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Express one quantity as a percentage of another

Start a set of 8
Step 3 of 10

Choose the reference

The quantity named after 'as a percentage of' is the reference. Put it in the denominator. The quantity being compared can be larger than the reference

Match units

Convert quantities to a common unit before dividing

\[\$3.20=320\text{ cents}\]

Form the ratio

Divide the compared quantity by the reference quantity

Compare 88 cents with $3.20

\[\frac{88}{320}=0.275\]

Convert the ratio

Multiply the ratio by 100 to express it as a percentage

\[0.275=27.5\%\]

Above one hundred

A percentage above one hundred means the compared quantity is larger than the reference

\[\frac{96}{80}=1.2=120\%\]
Year 9, Chapter 1, 3 difficulty levels, Calculator allowedBuild a worksheet

One quantity as a percentage of another

Choose the reference named by the question. Match the units and convert the resulting ratio to a percentage

\[\text{Ratio}=\frac{\text{compared quantity}}{\text{reference quantity}}\]
  1. Keep the requested order The reference goes in the denominator, even if it is smaller \(\displaystyle \frac{114}{80}=1.425=142.5\%\)
  2. Use common units Either unit is suitable if both quantities use it \(\displaystyle \frac{54\text{ cm}}{180\text{ cm}}=\frac{0.54\text{ m}}{1.8\text{ m}}\)
  3. Round the final percentage Keep the ratio exact until the requested percentage precision is applied \(\displaystyle \begin{aligned}\frac{17}{48}\times100&=35.41666\ldots\\\text{Percentage}&\approx35.42\%\end{aligned}\)
  4. Percentage more Compare the difference with the reference when the question asks how much more. This is different from comparing the full amount \(\displaystyle \begin{aligned}\text{Full amount ratio}&=\frac{126}{90}=1.4\\\text{Extra amount ratio}&=\frac{126-90}{90}=0.4\end{aligned}\)

Common mistakes

Comparing different units
✕\(\displaystyle \text{Ratio}=\frac{84}{2.4}\)✓\(\displaystyle \text{Ratio}=\frac{84}{240}\)
For a comparison between centimetres and metres, first express both lengths in the same unit
Reversing the reference
✕\(\displaystyle \text{Used share}=\frac{240}{84}\)✓\(\displaystyle \text{Used share}=\frac{84}{240}\)
The original length is the reference for the used share
Confusing of with more than
✕\(\displaystyle \text{Percentage more}=140\%\)✓\(\displaystyle \text{Percentage more}=40\%\)
If an amount is one hundred and forty percent of its reference, only the extra forty percent is more than the reference

Difficulty levels

introCompare quantities in the same unit with an exact percentage below one hundred
standardHandle percentages above one hundred and percentages that need rounding
challengeConvert units and distinguish a percentage of a reference from a percentage more than it

Questions about this topic

Which quantity is the reference?+

Use the quantity named after 'as a percentage of'

Does a percentage above one hundred mean an error?+

No. It means the compared amount exceeds the reference amount

Is a larger amount always the denominator?+

No. The wording determines the reference, not the sizes of the amounts

Can I use a calculator?+

A calculator is allowed unless a question is marked no calculator

Which year level and chapter is this?+

Year 9 Mathematics, chapter 1: Number and financial mathematics

In this chapter

Evaluate an integer expressionFactors, multiples, HCF, LCM and primesRound to decimal places or significant figuresEstimate an expression using rounded inputsConvert between fractions, mixed numbers and decimalsClassify real numbers and compare exact valuesAdd, subtract, multiply and divide fractions and mixed numbersWrite a ratio from countsWrite ratios in simplest formComplete equivalent ratiosUse a constant rateDivide a quantity in a given ratioDecide which option is the better valueConvert between fractions, decimals and percentagesFind a percentage of a quantityExpress one quantity as a percentage of another1F Percentages and money: Find the original amount from a percentageIncrease or decrease a quantity by a percentageFind percentage changePercentage error against a reference value1G Percentage change and percentage error: Find the original amount from a percentageProfit, mark-up and discountIncome and taxSimple interestCompound interest (optional extension)