Dividing in a given ratio
Lots of things in everyday life are divided or shared into A relationship between two quantities.. Money is shared, liquids are mixed and teams are assigned using ratios.
Drawing a diagram to represent the ratio can make these tasks easier.
Example
James and Helen are given pocket money in the ratio \(3:5\). The total amount of pocket money they are given is ÂŁ24. How much money is each person given?
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 ÂŁ24 between the 8 parts by dividing 24 by 8 and put the amount into each part of the diagram.
\(24 \div 8 = 3\)
The diagram shows that:
- James gets \(3 \times \pounds3 = \pounds9\)
- Helen gets \(5 \times \pounds3 = \pounds15\)
This can also be done when A fraction is a part of a whole, for example 1/2. are involved as in the example below.
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 paint and white paint do you need?
The ratio has \(1 + 2 = 3\) parts.
4 divided by 3 = \(\frac{4}{3}\)
Each part is worth \(\frac{4}{3}\) litres.
The diagram shows that:
- the amount of red paint needed is \(\frac{4}{3} \times 1 = \frac{4}{3} = 1 \frac{1}{3} \:\text{litres}\)
- the amount of white paint needed is \(\frac{4}{3} \times 2 = \frac{8}{3} = 2 \frac{2}{3} \:\text{litres}\)