Apply a percentage change
The percentage uses the amount before that change as its base. The multiplier includes the share of the original that remains
\[\begin{aligned}\text{Increase multiplier}&=1+\frac{p}{100}\\\text{Decrease multiplier}&=1-\frac{p}{100}\end{aligned}\]
- Find the changed amount Multiply the base by the appropriate multiplier
- Two changes Use the first result as the second base. Do not add the percentage numbers
- Compare two amounts Apply each change to its own base before comparing the results
- Round last Keep intermediate values exact and round the requested final amount
Common mistakes
Finding only the increase
✕\(\displaystyle \text{New price}=\$64\times0.18\)✓\(\displaystyle \text{New price}=\$64\times1.18\)
The changed price contains the original price as well as the increaseCombining percentage numbers
✕\(\displaystyle \text{Final price}=\$132\times0.97\)✓\(\displaystyle \text{Final price}=\$132\times1.07\times0.90\)
Start at $132, increase by 7%, then decrease by 10%. The second percentage uses the first changed price as its baseTreating the percentage as dollars
✕\(\displaystyle \text{New price}=\$86-\$12\)✓\(\displaystyle \text{New price}=\$86\times0.88\)
Find the percentage of the base rather than subtracting the percentage numberDifficulty levels
introFind both the change and the new amount for one increase or decrease
standardFind a changed amount independently, including totals and tables
challengeRound final amounts, compare changed amounts and apply two changes in order
Questions about this topic
Which amount is the base?+
Use the amount just before the change being applied
Do equal percentage increases and decreases cancel?+
Usually they do not. The second percentage uses a different base
Must I use a multiplier?+
No. Finding the percentage amount and then adding or subtracting it gives the same result
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)