### Word problems

When tackling word problems involving fractions, think carefully about which operations are required, and what is the 'whole'.

#### Example 2

Jack shares a liquorice strap equally between himself and 5 friends. If the strap is $$1\dfrac{2}{3}\ \text{m}$$ long, how much will each person get?

#### Solution

There are 5 + 1 = 6 shares.

\begin{align}\text{Hence the length for each person}\ &=1\dfrac{2}{3}÷6\\\\ &=\dfrac{5}{3}×\dfrac{1}{6}\\\\ &=\dfrac{5}{18}\ \text{m of liquorice}\end{align}

#### Example 3

A container of cooking oil is $$\dfrac{3}{5}$$ full. A further $$4\dfrac{1}{2}$$L of cooking oil is required to fill it. How much oil does the container hold?

#### Solution

$$\dfrac{2}{5}$$ of the container contains $$4\dfrac{1}{2}$$L.

That is, $$\dfrac{2}{5}$$ of the container contains $$\dfrac{9}{2}$$L.

\begin{align}\text{Thus}\ \dfrac{1}{5} \text{of the container contains}\ &\dfrac{1}{2}×\dfrac{9}{2}\\\\ &=\dfrac{9}{4}\ \text{L}\\\\ \text{Thus amount of oil when full}\ &=5×\dfrac{9}{4}\\\\ &=11\dfrac{1}{4}\ \text{L}\end{align}