Percentages — GCSE Maths

Calculate percentages, increases, decreases and reverse percentages

What are percentages?

  • A percentage is a number out of 100. The symbol is %.
  • At GCSE, you need to: find a percentage of an amount, calculate percentage increase and decrease, and find the original value.
  • Percentages appear in finance, data, and everyday situations.
  • A solid understanding of percentages will help across many GCSE topics.

Key Words

  • Percentage — A number out of 100
  • Multiplier — A decimal used to calculate a percentage change (e.g. 0.85 for 15% decrease)
  • Original value — The starting amount before a change

Finding a percentage of an amount

  • Method: convert the percentage to a decimal, then multiply.
  • 35% of £240: convert 35% → 0.35. Then 0.35 × 240 = £84.
  • To convert a percentage to a decimal, divide by 100.
  • 72% → 0.72. Then 0.72 × 300 = 216.
  • This method works for any percentage and any amount.

Percentage increase and decrease

  • Percentage increase: new value = original × (1 + rate).
  • Example: increase £150 by 20%. Multiplier = 1.20. 150 × 1.20 = £180.
  • Percentage decrease: new value = original × (1 − rate).
  • Example: decrease £200 by 15%. Multiplier = 0.85. 200 × 0.85 = £170.
  • The multiplier is the key — always calculate it first.

Percentage change

  • Percentage change = (change ÷ original) × 100.
  • Example: price rises from £40 to £50. Change = £10.
  • (10 ÷ 40) × 100 = 25% increase.
  • Example: value drops from £80 to £60. Change = £20.
  • (20 ÷ 80) × 100 = 25% decrease.

Worked Examples

Example 1: VAT at 20%

  1. A laptop costs £650 before VAT. Find the price with 20% VAT added.
  2. Multiplier for 20% increase: 1 + 0.20 = 1.20
  3. £650 × 1.20 = £780
  4. The price including VAT is £780.

Example 2: Sale price

  1. A jacket was £120. It is now 35% off. Find the sale price.
  2. Multiplier for 35% decrease: 1 − 0.35 = 0.65
  3. £120 × 0.65 = £78
  4. The sale price is £78.

Practice Questions

  • Find 40% of £350.
    Answer: £140
    40% as a decimal is 0.40. 0.40 × 350 = 140.
  • A TV costs £480. It is reduced by 25%. What is the new price?
    Answer: £360
    Multiplier = 1 − 0.25 = 0.75. 480 × 0.75 = 360.
  • A salary increases from £24,000 to £27,600. What is the % increase?
    Answer: 15%
    Change = 3600. (3600 ÷ 24000) × 100 = 15%.
  • Increase £560 by 12.5%.
    Answer: £630
    Multiplier = 1.125. 560 × 1.125 = 630.
  • A car was worth £8,000. It is now £6,400. What is the percentage decrease?
    Answer: 20%
    Change = 1600. (1600 ÷ 8000) × 100 = 20%.

Exam-Style Question

A coat costs £95 before a 30% reduction in a sale. After the sale, the price is increased by 20%. Calculate the final price. Show your working.

Mark Scheme

  • 1 mark: Sale price = 95 × 0.70 = £66.50
  • 1 mark: Final price = 66.50 × 1.20
  • 1 mark: Final price = £79.80

Model Answer: Sale price: £95 × 0.70 = £66.50 After 20% increase: £66.50 × 1.20 = £79.80 Final price = £79.80

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