GCSE Maths grade 4 basics · topic 3 of 9

Ratio: GCSE Maths grade 4 basics

Simplifying ratios, sharing an amount in a ratio, scaling recipes and comparing prices. Almost every ratio question comes down to one idea: find what one part is worth.

Practise: 11 questions Read the basics first

In plain English

Simplify a ratio like a fraction: divide every part by the same number until you can't go further.
Sharing in a ratio: add the parts to find the total number of parts, divide the amount by it to find one part, then multiply.
Recipes and scaling: find the amount for 1 (or for a handy number), then multiply up.
Best buys: work out the price of the same amount of each (per 100 g, or per item) and compare.

Worked example

Share £45 in the ratio 2 : 7.

Total parts: 2 + 7 = 9
One part: £45 ÷ 9 = £5
2 parts = £10 and 7 parts = £35
Check: £10 + £35 = £45

Answer: £10 and £35

Most common mistake

WrongShare £45 in the ratio 2 : 7: £45 ÷ 2 and £45 ÷ 7

Right£45 ÷ (2 + 7) = £5 per part, so £10 and £35

Divide by the total number of parts, not by each number in the ratio. Your answers should always add back to the amount you started with.

Practice questions (11)

Try each one on paper first, then open the worked answer and mark yourself. You don't need a calculator for any of these.

Q1.Simplify 12 : 18
Show worked answer
1. Both numbers divide by 6
2. 12 ÷ 6 = 2 and 18 ÷ 6 = 3
Answer: 2 : 3
Q2.Simplify 45 : 30 : 15
Show worked answer
1. All three divide by 15
2. 45 ÷ 15 = 3, 30 ÷ 15 = 2, 15 ÷ 15 = 1
Answer: 3 : 2 : 1
Q3.Share £40 in the ratio 3 : 5.
Show worked answer
1. Total parts: 3 + 5 = 8
2. One part: £40 ÷ 8 = £5
3. 3 × £5 = £15 and 5 × £5 = £25
Answer: £15 and £25
Q4.Share 72 sweets in the ratio 1 : 2 : 3.
Show worked answer
1. Total parts: 1 + 2 + 3 = 6
2. One part: 72 ÷ 6 = 12
3. 12, 24 and 36
Answer: 12, 24 and 36
Q5.The ratio of boys to girls in a club is 2 : 3. There are 12 boys. How many girls are there?
Show worked answer
1. 2 parts = 12 boys, so 1 part = 6
2. Girls: 3 parts = 3 × 6 = 18
Answer: 18
Q6.A recipe for 4 people uses 300 g of flour. How much flour is needed for 6 people?
Show worked answer
1. For 1 person: 300 ÷ 4 = 75 g
2. For 6 people: 6 × 75 = 450 g
Answer: 450 g
Q7.5 pens cost £3.50. How much do 8 pens cost?
Show worked answer
1. 1 pen: £3.50 ÷ 5 = £0.70
2. 8 pens: 8 × £0.70 = £5.60
Answer: £5.60
Q8.Red and blue counters are in the ratio 3 : 7. What fraction of the counters are red?
Show worked answer
1. Total parts: 3 + 7 = 10
2. Red is 3 parts out of 10
Answer: 3/10
Q9.Paint is mixed from red and white in the ratio 4 : 1. Sam makes 20 litres. How much red paint does she use?
Show worked answer
1. Total parts: 4 + 1 = 5
2. One part: 20 ÷ 5 = 4 litres
3. Red: 4 × 4 = 16 litres
Answer: 16 litres
Q10.A 500 g box of cereal costs £2.40. A 750 g box costs £3.45. Which is better value?
Show worked answer
1. 500 g box: £2.40 ÷ 5 = £0.48 per 100 g
2. 750 g box: £3.45 ÷ 7.5 = £0.46 per 100 g
3. The 750 g box is cheaper per 100 g
Answer: The 750 g box
Q11.Amy and Ben share some money in the ratio 5 : 3. Amy gets £10 more than Ben. How much does Amy get?
Show worked answer
1. The difference is 5 − 3 = 2 parts
2. 2 parts = £10, so 1 part = £5
3. Amy gets 5 parts: 5 × £5 = £25
Answer: £25

Can you do these?

Simplify a ratio
Share an amount in a given ratio
Use a ratio when one part is known
Scale a recipe and compare best buys

Tick them off on the printable checklist. Want more? The Core sections of our free number notes cover the same maths (they are written for IGCSE, but the basics are the same).