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GCSE/Mathematics/Edexcel

N12Interpret fractions and percentages as operators

Notes

Fractions and percentages as operators

Edexcel 1MA1 tests this throughout Paper 1F and 1H. The big idea: a fraction or percentage is a multiplier. "25% of 80" means "0.25 × 80".

Fraction as multiplier

3/4 of 60 = 3/4 × 60 = 45.

For non-calculator: divide first to keep numbers small. 60 ÷ 4 = 15, then × 3 = 45.

Percentage as multiplier

15% of 240 = 0.15 × 240 = 36.

For non-calculator: 10% = 24, 5% = 12, total 15% = 36.

Increase / decrease as a single multiplier

  • Increase by 12% → multiplier 1.12.
  • Decrease by 12% → multiplier 0.88.
  • Increase by 7.5% → multiplier 1.075.

Reverse percentages (Higher and top-end Foundation)

If a price after a 20% increase is £108, original = 108 ÷ 1.20 = £90.

If a sale price after 30% off is £42, original = 42 ÷ 0.70 = £60.

Compound multiplier

A 5% rise each year for 3 years multiplies by 1.05³ = 1.157625, so a 15.7625% overall rise.

Common Edexcel mark-scheme phrasing

  • M1 for a correct multiplier (e.g. 1.20 for "increase by 20%").
  • M1 for setting up the correct equation (especially in reverse-% problems).
  • A1 for the correct final value.
  • B1 for stating the original / final amount with units.

Common mistakesCommon errors

  • Adding 20% as "+20" (treating % as a count, not a multiplier).
  • Forgetting to apply the multiplier and instead computing the increase only.
  • On reverse-%: dividing by 1.2 vs subtracting 20% — the latter is wrong.

AI-generated · claude-opus-4-7 · v3-edexcel-maths-leaves

Practice questions

Try each before peeking at the worked solution.

  1. Question 15 marks

    Fraction of an amount — Foundation

    Edexcel Paper 1F (non-calculator)

    (a) Work out 2/5 of £35. (2 marks)
    (b) Increase 80 kg by 15%. (3 marks)

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  2. Question 25 marks

    Reverse percentage — sale price

    Edexcel Paper 2F (calculator)

    In a sale, all prices are reduced by 25%. A coat is on sale for £75.

    (a) Find the original price of the coat. (3 marks)
    (b) Tariq pays the sale price using a 10% loyalty discount on top. How much does he pay? (2 marks)

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  3. Question 36 marks

    Compound percentage — Higher

    Edexcel Paper 2H — Higher

    A car is bought for £18,000. Its value depreciates by 12% each year for the first 2 years, then by 8% each year after that.

    (a) Find the value after 2 years. (3 marks)
    (b) Find the value after 4 years (i.e. 2 more years at 8% pa). (3 marks)

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Flashcards

N12 — Interpret fractions and percentages as operators

7-card SR deck for Edexcel GCSE Mathematics (1MA1) — Leaves Batch 4 topic N12

7 cards · spaced repetition (SM-2)