Sharing in a given ratio

Lots of things in everyday life are shared in ratios. Money is shared, liquids are mixed and teams are assigned using ratios.

Drawing a table to represent the ratio can make these tasks easier.

Example

James and Helen get pocket money in the ratio 3:5. The total amount of pocket money they are given is £32. How much money do they each get?

The amount is divided into 8 equal parts since 3 + 5 = 8. Draw a rectangle with 8 sections and divide it in the ratio 3:5, labelling the two parts with the names James and Helen. Since James’ name comes first he gets three of the parts as the 3 is the first number in the ratio. Helen gets 5 parts, since her name is second.

Share the £32 between the 8 parts by dividing 32 by 8 and put the amount into each part of the diagram.

32 \div 8 = 4

James (3)Helen (5)
£4£4£4£4£4£4£4£4

The table shows that:

  • James gets 3 \times \pounds4 = \pounds12
  • Helen gets 5 \times \pounds4 = \pounds20

This can also be done when fractions are involved.

Example

To make pink paint, red and white paint can be mixed in the ratio 1:2. If you need to make 4 litres of paint, how much red and white paint would you need?

The ratio has 1 + 2 = 3 parts.

4 divided by 3 = \frac{4}{3}

Each part is worth \frac{4}{3} litres.

Red (1)White (2)
\frac{4}{3} \frac{4}{3} \frac{4}{3}

Each part is worth \frac{4}{3} litres.

The table shows that:

  • the amount of red paint needed is 1 \times \frac{4}{3} = \frac{4}{3} \:\text{litres}
  • the amount of white paint needed is 2 \times \frac{4}{3} = \frac{8}{3} \:\text{litres}