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Direct and Inverse Proportion

A self-marking exercise in solving direct and inverse variation problems.

Level 1 Level 2 Level 3 Unitary Method Description Help Exam Questions More Ratio Activities

This is level 2; Inverse proportion. You can earn a trophy if you get at least 7 correct.

1. If \(a\) is inversely proportional to \(b\) and \(a=4\) when \(b=6\)

      find \(a\) when \(b=8\)
Correct Wrong

      and find \(b\) when \(a=6\)
Correct Wrong

2. If \(c\) is inversely proportional to \(d\) and \(c=5\) when \(d=56\)

      find \(c\) when \(d=8\)
Correct Wrong

      and find \(d\) when \(c=7\)
Correct Wrong

3. If \(e\) is inversely proportional to \(f\) and \(e=6\) when \(f=80\)

      find \(e\) when \(f=10\)
Correct Wrong

      and find \(f\) when \(e=8\)
Correct Wrong

4. If \(g\) is inversely proportional to \(h\) and \(g=7\) when \(h=90\)

      find \(g\) when \(h=1\)
Correct Wrong

      and find \(h\) when \(g=0.9\)
Correct Wrong

5. A teacher shared some cherries between a group of children on the playground. There were six children in the group and they got four cherries each. How many cherries would they have got each if there were eight children in the group?
Correct Wrong

6. A fish pond can be filled in ten hours by three identical hose pipes. How many hours would it take to fill the pond by five identical hose pipes?
Correct Wrong

This is Direct and Inverse Proportion level 2. You can also try:
Level 1 Level 3


Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

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Featured Activity

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Without Lifting

Can you draw these diagrams without lifting your pencil from the paper? This is an interactive version of the traditional puzzle. Some diagrams are possible while others are not. What is the rule?


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Description of Levels



Level 1 - Direct proportion

Level 2 - Inverse proportion

Level 3 - Mixed non-linear questions

Unitary Method

Direct and Inverse Proportion

This video is from Mannel's Maths Music.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly.