James and Helen get pocket money in the ratio \(3:5\). The total amount of pocket money they are given is £24. 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.

\(24 \div 8 = 3\)

• James gets \(3 \times \pounds3 = \pounds9\)
• Helen gets \(5 \times \pounds3 = \pounds15\)

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.

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