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Percentages Cambridge IGCSE Mathematics (9–1) revision

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In plain words

Per cent means "out of a hundred". The quickest way to work with percentages is with a multiplier: to add 15%, multiply by 1.15; to take off 20%, multiply by 0.8. One step, and it works backwards too.

Three things to know

  1. To find a percentage of an amount, multiply by the percentage as a decimal: 35% of 240 = 0.35 × 240. To increase by 15% multiply by 1.15; to decrease by 20% multiply by 0.80.
  2. Percentage change = change ÷ original × 100.
  3. To go back to the original amount, divide by the multiplier. Simple interest = principal × rate × time ÷ 100.

Worked example

A coat costs $72 after a 20% reduction. Find the original price.

  1. A 20% reduction leaves 80%, so the multiplier was 0.8.
  2. Original × 0.8 = 72, so original = 72 ÷ 0.8.
  3. = $90.

Tips and tricks

  • For "find the original", never add the percentage back on. 20% of 72 is not 20% of the original.
  • Percentage change is always out of the original amount.
5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Percentages: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

  1. What is 20% of 150?
    • 20
    • 30 (the answer)
    • 75
    • 130

    0.2 × 150.

  2. Which multiplier increases an amount by 12%?
    • 0.12
    • 0.88
    • 1.12 (the answer)
    • 12

    100% + 12% = 112% = 1.12.

  3. A price falls from $80 to $60. What is the percentage decrease?
    • 20%
    • 25% (the answer)
    • 33%
    • 75%

    20 ÷ 80 × 100.

  4. What is the simple interest on $200 at 5% per year for 2 years?
    • $10
    • $20 (the answer)
    • $210
    • $220

    200 × 5 × 2 ÷ 100.

  5. After a 10% increase, a price is $55. What was it before?
    • $45
    • $49.50
    • $50 (the answer)
    • $60.50

    55 ÷ 1.1.

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