Deriving Proportions

## Deriving Proportions

A proportion is used to describe how a part relates to a whole.

A ratio relates how parts are related to each other.

This can be shown operating as fractions. If £20 was split in the ratio 7:13 then the fractions are:

frac(7)(20) and frac(13)(20)

with the ratios being a comparison of the numerators (7:13), and the proportions being the numerator and the denominator.

## Example 1

A road crew has relaid part of a new road with fresh tarmac. They completed 6km in 6 days. A second road crew has become available. If both road crews can work at the same time, how long should it take to complete 10km?

It takes a road crew 1 day to lay 1km.

Two road crews should complete 2km per day.

10km ÷ 2 = 5 days

## Example 2

A prize draw distributes first, second and third place prizes in the ratio 5:3:2. What proportion of the prize money does the first place winner receive? Show the proportion as a fraction.

Total of the ratios is 5 + 3 + 2 = 10

First place gets 5 out of 10, or frac(1)(2)

Answer: frac(1)(2)