Deriving Proportions

Deriving Proportions


A proportion is used to describe how a part relates to a whole and is shown as

part : whole

where the first number is the selected amount, and the second number is the total amount.

For example, if there are 8 red cars in a car park and there are 42 cars altogether. The proportion is shown as

8 (red cars) : 42 (total cars); then simplify to 4:21

Make sure that you understand if the question is asking for part:part (ratio) or part:whole (proportion).

Use the unitary method to derive proportions when comparing amounts such as value-for-money items. This involves making one side of the proportion equal to 1.


1. A road crew have relaid part of a new road with fresh tarmac. They have completed 6km. They need to complete 8km altogether. What proportion of the road has been relaid?

Answer: 3 : 4

The proportion is 6km out of the 8km

Rewrite as 6 : 8, and simplify to 3 : 4

2. A recipe requires 100ml of cream. Some of the cream is used for the sauce, and the rest is used for a topping. If the proportion used for the sauce is 7 : 20, how much cream was used for the sauce?

Answer: 35 ml

Proportion is 7 : 20

Multiply up to get the total out of 100ml

7 x 5 : 20 x 5

35 : 100

35ml was used for the sauce