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In this worksheet, students find the missing numbers in tables showing pairs in direct proportion.

'Proportion' worksheet

Key stage:  KS 3

Curriculum topic:   Ratio, Proportion and Rates of Change

Curriculum subtopic:   Solve Problems Involving Direct and Inverse Proportion

Difficulty level:  

Worksheet Overview

This worksheet is about keeping pairs of numbers in the same ratio.


If two quantities are in direct proportion, the ratio between corresponding values will always be the same.


a = 1 2 3 4 5
b = 1.5 3 4.5 6 7.5



In this table the ratio between a and b can be found by dividing the value of b by its corresponding value of a.


3 ÷ 2 = 1.5

4.5 ÷ 2 = 1.5


Now we know the ratio between the two values we can find b by multiplying a by 1.5.


For example, if a = 6 then b = 1.5 × 6 = 9


We can also use this ratio to find the value of a if we know what b is.


For example if b = 15, then a = 15 ÷ 1.5 = 10 


As we are doing the inverse we divide.

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