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AQA GCSE Maths

Fractions, percentages and standard form — AQA GCSE Maths revision

Free revision notes, key terms, common exam traps and 5 practice questions with answers. About 4 minutes to read.

Percentages fast

  • Percentage increase of 12% → multiply by 1.12. Decrease of 12% → multiply by 0.88.
  • Reverse percentage: divide by the multiplier, don't subtract.
  • Percentage change = (change ÷ original) × 100.

Fractions and standard form

  • To divide fractions, flip the second one and multiply.
  • Standard form is A × 10ⁿ where 1 ≤ A < 10.
  • Multiplying standard form: multiply the numbers, add the powers.

Key terms

Multiplier
The decimal you multiply by to apply a percentage change.
Reciprocal
1 divided by the number — flip the fraction.
Standard form
A number written as A × 10ⁿ with 1 ≤ A < 10.
Surd
An irrational root, like √2, left in root form for exact accuracy.
Rationalise
To remove a surd from the denominator of a fraction.
Significant figure
A digit that contributes to the accuracy of a number, counted from the first non-zero digit.

Common exam traps

  • Doing reverse percentages by subtracting instead of dividing.
  • Leaving standard form with A ≥ 10 (e.g. 12 × 10³).
  • Adding denominators when adding fractions.

Practice questions with answers

  1. 1. A price rises 20% to £60. What was the original price?

    Answer: £50

    60 ÷ 1.2 = 50 — divide by the multiplier.

  2. 2. Which multiplier represents a 15% decrease?

    • • 1.15
    • • 0.15
    • • 0.85
    • • 0.15%

    Answer: 0.85

    100% − 15% = 85% = 0.85.

  3. 3. Write 0.00042 in standard form.

    Answer: 4.2 × 10⁻⁴

    Move the point four places right, so the power is −4.

  4. 4. Work out ⅔ ÷ ⅘ as a fraction in its simplest form.

    Answer: 5/6

    ⅔ × 5/4 = 10/12 = 5/6.

  5. 5. Work out 3/5 of £45.

    Answer: £27

    45 ÷ 5 = 9, then 9 × 3 = 27.

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