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

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: $$\underline{\frac{3}{4}}$$​​

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.

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: $$\frac{2}{3}$$​​

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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.

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