Year 9 Ratio and Proportion Worksheet - Beginner

Year 9 Ratio and Proportion worksheet for Year 9 (Key Stage 3 / Year 7-9 (Ages 11-14)). Beginner 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 Proportionbeginner

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Ratio & Proportion: Year 9 Skills in Action

Year 9 • Ages 13–14 • Beginner

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Instructions: Work through the activities in order, showing clear working in each answer space. Use the formulae and worked example below as a guide, and include units in your answers where appropriate.

Inverse Proportion: Workers and Time

For a fixed amount of work, the number of workers and the time taken are inversely proportional. Use workers × days = a constant. In the example, 4 workers take 12 days, so the total is 48 worker-days. Show the calculation and include units.

1. 6 workers take 8 days to complete a job. How many days would 4 workers take at the same rate? [3 marks]

2. 5 identical pumps empty a tank in 18 hours. How long would 6 pumps take? [3 marks]

3. A journey takes 3 hours at an average speed of 80 km/h. How long would it take at 120 km/h for the same distance? [3 marks]

4. 8 people share a fixed amount of food equally for 15 days. For how many days would it last if 10 people shared it equally? [3 marks]

Compound Measures: Speed, Density and Pressure

Choose the relationship that fits each situation: speed = distance ÷ time, density = mass ÷ volume, and pressure = force ÷ area. Rearrange the relationship if needed, show your working, and give a suitable unit.

1. A cyclist travels 42 km in 2 hours. Calculate the average speed in km/h. [2 marks]

2. A metal block has a mass of 540 g and a volume of 200 cm³. Calculate its density in g/cm³. [2 marks]

3. A force of 600 N acts evenly over an area of 3 m². Calculate the pressure in N/m². [2 marks]

4. A runner travels at 5 m/s for 24 seconds. Calculate the distance travelled in metres. [2 marks]

Similar Shapes: Ratios and Scale Factors

Corresponding lengths in similar shapes are in the same ratio. Find the scale factor by comparing corresponding lengths, then apply it to the other length. State whether the scale factor enlarges or reduces the shape where asked.

1. Two similar triangles have corresponding sides of 4 cm and 10 cm. The smaller triangle has another side of 6 cm. Find the corresponding side on the larger triangle. [2 marks]

2. A model has a scale factor of 3 from a small shape to a larger similar shape. A side of the small shape is 7 cm. Find the corresponding side of the larger shape. [2 marks]

3. Similar rectangles have corresponding widths of 12 cm and 8 cm. A side of the 12 cm rectangle is 15 cm. Find the corresponding side of the 8 cm rectangle. [2 marks]

4. A photograph is enlarged so that a 5 cm length becomes 8 cm. Find the scale factor and the new length of a 12 cm feature. [3 marks]

Recognising Direct and Inverse Proportion

Use the table values to identify how each pair of quantities changes. For direct proportion, the ratio y ÷ x stays constant; for inverse proportion, the product x × y stays constant. Answer each question using the data shown.

Table A: x	Table A: y
Table B: x	Table B: y
1	4
1	24
2	8
2	12
3	12
3	8

1. In Table A, what is the constant value of y ÷ x? [2 marks]

2. In Table B, what is the constant value of x × y? [2 marks]

3. Which table shows direct proportion, and which shows inverse proportion? [2 marks]

Proportion Graphs: Match the Relationship

Each description gives enough information to recognise the shape of a graph through the origin. Match the relationship type to the description by writing the correct letter in each answer space. Use each letter once.

Relationship types: Direct proportion; Inverse proportion

A. A straight line rising from the origin; as x doubles, y doubles.

B. A curve that falls as x increases; x × y stays constant.

C. A straight line rising from the origin; as x triples, y triples.

D. A curve that rises as x increases; x ÷ y stays constant.

1. Which description represents direct proportion?

2. Which description represents inverse proportion?

3. In an inverse proportion graph, what happens to y as x increases?

Answer Key

Activity 1: 1. 12 days ; 2. 15 hours ; 3. 2 hours ; 4. 12 days

Activity 2: 1. 21 km/h ; 2. 2.7 g/cm³ ; 3. 200 N/m² ; 4. 120 m

Activity 3: 1. 15 cm ; 2. 21 cm ; 3. 10 cm ; 4. Scale factor 1.6; new length 19.2 cm