Finding a percentage of an amount is one of the most useful skills in GCSE Maths and in everyday life. From calculating discounts to working out VAT, this topic appears on both calculator and non-calculator papers across AQA, Edexcel, and OCR.
What Is a Percentage of an Amount?
A percentage means "out of 100." Finding a percentage of an amount means working out what that fraction of 100 represents when applied to a given number. For example, 25% of 80 means 25/100 of 80.
There are two main approaches. On non-calculator papers, you build up to the required percentage using benchmarks like 10%, 5%, and 1%. On calculator papers, you use the multiplier method — convert the percentage to a decimal and multiply.
Both methods give the same answer, so choose whichever is faster for the numbers involved. The multiplier method is especially efficient for awkward percentages like 17.5%.
Key Formulas
Step-by-Step Method
- Non-calculator approach: Find 10% by dividing by 10. From there, find 5% (halve the 10%), 1% (divide the original by 100), and build up to the required percentage.
- Calculator/multiplier approach: Divide the percentage by 100 to get a decimal. Multiply the amount by this decimal.
- Check your answer makes sense — e.g. 25% of something should be roughly a quarter.
Worked Example 1 — Foundation Level
Question: Find 35% of 240 without a calculator.
Working:
Step 1 — Find 10% of 240: 240 ÷ 10 = 24.
Step 2 — Find 30%: 24 × 3 = 72.
Step 3 — Find 5%: half of 10% = 24 ÷ 2 = 12.
Step 4 — Add 30% + 5%: 72 + 12 = 84.
Answer: 84
Worked Example 2 — Higher Level
Question: A laptop costs £649. VAT at 20% is added. What is the total cost?
Working:
Step 1 — Find 20% of £649 using the multiplier: 0.20 × 649 = 129.80.
Step 2 — Add to the original: 649 + 129.80 = 778.80.
Answer: £778.80
Worked Example 3 — Exam Style
Question: There are 1200 students in a school. 45% of them are boys. 30% of the boys play football. How many boys play football? (3 marks)
Working:
Step 1 — Find the number of boys: 45% of 1200 = 0.45 × 1200 = 540.
Step 2 — Find 30% of the boys: 0.30 × 540 = 162.
Answer: 162 boys play football
Common Mistakes
- Moving the decimal point the wrong way. When finding 10%, divide by 10 (move the decimal one place left), not multiply. Students sometimes multiply by 10 instead.
- Forgetting to add the percentage back on. If a question asks for the total cost after adding VAT, you must add the VAT amount to the original price — do not give just the VAT amount.
- Using the wrong multiplier. 15% as a decimal is 0.15, not 1.5 or 0.015. Always divide the percentage by 100 carefully.
Exam Tips
- On non-calculator papers, show the 10% and 1% building blocks clearly. Examiners award method marks for these intermediate steps.
- On calculator papers, writing the multiplier calculation (e.g. 0.35 × 240) earns a method mark even if you press the wrong button.
- Read the question carefully — does it ask for the percentage amount only, or the new total?
Practice Questions
Q1 (Foundation): Find 15% of 360 without a calculator.
Q2 (Foundation): Find 12.5% of 480.
Q3 (Higher): A car is worth £18,500. Its value decreases by 8.5%. What is the new value?
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Related Topics
Summary
- A percentage of an amount = (percentage ÷ 100) × amount.
- On non-calculator papers, build up from 10% and 1%.
- On calculator papers, use the multiplier method (decimal × amount).
- Always check whether the question wants just the percentage amount or the new total.
- Show your working clearly to earn method marks on every GCSE exam board.
Test your understanding
5 quick MCQs to identify any misconceptions on this topic.
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