Sharing in a Ratio

How do I share an amount in a given ratio?

Add together all parts in the ratio to find the total number of parts in the whole
- $200 is to be shared between two people; A and B, in the ratio 5:3
- There are 8 “parts” in total, as A receives 5 parts and B receives 3 parts
Divide the amount being shared by the total number of parts
- $200 must be split into 8 parts, so this means that 1 part must be worth $25
  - 200 ÷ 8 = 25
Multiply the amount each part is worth by the number of parts for each quantity in the ratio
- Person A receives 5 parts, each worth $25
  - 5 × 25 = $125 for person A
- Person B receives 3 parts, each worth $25
  - 3 × 25 = $75 for person B
Check the values in the new ratio add up to the total amount being shared
- $125 + $75 = $200

Examiner Tip

Adding labels to your ratios will help make your working clearer and help you remember which number represents which quantity, e.g., $\begin{matrix} A & : & B \\ 3 & : & 4 \end{matrix}$

Worked example

A particular shade of pink paint is made using three parts red paint, to two parts white paint.
Mark needs 60 litres of pink paint in order to decorate a room in his house.

Calculate the volume of red and white paint that Mark needs to purchase in order to have enough paint to decorate the room.

The ratio of red to white is

3 : 2

Adding these together gives the total number of parts

3 + 2 = 5

The total number amount of paint is 60 litres

∴ 5 parts = 60 litres

Divide both sides by 5 to find out the number of litres in one part

$\begin{array}{rcl} 5 parts & = & 60 litres \\ \div 5 & = & \div 5 \\ 1 part & = & 12 litres \end{array}$

The ratio was 3:2, so multiply both number of parts by 12

$\begin{matrix} R & : & W \\ 3 & : & 2 \\ \begin{matrix} \times 12 & ↓ \end{matrix} & \begin{matrix} ↓ & \times 12 \end{matrix} \\ 36 & : & 24 \end{matrix}$

Answer in context, making sure you make it clear which value is associated with which colour paint

Mark will need to buy 36 litres of red paint and 24 litres of white paint

Sharing in a Ratio (Edexcel GCSE Maths: Foundation)

Revision Note