and practice questions. For the full list of topics you should be revising, see our complete GCSE Maths topics list.
What Is a Percentage?
A percentage is a number expressed as a fraction of 100. The word itself comes from the Latin "per centum", meaning "out of one hundred". So 45% means 45 out of 100, or 45/100, or 0.45.
Key Formulas
Converting Between Forms
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 3/10 | 0.3 | 30% |
To convert a percentage to a decimal, divide by 100. To convert a decimal to a percentage, multiply by 100. To convert a fraction to a percentage, divide the numerator by the denominator and multiply by 100.
Step-by-Step Method
Finding a Percentage of an Amount (Non-Calculator)
- Find 10% by dividing the amount by 10.
- Use 10% to build up the percentage you need. For example, 35% = 3 × 10% + 5% (and 5% is half of 10%).
- Alternatively, convert the percentage to a decimal and multiply.
Percentage Increase or Decrease
- Work out the percentage of the amount (the increase or decrease).
- Add it to the original (for an increase) or subtract it (for a decrease).
- Alternatively, use the multiplier method: multiply the original by 1.r for an r% increase or by (1 − r/100) for a decrease.
Percentage Change
- Find the difference between the new value and the original value.
- Divide this difference by the original value.
- Multiply by 100 to convert to a percentage.
- State whether it is an increase or decrease.
Reverse Percentages (Higher)
- Identify the multiplier that was used (e.g. a 20% increase uses a multiplier of 1.2).
- Divide the final amount by this multiplier to find the original.
Compound Change (Higher)
- Identify the multiplier for one period.
- Raise the multiplier to the power of the number of periods.
- Multiply the original amount by this result.
Worked Example 1 — Foundation Level
Question: A laptop costs £480. It is reduced by 15% in a sale. Work out the sale price.
Working:
Method — using the multiplier: a 15% decrease has a multiplier of 1 − 0.15 = 0.85.
Sale price = £480 × 0.85
480 × 0.85: 480 × 0.8 = 384; 480 × 0.05 = 24; 384 + 24 = 408.
Answer: £408
Worked Example 2 — Higher Level
Question: After a 12% increase, a house is worth £235,200. Work out the original price of the house.
Working:
Step 1 — A 12% increase uses a multiplier of 1.12.
Step 2 — The final value equals the original × 1.12. So the original = £235,200 ÷ 1.12.
Step 3 — 235200 ÷ 1.12 = 210000.
Answer: £210,000
Common Mistakes
- Using the new value instead of the original when calculating percentage change. The denominator must always be the original amount, not the new one.
- Adding or subtracting the percentage from the final value in reverse percentage questions. You must divide by the multiplier, not subtract the percentage of the given amount. For example, if a price after a 20% increase is £60, the original is NOT £60 − 20% of £60 = £48. It is £60 ÷ 1.2 = £50.
- Confusing simple and compound interest. Simple interest is the same amount each period. Compound interest applies the percentage to the new total each period, so it grows faster.
- Forgetting to state increase or decrease in percentage change questions. The examiner expects you to label the direction of change clearly.
Exam Tips
- Learn the multiplier method. It is faster than finding the percentage and adding/subtracting separately, and it is essential for compound change questions.
- On non-calculator papers, build percentages from 10% and 1%. This is reliable and quick — see our formulas guide for the key relationships to memorise.
- Read the question carefully to see if it asks for the new amount or the change. These are different values and confusing them loses marks.
- Use estimation to sense-check. A 15% decrease on £480 should give something a bit less than £480. If you get £552, you know you added instead of subtracting.
Practice Questions
Q1 (Foundation): Find 35% of £260.
Q2 (Foundation): A jumper originally costs £45. Its price increases by 8%. What is the new price?
Q3 (Higher): £5,000 is invested at 3% compound interest per year. Work out the value of the investment after 4 years. Give your answer to the nearest penny.
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Related Topics
Summary
- A percentage means "out of 100" and can be written as a fraction or a decimal.
- Use the multiplier method for percentage increase, decrease, and compound change.
- Percentage change = (change ÷ original) × 100 — always divide by the original.
- For reverse percentages, divide the final amount by the multiplier to find the original.
- Compound interest applies the percentage to the running total each period.
- Always check whether a question asks for the change or the new amount.
- Estimation is your best friend for catching errors on percentage questions.