Fractions and percentages as operators

A fraction or percentage placed in front of a quantity acts as a multiplier — an "operator" that scales the value.

Fraction as operator

3/4 of 80 means 3/4 × 80 = 60.

The word "of" translates to multiplication.

Percentage as operator

25% of 80 = 0.25 × 80 = 20.

Convert percentage to decimal first (divide by 100), then multiply.

Increase and decrease multipliers

• Increase by 20% → multiply by 1.20.
• Decrease by 15% → multiply by 0.85.
• Increase by 100% → multiply by 2.

These are standard WJEC Higher tools because they chain easily.

Reverse operations (finding the original)

If a price after a 20% increase is £72, the original was £72 ÷ 1.20 = £60.

DO NOT subtract 20% of £72 — that gives a wrong answer of £57.60.

Compound operators

Increase 200 by 10%, then decrease the result by 10%.

• After increase: 200 × 1.10 = 220.
• After decrease: 220 × 0.90 = 198.
• Net change: −1% (NOT 0%).

Repeated percentage change

A 5% per annum increase over 3 years on £400: £400 × 1.05³ = £400 × 1.157625 = £463.05.

Fractions and percentages combined

3/5 of 70% of 200:

• 70% of 200 = 140.
• 3/5 of 140 = 84.

Or single line: 3/5 × 0.7 × 200 = 84.

WJEC exam tip

Percent-decrease questions phrased "what is the new price" are calculator marks. Percent-decrease questions phrased "find the original price before the discount" need the REVERSE operation (divide by 0.85, not multiply). Read carefully — examiners deliberately mix these two patterns to catch hasty candidates.