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
\[\begin{gathered}\text{Increase multiplier}\\=1+\frac{p}{100}\\\text{Decrease multiplier}\\=1-\frac{p}{100}\end{gathered}\]
- The percentage p For an 18% change, substitute 18 for the percentage in the formula
- 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
Worked example
Find the final price after the two changes, to the nearest cent
\[\begin{gathered}\text{Starting price}=\$132\\\text{First: }7\%\text{ increase}\\\text{Second: }10\%\text{ decrease}\end{gathered}\]
- \(\displaystyle 1+\frac{7}{100}=1.07\)Include the original whole and the increase
- \(\displaystyle \$132\times1.07=\$141.24\)Find the first changed price
- \(\displaystyle 1-\frac{10}{100}=0.90\)Find the share left after the decrease
- \(\displaystyle \begin{gathered}\$141.24\times0.90\\=\$127.116\end{gathered}\)Apply the second multiplier to the first result
- \(\displaystyle \$127.116\approx\$127.12\)Round the final price to the nearest cent
Common mistakes
Finding only the increase
✕\(\displaystyle \begin{gathered}\text{New price}\\=\$64\times0.18\end{gathered}\)✓\(\displaystyle \begin{gathered}\text{New price}\\=\$64\times1.18\end{gathered}\)
The changed price contains the original price as well as the increaseCombining percentage numbers
✕\(\displaystyle \begin{gathered}\text{Final price}\\=\$132\times0.97\end{gathered}\)✓\(\displaystyle \begin{gathered}\text{Final price}\\=\$132\times1.07\times0.90\end{gathered}\)
The second percentage uses the first changed price as its baseTreating the percentage as dollars
✕\(\displaystyle \begin{gathered}\text{New price}\\=\$86-\$12\end{gathered}\)✓\(\displaystyle \begin{gathered}\text{New price}\\=\$86\times0.88\end{gathered}\)
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 11, VCE Units 1 & 2, General Mathematics, chapter 1: Percentages and ratios
In this chapter
Convert between fractions, decimals and percentagesFind a percentage of a quantityExpress one quantity as a percentage of another1A Percentages: Find the original amount from a percentageIncrease or decrease a quantity by a percentageFind percentage changeAdd GST to a priceFind the GST and the pre-GST price from an inclusive priceExpress a ratio in simplest formComplete an equivalent ratioDivide a quantity in a given ratio1E Dividing in a ratio: Use one known part of a ratio to find the others1F Unitary method: Find the original amount from a percentage1F Unitary method: Use one known part of a ratio to find the othersScale a proportional quantity with the unitary methodDecide which option is the better value