Expressing one quantity as a fraction of another
A small but reliable Foundation/Intermediate topic. WJEC asks 1–2 marks routinely.
Same units first
Always convert both quantities to the same unit before forming the fraction.
Example: 45p as a fraction of £3.
- Convert £3 = 300p.
- Fraction = 45/300 = 9/60 = 3/20.
Simplification
Cancel by the highest common factor (HCF) until the fraction is in lowest terms.
Compound contexts
Often combined with percentages or ratios.
Example: in a school of 800 students, 320 study Welsh. What fraction of students study Welsh?
- 320/800. HCF(320, 800) = 160.
- 320 ÷ 160 = 2; 800 ÷ 160 = 5.
- Answer: 2/5.
To express the same information as a percentage: 2/5 = 40%.
"Of" means multiply
If the question follows up with "find 2/5 of 1200", that means 2/5 × 1200 = 480.
Improper fractions
If quantity A is bigger than quantity B, A as a fraction of B is bigger than 1.
Example: 90 minutes as a fraction of 1 hour. 1 hour = 60 min, so 90/60 = 3/2.
WJEC exam tip
Always (1) convert units first, (2) simplify fully — leaving 320/800 unsimplified loses A1, (3) check the question asked for fraction (not percentage or decimal).
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