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Grade 7–9Curriculum · Maths: relationships and change

Proportion and Inverse Proportion — Worksheets with Answers

Practise direct and inverse proportion with everyday word problems and a full answer key.

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Areas on this sheet

  • Relationships and change · 20Linear functions, proportionality, percentage change and interest.

Inverse proportion · 12-14 years

Name: ____________________
1.x · y is constant. x = 3 gives y = 12. Find y when x = 2.

2.A bag of sweets gives 8 sweets each to 6 children. How many does each get if 8 children share it?

3.x · y is constant. x = 2 gives y = 12. Find y when x = 8.

4.Facts: A trip takes 4 hours at 60 km/h. Question: How long does it take at 80 km/h?

5.x · y is constant. x = 4 gives y = 9. Find y when x = 3.

6.2 painters need 36 days to paint a house. How many days would 3 painters need?

7.x · y is constant. x = 4 gives y = 15. Find y when x = 2.

8.Facts: 4 painters need 15 days to paint a house. Question: How many days would 3 painters need? Show how you worked it out.

9.x · y is constant. x = 12 gives y = 10. Find y when x = 2.

10.A trip takes 3 hours at 80 km/h. How long does it take at 40 km/h?

11.x · y is constant. x = 4 gives y = 12. Find y when x = 8.

12.Facts: 3 painters need 24 days to paint a house. Question: How many days would 8 painters need?

13.x · y is constant. x = 12 gives y = 4. Find y when x = 2.

14.Facts: A trip takes 2 hours at 120 km/h. Question: How long does it take at 40 km/h? Answer with the correct unit.

15.x · y is constant. x = 12 gives y = 4. Find y when x = 3.

16.8 painters need 9 days to paint a house. How many days would 6 painters need?

17.x · y is constant. x = 3 gives y = 4. Find y when x = 2.

18.Facts: A trip takes 4 hours at 60 km/h. Question: How long does it take at 40 km/h? Answer with the correct unit.

19.x · y is constant. x = 6 gives y = 2. Find y when x = 2.

20.Facts: A trip takes 6 hours at 40 km/h. Question: How long does it take at 80 km/h?

Answer key

  1. 1. y = 18
  2. 2. 6
  3. 3. y = 3
  4. 4. 3 h
  5. 5. y = 12
  6. 6. 24 days
  7. 7. y = 30
  8. 8. 20 days
  9. 9. y = 60
  10. 10. 6 h
  11. 11. y = 6
  12. 12. 9 days
  13. 13. y = 24
  14. 14. 6 h
  15. 15. y = 16
  16. 16. 12 days
  17. 17. y = 6
  18. 18. 6 h
  19. 19. y = 6
  20. 20. 3 h

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  1. Choose the exercise type proportionality or inverse proportion.
  2. Pick age group 12–14 or 14–16, difficulty and calculations, word problems or a mix.
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About this generator

Proportional reasoning is one of the most important skills in maths. With direct proportion, doubling one quantity doubles the other: prices, recipes and fuel. With inverse proportion the product stays the same: more painters need fewer days and a faster speed gives a shorter trip. Choose either exercise type in the generator to compare them side by side. The answer key is calculated by the website, so it always matches the tasks. No sign-up is needed and no personal data is collected.

Popular uses

  • Direct vs inverse proportion
  • Recipes, prices and speed
  • Revision before a test
  • Differentiated homework

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Frequently asked questions

What is inverse proportion?
When one quantity doubles the other halves, so x · y stays constant.
How do I spot it?
Ask whether more of one means less of the other, like workers and days.

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