Ratio and Proportion

A recipe uses flour and sugar in the ratio 3:1. If you use 6 cups of flour, how much sugar do you need?

• A1 cup
• B2 cups✓
• C3 cups
• D6 cups

Answer: The ratio 3:1 means for every 3 parts flour, you need 1 part sugar. If flour is 6 cups, then sugar is 6 ÷ 3 = 2 cups.

A map scale is 1:1000. A distance of 5 cm on the map represents how many metres in real life?

• A50 metres✓
• B500 metres
• C5,000 metres
• D50,000 metres

Answer: If 1 cm on the map = 1,000 cm in real life, then 5 cm = 5 × 1,000 = 5,000 cm = 50 metres.

In a classroom, the ratio of boys to girls is 2:3. If there are 10 boys, how many girls are there?

• A10
• B12
• C15✓
• D20

Answer: The ratio 2:3 means for every 2 boys, there are 3 girls. If there are 10 boys, then 10 ÷ 2 = 5 groups, so there are 5 × 3 = 15 girls.

Which ratio is equivalent to 2:5?

• A3:7
• B4:10✓
• C6:20
• D8:15

Answer: 2:5 = 4:10 (multiply both by 2). Check: 2:5 = 2×2:5×2 = 4:10.

A painter mixes red and blue paint in the ratio 3:2. If he uses 9 litres of red paint, how much blue paint does he use?

• A4 litres
• B6 litres✓
• C9 litres
• D12 litres

Answer: The ratio 3:2 means for every 3 parts red, there are 2 parts blue. If red is 9 litres, then 9 ÷ 3 = 3 groups, so blue is 3 × 2 = 6 litres.

If 3 pens cost £1.50, what is the cost of 1 pen?

• A£0.40
• B£0.50✓
• C£0.60
• D£0.70

Answer: Cost of 1 pen = £1.50 ÷ 3 = £0.50.

A recipe serves 4 people and needs 200g of flour. How much flour is needed for 8 people?

• A100g
• B200g
• C300g
• D400g✓

Answer: 8 people is double 4 people, so you need double the flour: 200g × 2 = 400g.

What is the ratio 10:15 in its simplest form?

• A1:2
• B2:3✓
• C5:10
• D10:15

Answer: 10:15 can be simplified by dividing both by 5. 10÷5:15÷5 = 2:3.

If 5 apples cost £2, how much do 15 apples cost?

• A£4
• B£6✓
• C£8
• D£10

Answer: 15 apples is 3 times 5 apples, so the cost is 3 × £2 = £6.

A model car is made to a scale of 1:64. If the real car is 4 metres long, how long is the model car?

• A5 cm
• B6 cm
• C6.25 cm✓
• D8 cm

Answer: 4 metres = 400 cm. Model length = 400 ÷ 64 = 6.25 cm.

In a bag of sweets, the ratio of red to yellow is 3:2. If there are 15 red sweets, how many sweets are there in total?

• A20
• B25✓
• C30
• D35

Answer: Red:Yellow = 3:2. If red = 15, then 15 ÷ 3 = 5 groups. Yellow = 5 × 2 = 10. Total = 15 + 10 = 25.

Which ratio is in its simplest form?

• A2:4
• B3:6
• C4:5✓
• D6:9

Answer: 4:5 cannot be simplified further (they share no common factors). All others can be simplified: 2:4 = 1:2, 3:6 = 1:2, 6:9 = 2:3.