Find a percentage of a quantity lesson | Mathematical Methods (Year 12, VCE Units 3 & 4)

Percentage of a quantity

Identify the quantity that the percentage applies to. Convert the percentage, multiply, then round if required

p\%\text{ of }Q=\frac{p}{100}Q

Convert the percentage Use a fraction or an exact decimal $\displaystyle 17.5\%=\frac{7}{40}=0.175$
Keep the base and unit A percentage of a money amount is another money amount $\displaystyle 0.175\times\$46.30=\$8.1025$
Apply the final precision For money, use cents when the question requires it $\displaystyle \$8.1025\approx\$8.10$

Find the amount reserved for materials, to the nearest cent

\begin{gathered}\text{Budget}=\$94.60\\\text{Materials share}=18.5\%\end{gathered}

$\displaystyle 18.5\%=0.185$Convert the percentage into its decimal multiplier
$\displaystyle \text{Materials amount}=0.185\times\$94.60$Apply that multiplier to the whole budget
$\displaystyle =\$17.501$Keep the product exact before rounding
$\displaystyle \approx\$17.50$Round the final amount to the nearest cent

Using the percentage number directly

✕$\displaystyle 22\%=22$✓$\displaystyle 22\%=0.22$

The percentage number counts hundredths. Convert it before using it as a multiplier

Dividing to find a share

✕$\displaystyle 22\%\text{ of }\$68=\$68\div0.22$✓$\displaystyle 22\%\text{ of }\$68=0.22\times\$68$

Finding a percentage of a known quantity uses multiplication

Rounding the multiplier

✕$\displaystyle 18.5\%=0.2$✓$\displaystyle 18.5\%=0.185$

Rounding the percentage first changes the requested share

introFind familiar percentages with exact answers

standardApply general whole-number percentages to money and measurements

challengeApply fractional percentages and round money or measurements when needed

Can the percentage amount exceed the starting quantity?+

Yes, if the percentage exceeds one hundred

Why keep the original unit?+

The calculation scales the quantity. It does not change what the quantity measures

Can I use a calculator?+

A calculator is allowed unless a question is marked no calculator

Which year level and chapter is this?+

Year 12, VCE Units 3 & 4, Mathematical Methods, chapter 14: Statistical inference