Sharing in a given ratio

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Lots of things in everyday life are shared in . 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

James (3)
	£4
	£4
	£4
Helen (5)
	£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 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)
	\(\frac{4}{3}\)		\(\frac{4}{3}\)	\(\frac{4}{3}\)

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

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 \(2 \times \frac{4}{3} = \frac{8}{3} \:\text{litres}\)

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Ratio in context - OCRSharing in a given ratio