Fractions and percentages as operators

"Find 3/5 of £40" or "Increase 250 by 18%" — both ask you to operate on a quantity using a fraction or percentage. OCR J560 examines this on every paper, from simple share-of to repeated percentage change.

Fraction of a quantity

a/b of N means (a × N) ÷ b. Or equivalently, divide by b first then multiply by a.

Example: 3/5 of £40 = (3 × 40)/5 = 120/5 = £24. Or: 40 ÷ 5 = 8, 8 × 3 = 24.

Percentage of a quantity

x% of N means (x/100) × N.

Example: 18% of 250 = 0.18 × 250 = 45.

Quick mental tools:

• 10% = divide by 10.
• 5% = half of 10%.
• 1% = divide by 100.
• 25% = quarter; 50% = half; 75% = three-quarters.

Percentage increase / decrease (multiplier method)

Use a single multiplier — the most efficient method, and the one OCR mark schemes prefer at Higher.

• Increase by 18% → × 1.18.
• Decrease by 18% → × 0.82.
• Increase by 200% → × 3 (because 100% + 200% = 300%).

Example: a price of £80 rises by 15%. New price = 80 × 1.15 = £92.

Repeated percentage change (compound)

For n applications of multiplier r: Final = Initial × r^n.

Example: a £5,000 investment earning 4% per year compound for 6 years: Final = 5000 × 1.04^6 = 5000 × 1.2653... = £6,326.60 (to 2 d.p.).

Reverse percentages (Higher)

If a price after a 20% increase is £108, what was it before? Multiplier was 1.2. Original = 108 ÷ 1.2 = £90.

If a sale price is £45 after a 25% reduction: Multiplier was 0.75. Original = 45 ÷ 0.75 = £60.

The classic OCR trap: students compute "25% of £45 = £11.25" and add it. WRONG — that gives £56.25, not £60.

Fraction increase / decrease

Increase by 1/4 → multiply by 5/4. Decrease by 2/5 → multiply by 3/5.

OCR mark scheme conventions

• M1 for the multiplier (e.g. 1.18 or 0.82).
• M1 for the calculation.
• A1 for the answer with correct units (£ to 2 d.p. for money).
• Reverse percentage: M1 for dividing (not multiplying) by the multiplier.