Topics / Maths
Proportion
Proportion questions ask you to scale a quantity up or down, or to reason about how one thing changes when another changes. The unitary method (find one, then scale) solves almost all of them.
What is tested
- Direct proportion (more of one means more of the other)
- Inverse proportion (more workers means fewer days)
- Recipes and best-value comparisons
Worked example
5 pens cost £3.50. How much do 8 pens cost?
- One pen: £3.50 ÷ 5 = £0.70.
- Eight pens: 8 × £0.70 = £5.60.
Answer: £5.60
Exam-day checklist
- Decide: direct or inverse proportion?
- Find the value of ONE unit first.
- Then scale to the amount asked for.
- Sense-check: does the answer go the right way?
Common mistakes
- Treating an inverse problem (workers and days) as direct.
- Adding instead of scaling.
- Forgetting units in the final answer.
Try it yourself
1. 4 workers build a wall in 6 days. How long would 8 workers take, working at the same rate?
Show answer
3 days
Total work is 4 × 6 = 24 worker-days; 24 ÷ 8 = 3 days.
2. A recipe uses 300 g of flour for 6 people. How much for 10 people?
Show answer
500 g
300 ÷ 6 = 50 g each, so 10 × 50 = 500 g.
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