Ratio and Proportion Worksheet — KS3 — Intermediate
Ratio and Proportion worksheet for 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.
Mastering Ratios and Proportions
Key Stage 3 / Year 7-9 (Ages 11-14) - Intermediate Level
Instructions: This worksheet is designed to enhance your understanding of ratios and proportions. You will explore various problems and scenarios where these mathematical concepts are applied. Follow the instructions for each activity carefully and write your answers in the provided spaces.
Understanding Ratios
Express each of the following scenarios as a ratio in its simplest form. Write your answer in the box provided.
1. There are 8 apples and 12 oranges. What is the ratio of apples to oranges?
2. A class has 15 boys and 10 girls. What is the ratio of boys to girls?
3. A recipe uses 3 cups of flour and 2 cups of sugar. What is the ratio of flour to sugar?
Proportion Problems
Solve the following proportion problems. Cross-multiply to find the unknown value. Show your working clearly.
1. If 4/5 = x/25, find the value of x.
2. 7/9 = 21/y, find the value of y.
3. 3/4 = 9/z, find the value of z.
Real-World Ratio Applications
Apply your knowledge of ratios to solve these real-world problems. Show all your calculations.
1. A map has a scale of 1:1000. If the distance between two points on the map is 5 cm, what is the actual distance in metres?
2. A car travels 150 km using 10 litres of petrol. What is the car's fuel efficiency in km per litre?
3. A mixture contains 2 parts water and 3 parts juice. If there are 15 litres of juice, how much water is in the mixture?
Ratio Tables
Complete the table by finding the missing values. Use the given ratios to guide your calculations.
| Item | Quantity | Ratio | Missing Value |
| Apples | 12 | 3:1 | |
| Bananas | 18 | 3:2 | |
| Oranges | 24 | 4:3 |
1. Calculate the missing values for each item.
Scaling Up and Down
Use the given ratios to scale up or down. Write your answers clearly in the boxes provided.
1. A model car is built at a scale of 1:20. If the model is 15 cm long, how long is the actual car?
2. A recipe for 4 people uses 200g of pasta. How much pasta is needed for 10 people?
3. A photograph is enlarged from 10 cm to 25 cm. What is the scale factor?
Word Problems with Proportions
Read each word problem carefully and solve using proportions. Show all your working.
1. If 5 pencils cost £2, how much do 12 pencils cost?
2. A car travels 60 miles in 1.5 hours. How far will it travel in 4 hours at the same speed?
3. If 8 shirts cost £56, what is the cost of 15 shirts?
Ratio and Proportion in Geometry
Solve these geometry problems using ratios and proportions. Ensure to show your calculations.
1. The ratio of the sides of a triangle is 3:4:5. If the perimeter is 36 cm, find the length of each side.
2. A rectangle has a length to width ratio of 5:2. If the width is 8 cm, what is the length?
3. The angles of a triangle are in the ratio 2:3:5. Find the measure of each angle.
Proportional Relationships in Graphs
Interpret the graph to answer the questions below. Use the graph to identify proportional relationships.
Graph: A straight line graph showing a proportional relationship between x and y.
1. What is the constant of proportionality?
2. If x = 8, what is the value of y?
3. Describe the relationship between x and y.
Activity 1: 2:3 ; 3:2 ; 3:2
Activity 2: x = 20 ; y = 27 ; z = 12
Activity 3: 50 metres ; 15 km/litre ; 10 litres
Activity 4: 4 ; 12 ; 18
Activity 5: 300 cm ; 500g ; 2.5
Activity 6: £4.80 ; 160 miles ; £105
Activity 7: 9 cm, 12 cm, 15 cm ; 20 cm ; 36°, 54°, 90°
Activity 8: 2 ; 16 ; y is directly proportional to x
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