Quantities as fractions of each other
A simple but mark-rich Edexcel topic — appears on every Foundation paper, often as a 2-mark opener or as part of a worded ratio problem.
Core idea
To express A as a fraction of B: write A/B, then simplify.
Worked example: 12 cm as a fraction of 30 cm. 12/30 = 6/15 = 2/5. So 12 cm is 2/5 of 30 cm.
Same units first!
Both quantities must be in the same units before forming the fraction.
Worked example: 25p as a fraction of £2. £2 = 200p. 25/200 = 1/8.
If you forget to convert: 25/2 = 12.5 — meaningless.
Worded contexts
"Sarah scored 18 out of 24 in a test. Express her score as a fraction." → 18/24 = 3/4. "A class of 30 has 12 girls. The fraction of girls is…" → 12/30 = 2/5.
Fraction → percentage
Multiply by 100% (or convert by ×100). 2/5 = 0.4 = 40%. 3/4 = 0.75 = 75%.
Fraction → ratio
n/(n+m) of a quantity ⇔ ratio n : m of that quantity. Example: girls are 12/30, boys are 18/30. Ratio girls : boys = 12 : 18 = 2 : 3.
Edexcel exam tip
Always simplify the final fraction. An unsimplified fraction risks losing the A1 accuracy mark unless the question states "in simplest form is not required" — which it almost never does.
⚠Common mistakes— Common errors
- Forgetting unit conversion.
- Inverting: 12 of 30 written as 30/12 instead of 12/30.
- Not simplifying.
- Misreading "out of" — "12 out of 30" means 12/30, with 30 as the total.
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