The idea, step by step
Identify the whole
A percentage always uses a reference amount. For a discount, use the original price; for a percentage profit on cost, use the cost. Write that reference before calculating. A rate of 7.5% is 0.075 as a decimal.
Use to increase a value and to decrease it. Consecutive changes multiply their factors because each change acts on the current amount.
Reverse a change
After a 15% discount, a price is 85% of its original. Divide the final price by 0.85 to recover the original; adding 15% to the smaller price does not reverse the change.
Keep unrounded values until the final money answer. Estimate the direction of the change first so an incorrect factor is easier to notice.
A common trap
Equal percentage increases and decreases cancel.
Instead: A 20% decrease followed by 20% increase multiplies by 0.8×1.2=0.96, leaving a 4% decrease.
See the thinking
Worked example
A bicycle costs AUD 240 before a 12.5% discount. Delivery adds AUD 18. Find the total.
- Sale factor=0.875.
- 240×0.875=210.
- Add delivery:210+18=228.
Worked example
A yearly fee is AUD 378 after an 8% increase. Find its previous value.
- 1.08 P=378.
- P=378/1.08=350.
- Check:350+0.08×350=378.
Check your understanding
Find 7.5% of AUD 640.
Show answer
AUD 48.00
0.075×640=48.
Your turn
6 questions · 12 marks · Work at your own pace.
Read the questions online
- Find 6% of AUD 850.2 marks
- Reduce AUD 96 by 15%.2 marks
- A bill rises from AUD 125 to AUD 140. Find its percentage increase.2 marks
- A jacket costs AUD 108 after a 25% discount. Find the original price.2 marks
- AUD 500 increases 10%, then decreases 10%. Find the final value and overall change.2 marks
- Add 8% tax to a tax-exclusive price of AUD 225. Find tax and total.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Find 6% of AUD 850.2 marks
0.06×850=51.
AUD 51.00 - Reduce AUD 96 by 15%.2 marks
96×0.85=81.60.
AUD 81.60 - A bill rises from AUD 125 to AUD 140. Find its percentage increase.2 marks
Change=15.
15/125×100=12%.
12% - A jacket costs AUD 108 after a 25% discount. Find the original price.2 marks
0.75 P=108.
P=144.
AUD 144.00 - AUD 500 increases 10%, then decreases 10%. Find the final value and overall change.2 marks
500×1.1×0.9=495.
5/500=0.01.
AUD 495.00;1% decrease - Add 8% tax to a tax-exclusive price of AUD 225. Find tax and total.2 marks
0.08×225=18.
225+18=243.
AUD 18 tax; AUD 243 total
Curriculum reference & lesson scope
SACE Board of South Australia
Stage 1 General Mathematics: investing and borrowing. Supplied educational models cover interest, investment comparisons, shares and credit; they are not recommendations of real products or statements of personal tax liability.
Official curriculum source ↗