Percentages
Year 10 students frequently struggle with percentage calculations, often confusing the decimal conversion or applying percentages incorrectly in real-world contexts. The GCSE Foundation specification requires mastery of percentage calculations, including finding percentages of amounts and calculating percentage increases and decreases.
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Why it matters
Percentage calculations appear in every aspect of adult life, from calculating VAT at 20% on a £50 purchase (£10 tax) to understanding mortgage rates and salary increases. Students use percentages to interpret data in geography coursework, calculate concentrations in science experiments, and analyse statistics in history. Shop discounts during sales events provide immediate context—a 25% discount on £80 trainers saves £20. GCSE maths papers consistently include percentage questions worth 15-20 marks across different difficulty levels. Financial literacy depends on percentage understanding, whether calculating compound interest on savings accounts or determining the real cost of credit card debt at 18% APR annually.
How to solve percentages
Percentages — how to
- Convert the percent to a decimal by dividing by 100.
- Multiply the decimal by the base number.
- For discounts: subtract the discount from the original.
Example: 20% of 80 → 0.20 × 80 = 16.
Worked examples
A class has 20 students. 10% are absent. How many are absent?
Answer: 2
- Convert percent to fraction → 10% = 1/10 — 10% is a common fraction — memorise these.
- Apply to the base → 20 × 10/100 = 2 — Take a tenth of 20.
- Verify → 2 × 100 ÷ 20 = 10% ✓ — Check backwards.
What is 50% of 40?
Answer: 20
- Convert percent to decimal → 50% = 0.5 — 50% means 50 per hundred, so divide by 100.
- Multiply by the base → 0.5 × 40 = 20 — Multiplying the decimal by the base gives the percentage amount.
- Verify → 20 ÷ 40 × 100 = 50% ✓ — Working backwards confirms the percent.
What is 20% of 100?
Answer: 20
- Convert to decimal → 20% = 0.2 — Divide the percent by 100.
- Multiply → 0.2 × 100 = 20 — Multiply the decimal by the base.
- Verify → 20 ÷ 100 × 100 = 20% ✓ — Check in reverse.
Common mistakes
- Students often calculate 20% of 60 as 20 × 60 = 1200 instead of converting to 0.2 × 60 = 12
- When finding percentage increases, pupils frequently add the percentage directly rather than calculating the increase first—finding 15% increase of £40 as £55 instead of £40 + (0.15 × £40) = £46
- Converting percentages to decimals incorrectly, writing 25% as 0.025 instead of 0.25, leading to answers that are 10 times too small