Year 8 Ratio and Proportion Worksheet - Intermediate

Year 8 Ratio and Proportion worksheet for Year 8 (Key Stage 3 / Year 7-9 (Ages 11-14)). Intermediate level maths practice, aligned to the UK National Curriculum. Print-ready with answer key included.

Maths•Key Stage 3 / Year 7-9 (Ages 11-14)•Ratio and Proportionintermediate

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Ratio in Real Life: Year 8 Challenge

Key Stage 3 Mathematics • Ages 12–13 • Intermediate

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Instructions: Show your working clearly, especially when using the unitary method. Include units in your answers and round money to the nearest penny where needed. For currency conversions, use the exchange rate given in the question.

Direct Proportion: The Unitary Method

Find the amount for one unit first, then multiply to find the amount required. Show each step of your working and include units in your final answer.

1. 6 notebooks cost £9.00. How much do 10 notebooks cost? [3 marks]

2. A car uses 12 litres of fuel to travel 150 km. At the same rate, how many litres are needed for 275 km? [3 marks]

3. 8 metres of ribbon cost £5.60. What is the cost of 13 metres? [3 marks]

4. A recipe uses 300 g of flour to make 12 biscuits. How much flour is needed for 30 biscuits? [3 marks]

Best Buy: Compare Unit Prices

Work out the price per item or per kilogram for each option. Compare like with like, then state which option is better value and support your choice with calculations.

1. A pack of 6 juice cartons costs £2.10. A pack of 10 costs £3.30. Which pack is better value per carton, and by how much per carton? [3 marks]

2. A 750 g bag of rice costs £1.80. A 1.2 kg bag costs £2.76. Which bag is better value per kilogram, and by how much per kilogram? [3 marks]

3. Pack A has 8 pens for £3.20. Pack B has 12 pens for £4.50. Which pack is cheaper per pen? [3 marks]

4. A 500 ml bottle of shampoo costs £2.25. A 900 ml bottle costs £3.78. Which bottle is better value per litre? [3 marks]

Map Scales and Real Distances

Use each stated scale to convert the measured map or drawing distance into the real distance. Keep units consistent and show your calculation.

1. A map has a scale of 1 cm represents 4 km. Two villages are 7.5 cm apart on the map. What is their actual distance? [2 marks]

2. On a map, 3 cm represents 12 km. A walking route measures 8.25 cm. How long is the route in kilometres? [2 marks]

3. A scale drawing uses 1:50. A desk is 2.4 cm long on the drawing. What is its actual length in centimetres? [2 marks]

4. A garden plan uses a scale of 1:200. A path is 3.6 cm long on the plan. What is its actual length in metres? [3 marks]

Convert Units in Proportion Problems

Convert the units before comparing or calculating. Write the converted value with its unit, then complete the proportion calculation where needed.

1. Convert 2.4 kg to grams. [1 mark]

2. Convert 750 ml to litres. [1 mark]

3. A cyclist travels 18 km in 45 minutes at a constant speed. How far will the cyclist travel in 2 hours? Give your answer in kilometres. [3 marks]

4. A machine fills 2.5 litres of juice in 20 seconds. How many millilitres does it fill in 1 minute at the same rate? [3 marks]

Currency Conversion

Use the exchange rates supplied in each question; do not use a current exchange rate. Multiply or divide by the rate as appropriate, and give money answers to two decimal places.

1. The exchange rate is £1 = €1.17. How many euros will £45 buy? [2 marks]

2. The exchange rate is £1 = $1.25. How many pounds is $80 worth? [2 marks]

3. The exchange rate is £1 = ¥185. How many yen will £32 buy? [2 marks]

4. The exchange rate is £1 = €1.20. A museum ticket costs €18. How much is this in pounds? [2 marks]

Answer Key

Activity 1: 1. £15.00 ; 2. 22 litres ; 3. £9.10 ; 4. 750 g

Activity 2: 1. 6-pack: £0.35 per carton; 10-pack: £0.33 per carton; the 10-pack is better by £0.02 per carton ; 2. 750 g bag: £2.40 per kg; 1.2 kg bag: £2.30 per kg; the 1.2 kg bag is better by £0.10 per kg ; 3. Pack A: £0.40 per pen; Pack B: £0.375 per pen; Pack B is cheaper ; 4. 500 ml bottle: £4.50 per litre; 900 ml bottle: £4.20 per litre; the 900 ml bottle is better value

Activity 3: 1. 30 km ; 2. 33 km ; 3. 120 cm ; 4. 7.2 m

Activity 4: 1. 2,400 g ; 2. 0.75 litres ; 3. 48 km ; 4. 7,500 ml

Activity 5: 1. €52.65 ; 2. £64.00 ; 3. ¥5,920 ; 4. £15.00