Using percentages

Expressing one quantity as a percentage of another

Sometimes we want to describe one quantity as a percentage of another.

Example 1

There are 50 people in a swimming club, and 35 go to squad training on one occasion. Calculate the number of people who go to squad training as a percentage of the number of swimming club members.

Solution

35 of the 50 go to squad training.

\begin{align}\text{Percentage in squad} &= \dfrac{35}{50} × 100\%\\\\ &= \dfrac{35}{50} × \dfrac{100}{1}\%\\\\ &= 70\%\end{align}

So, 70% of the swimming club members go to squad training.

Percentage of a quantity

We often use percentages in the following way.

Example 2

25% of people in a city watched the tennis grand final. Calculate how many people watched the tennis grand final if the population of the city is 3 000 000.

Solution

\begin{align}\text{Number of people watching}&=25\%\ \text{of}\ 3\ 000\ 000\\\\ &=\dfrac{25}{100}×\dfrac{3\ 000\ 000}{1}\\\\ &=750\ 000\end{align}