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Direct Proportion Calculations
Until you are more familiar with direct proportion calculations you are advised
to use explanations based on the “method of one” as shown below.
Example 1
If 3kg of apples cost £1.20, what will 5kg cost?
All questions like this assume a constant ratio between the two quantities (in this
example, the amount of apples and the cost). Therefore the cost and the amount
are directly proportional. A full explanation is included below, but not required.
Because the quantities are proportional, one-third (1kg) of the apples is one-
third of the cost. Therefore divide the cost of 3kg by 3 to obtain the cost of 1kg.
1 kg
costs £1.20 ÷ 3
= £0.40
Five times the apples is five times the cost. Multiply the cost of 1kg by 5.
5 kg
cost £0.40 × 5
= £2.00
Here’s the same “method of one” calculation but without all the explanation:
3 kg
cost £1.20
1 kg
costs £1.20 ÷ 3
= £0.40
5 kg
cost £0.40 × 5
= £2.00
Alternative, using fractions:
5 kg cost
5
3
× £1.20 = £2.00
Or, if you wish, use ratios as in:
3kg:£1.20 = 3kg ÷ 3:£1.20 ÷ 3 = 1kg:£0.40 = 1kg × 5:£0.40 × 5 = 5kg: £2.00
Example 2
A car travels 100 km in 2 hours. How long will it take to travel 250 km?
100 km
takes 2 hours
1 km
takes 2 hours ÷ 100 = 0.02 hours (or
1
50
hour )
250 km
takes 0.02 × 250 hours (or
1
50
× 250 hours ) = 5 hours
or, using fractions:
250 km takes
250
100
× 2 hours = 5 hours
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