Find percentage change
The original amount is the reference. It must be positive in these questions
\[\text{Relative change}=\frac{\text{new}-\text{original}}{\text{original}}\]
- Find the difference Use new minus original for signed change
- Divide by the original Express the difference as a share of the starting amount
- Convert the share Write the decimal ratio as an equivalent percentage \(\displaystyle -0.175=-17.5\%\)
- State the direction A signed negative change is a decrease. A question asking how much it decreased wants the size of that decrease
Common mistakes
Using the new amount as the base
✕\(\displaystyle \text{Relative change}=\frac{72-90}{72}\)✓\(\displaystyle \text{Relative change}=\frac{72-90}{90}\)
The comparison starts with the original amountKeeping the original whole in the numerator
✕\(\displaystyle \text{Relative change}=\frac{120}{96}\)✓\(\displaystyle \text{Relative change}=\frac{120-96}{96}\)
Subtract the original before comparing the changeDropping direction
✕\(\displaystyle \text{Signed change}=17.5\%\)✓\(\displaystyle \text{Signed change}=-17.5\%\)
For a fall from 240 folders to 198 folders, the signed change is negative. A percentage decrease would instead be reported as a positive sizeDifficulty levels
introFind an exact whole-number percentage increase or decrease
standardFind signed changes from direct statements, tables and short contexts
challengeSelect the starting value and round a percentage with discarded digits
Questions about this topic
Which value is the denominator?+
Use the original value for the requested comparison
Why do equal dollar changes give different percentages?+
Each percentage compares the dollar change with its own original amount
Can the original value be zero?+
This calculation is undefined when the original is zero because it would require division by zero
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)