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Grade 7–9Common Core (CCSS) · Math: 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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Inverse proportion · 12-14 years

Name: ____________________

Worked example

  1. The goal: find a new value when one quantity falls as the other rises (more workers – less time).
  2. With inverse proportion, one thing decreases as the other increases. Example: 4 painters paint a house in 6 days.
  3. Work out the total work: 4 × 6 = 24 workdays.
  4. With 8 painters: 24 ÷ 8 = 3 days. More painters – fewer days.
  5. Check: read the question again. Does your answer give what was asked, with the right unit? Work backwards to see that it fits. ✓
Example: how to solve it
1.

Find y when x = 2, if x · y is constant and x = 3 gives y = 12.

2.

A bag of sweets gives 8 sweets each to 6 children. How many does each get if 8 children share it? Answer with the correct unit.

3.

Find y when x = 3, if x · y is constant and x = 2 gives y = 12.

4.

A trip takes 3 hours at 80 km/h. How long does it take at 60 km/h? Answer with the correct unit.

5.

Find y when x = 4, if x · y is constant and x = 8 gives y = 6.

6.

3 painters need 20 days to paint a house. How many days would 12 painters need? Answer with the correct unit.

7.

Find y when x = 2, if x · y is constant and x = 4 gives y = 15.

8.

4 painters need 15 days to paint a house. How many days would 3 painters need? Answer with the correct unit.

9.

Find y when x = 2, if x · y is constant and x = 12 gives y = 6.

10.

A bag of sweets gives 4 sweets each to 3 children. How many does each get if 2 children share it? Answer with the correct unit.

11.

Find y when x = 2, if x · y is constant and x = 6 gives y = 6.

12.

3 painters need 24 days to paint a house. How many days would 8 painters need? Answer with the correct unit.

13.

Find y when x = 12, if x · y is constant and x = 4 gives y = 12.

14.

A trip takes 4 hours at 60 km/h. How long does it take at 120 km/h? Answer with the correct unit.

15.

Find y when x = 6, if x · y is constant and x = 12 gives y = 10.

16.

A bag of sweets gives 40 sweets each to 3 children. How many does each get if 8 children share it? Answer with the correct unit.

17.

Find y when x = 2, if x · y is constant and x = 3 gives y = 16.

18.

3 painters need 4 days to paint a house. How many days would 2 painters need? Answer with the correct unit.

19.

Find y when x = 4, if x · y is constant and x = 3 gives y = 24.

20.

3 painters need 12 days to paint a house. How many days would 12 painters need? Answer with the correct unit.

Answer key

  1. 1. y = 18
  2. 2. 6 each
  3. 3. y = 8
  4. 4. 4 h
  5. 5. y = 12
  6. 6. 5 days
  7. 7. y = 30
  8. 8. 20 days
  9. 9. y = 36
  10. 10. 6 each
  11. 11. y = 18
  12. 12. 9 days
  13. 13. y = 4
  14. 14. 2 h
  15. 15. y = 20
  16. 16. 15 each
  17. 17. y = 24
  18. 18. 6 days
  19. 19. y = 18
  20. 20. 3 days

Created with WorksheetMint

Topics on this worksheet

Areas on this sheet

  • Relationships and change · 20

Step 1 of 5

Choose an area

Your choices

Area
Percentages
Exercise type
Inverse proportion
Age
12–14 years
Difficulty
Easy
Number of tasks
20
Task format
Mixed
Paper size
US Letter
1. Choose content
Area
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How to use the tool

  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.
  3. Print or save as PDF. “Create new version” gives new numbers with a matching answer key.

About this generator

Proportional reasoning is one of the most important skills in math. 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

How do I pick the right level?
Choose an age or grade in step 2. Start easier if the pupil is unsure – you can switch anytime and get new problems instantly.
Can I see the problems before printing?
Yes. The sheet shows exactly the problems that will print. Click New problems to swap them.
How do I include an answer key?
Turn on Answer key in the last step. It prints on its own page after the problems, with the same numbering.
What does the question mark next to a problem do?
It opens a step-by-step explanation of the method on screen. It is not printed and does not reveal the answer.
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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