### Percentage 'of'

Frequently, we need to express one quantity as a percentage of another.

Here is an example where we colour different percentages of a set of 20 stars.

- If 100% of the stars are to be orange,

\begin{align}100\%\ \text{of}\ 20&=\dfrac{100}{100}×20\\\\ &=1×20\\\\ &=20\end{align} We colour 20 out of the 20 stars.

100% of 20 is 20. - If 50% of the stars are to be orange,

\begin{align}50\%\ \text{of}\ 20&=\dfrac{50}{100}×20\\\\ &=\dfrac{1}{2}×\dfrac{20}{1}\\\\ &=\dfrac{20}{2}\\\\ &=10\end{align} We colour ten out of the 20 stars.

50% of 20 is ten. - If 10% of the stars are to be orange,

\begin{align}10\%\ \text{of}\ 20 &=\dfrac{10}{100}×20\\\\ &=\dfrac{1}{10}×\dfrac{20}{1}\\\\ &=\dfrac{20}{10}\\\\ &=2\end{align}We colour two out of the 20 stars.

10% of 20 is two. - If 5% of the stars are to be orange,

\begin{align}5\%\ \text{of}\ 20&=\dfrac{5}{100}×20\\\\ &=\dfrac{1}{20}×\dfrac{20}{1}\\\\ &=\dfrac{20}{20}\\\\ &=1\end{align} We colour one out of the 20 stars.

5% of 20 is one. - If 35% of the stars are to be orange,

\begin{align}35\%\ \text{of}\ 20&=\dfrac{35}{100}×20\\\\ &=\dfrac{35}{100}×\dfrac{20}{1}\\\\ &=\dfrac{35}{5}×\dfrac{1}{1}\\\\ &=7\end{align} We colour seven out of 20 stars.

35% of 20 is seven.

### Summary

To calculate the percentage of an amount, we convert the percentage to a fraction and multiply. The word 'of' tells us to multiply fractions.