Unequal sharing

In a nutshell

Ratios can be used in lots of different scenarios - one of the most common being when things are shared unequally.

Ratio vs proportion

Definitions

Ratio	Compares one part to another.
Proportion	Compares one part to the whole thing

Example 1

Look at the squares.

The ratio of shaded to unshaded squares can be written:

$3:1$

The proportion of shaded squares is three (the number shaded) out of four (the total number of squares). Written as a fraction:

$\underline{\frac{3}{4}}$ 

Maths; Ratio and proportion; KS2 Year 6; Unequal sharing

Unequal sharing problems

When things are shared unequally, ratios and proportions can both be used to work out how many things each person gets.

Example 2

For every one slice of pizza that Rachel eats, her older sister Anna eats two. There are six slices in a whole pizza. Work out how many each of them get and write your answer as a ratio.

Maths; Ratio and proportion; KS2 Year 6; Unequal sharing

Write the information as a ratio.

Rachel : Anna

$1:2$

Add up the ratio and work out the proportion eaten by each person.

$1+2=3$

Rachel eats a third: $\frac{1}{3}$

Anna eats two thirds: $\frac{2}{3}$

Work out each fraction of the total amount to find out how much eat person gets.

Rachel: $\frac{1}{3}$ of $6=6\div3=2$

Anna:  $\frac{2}{3}$ of $6=(6\div3)\times2=4$

Therefore, Rachel and Anna get pizza in a ratio of $\underline{2:4}.$

Note: The numbers in the ratio should be given in the same order as the words in the question. Rachel is listed first, so her number in the ratio comes first.