Expressing Quantity as Percentage

To express one quantity as a percentage of another, divide the first quantity by the second quantity, then multiply by \(100\%\). Convert both quantities to the same units first if needed.

Common mistake: Make sure the quantity you are comparing goes on top of the fraction. For example, to express 18 as a percentage of 60, use \(\dfrac{18}{60} \times 100\%\), not \(\dfrac{60}{18} \times 100\%\).

Worked example:
Express 12 as a percentage of 30.
  1. Put the first quantity over the second quantity.
    \[\frac{12}{30} \times 100\%\]
    \[0.4 \times 100\% = 40\%\]
Answer:
\[40\%\]
Worked example:
Express 45 cm as a percentage of 1.2 m.
  1. Convert 1.2 m to centimetres first.
    \[1.2\text{ m} = 120\text{ cm}\]
    \[\frac{45}{120} \times 100\%\]
    \[0.375 \times 100\% = 37.5\%\]
Answer:
\[37.5\%\]
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