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}