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: $\underline{\frac{3}{4}}$
 
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: $\frac{2}{3}$
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.