GCSE Ratio and Proportion (Foundation Maths) — Questions and Answers
Question 1: Simplify the ratio 18 : 24 to its simplest form.
- 9 : 12
- 6 : 8
- 3 : 4 (Correct answer)
- 2 : 3
Correct answer: 3 : 4
The highest common factor of 18 and 24 is 6, so dividing both parts by 6 gives 3 : 4.
To simplify a ratio, divide every part by the same number until there is no common factor left. Both 18 and 24 are divisible by 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4, giving 3 : 4. The ratios 9 : 12 and 6 : 8 are equivalent to 18 : 24 but are not in their simplest form because they can still be divided further.
Question 2: Share £150 between Amy and Ben in the ratio 2 : 3. How much does Ben get?
- £60
- £75
- £90 (Correct answer)
- £100
Correct answer: £90
There are 2 + 3 = 5 parts, so one part is £150 ÷ 5 = £30. Ben gets 3 parts = £90.
When sharing an amount in a given ratio, first add the parts together: 2 + 3 = 5 parts. Divide the total by the number of parts to find the value of one part: £150 ÷ 5 = £30. Then multiply by each person's share: Amy gets 2 × £30 = £60 and Ben gets 3 × £30 = £90. Check that the shares add back to the total: £60 + £90 = £150.
Question 3: A recipe for 4 people uses 300 g of flour. How much flour is needed for 10 people?
- 600 g
- 700 g
- 750 g (Correct answer)
- 1200 g
Correct answer: 750 g
For 1 person, 300 ÷ 4 = 75 g. For 10 people, 75 × 10 = 750 g.
This is a direct proportion problem: doubling the number of people doubles the flour. The unitary method finds the amount for one person: 300 g ÷ 4 = 75 g. Multiply by 10 to get 750 g. Alternatively, notice that 10 people is 2.5 times 4 people, so multiply 300 g by 2.5 to get the same answer.
Question 4: Write the ratio 2 : 5 in the form 1 : n.
- 1 : 2.5 (Correct answer)
- 1 : 3
- 1 : 0.4
- 1 : 10
Correct answer: 1 : 2.5
Divide both parts by 2: 2 ÷ 2 = 1 and 5 ÷ 2 = 2.5, giving 1 : 2.5.
To write a ratio in the form 1 : n, divide both parts by the first number so that the first part becomes 1. Here 2 : 5 becomes (2 ÷ 2) : (5 ÷ 2) = 1 : 2.5. Ratios written this way can include decimals. The ratio 1 : 0.4 would be the form n : 1 written the wrong way round (5 : 2 → 1 : 0.4).
Question 5: The exchange rate is £1 = €1.15. How many euros would you get for £240?
- €208.70
- €255.00
- €276.00 (Correct answer)
- €300.00
Correct answer: €276.00
Multiply the pounds by the rate: 240 × 1.15 = €276.
Currency conversion is a direct proportion problem. Because £1 is worth €1.15, £240 is worth 240 × 1.15 = €276. To convert the other way (euros to pounds) you would divide by 1.15. A quick check: 240 × 1 = 240 and 240 × 0.15 = 36, so 240 + 36 = 276.
Question 6: In a class, the ratio of boys to girls is 3 : 4. There are 12 boys. How many students are in the class altogether?
- 16
- 21
- 24
- 28 (Correct answer)
Correct answer: 28
3 parts = 12 boys, so 1 part = 4. Girls = 4 × 4 = 16. Total = 12 + 16 = 28.
The ratio 3 : 4 means for every 3 boys there are 4 girls. Since 3 parts represent 12 boys, one part is 12 ÷ 3 = 4 students. The girls make up 4 parts, so there are 4 × 4 = 16 girls. The total is 12 + 16 = 28, which is also 7 parts × 4. The answer 16 is only the number of girls, not the whole class.
GCSE Ratio and Proportion (Foundation Maths)
Simplify the ratio 18 : 24 to its simplest form.