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GCSE/Mathematics/WJEC

R3Express one quantity as a fraction of another

Notes

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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Practice questions

Try each before peeking at the worked solution.

  1. Question 14 marks

    Express money quantities as a fraction

    WJEC Unit 1 (Non-calculator) — Foundation

    (a) Express 80p as a fraction of £4. Give your answer in its simplest form. (2 marks)
    (b) Express 45 minutes as a fraction of 2 hours. Give your answer in its simplest form. (2 marks)

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  2. Question 23 marks

    Express in a real-world context

    WJEC Unit 2 (Calculator) — Foundation

    In an Eisteddfod choir of 60 members, 24 are sopranos.

    (a) Express the number of sopranos as a fraction of the choir, in simplest form. (2 marks)
    (b) Express your answer to (a) as a percentage. (1 mark)

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  3. Question 34 marks

    Improper-fraction context with units

    WJEC Unit 1 (Non-calculator) — Intermediate

    A piece of timber is 2.4 m long. A second piece is 90 cm long.

    (a) Express the length of the second piece as a fraction of the first, in simplest form. (3 marks)
    (b) Hence, express the length of the first piece as a fraction of the second. (1 mark)

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Flashcards

R3 — Express one quantity as a fraction of another

7-card SR deck for WJEC GCSE Mathematics — Leaves Batch 1 topic R3

7 cards · spaced repetition (SM-2)