Key Stage 3 Ratio and Proportion

Direct and Inverse Proportion

Recognise and solve direct and inverse proportion problems in tables, graphs and equations.

Key idea

Find the multiplier or unit amount, then apply the same proportional change to the value you need.

What you will learn

Use direct proportion confidently.

Use inverse proportion confidently.

Use graphs confidently.

Use unitary method confidently.

✓I can explain what direct and inverse proportion means.

✓I can choose a suitable method without being told.

✓I can show clear working and check my answer.

Worked example

Model method

Step 1

There are 3 + 5 = 8 parts.

Step 2

Each part is £40 ÷ 8 = £5.

Step 3

The shares are 3 × £5 and 5 × £5.

Answer

£15 and £25

Question 1

Share £60 in the ratio 2:3.

Question 2

5 pens cost £3. Find the cost of 12 pens.

Question 3

Increase £80 by 15%.

These are linked to the wider Ratio and Proportion topic for now.

A compact Ratio and Proportion summary with key facts, methods, reminders and common mistakes.

KS3 exam-style Ratio and Proportion questions with mixed practice, marks-style prompts and model answers.