Understand the idea.
Identify the whole
A percentage describes a part of a reference amount. Identify that reference before calculating: a discount uses the original price, while profit as a percentage of cost uses the cost. Convert the percentage to a decimal by dividing by 100.
An increase of decimal rate multiplies the current amount by ; a decrease multiplies it by . Keep fixed charges separate unless the question says the percentage also applies to those charges.
Reverse a change
To reverse a percentage change, divide by the factor that produced the final value. After a 15% discount, the final price is times the original. Dividing by recovers the original; adding 15% to the discounted amount does not.
Successive changes act on successive amounts, so multiply their factors in order. Estimate whether the answer should be larger or smaller before using a calculator, keep intermediate values unrounded, and round the final monetary result to cents.
See the method in action.
Worked example
A bicycle costs AUD 240 before a 12.5% discount. Delivery adds AUD 18. Find the total.
Worked solution
- 1
Write the discount factor.
A 12.5% discount leaves 87.5% of the original bicycle price.
- 2
Calculate the discounted price.
The discount applies to the bicycle's stated original price.
- 3
Add the delivery charge.
Delivery is an additional fixed charge, not another amount to discount.
AUD 228.00
Worked example
A yearly fee is AUD 378 after an 8% increase. Find its previous value.
Worked solution
- 1
Relate the previous fee to the increased fee.
An 8% increase makes the new fee 108% of the previous fee.
- 2
Reverse the increase by division.
Dividing by the growth factor isolates the original amount.
- 3
Check using the original reference amount.
The proposed previous fee produces the stated increased fee.
AUD 350.00
Try it yourself.
Check your understanding
Find 7.5% of AUD 640.
Show answer & reasoning
AUD 48.00
Use AUD 640 as the reference amount and convert to . Then .
Keep practising
6 worksheet questions · 12 marks
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
.
AUD 51.00 - Reduce AUD 96 by 15%.2 marks
.
AUD 81.60 - A bill rises from AUD 125 to AUD 140. Find its percentage increase.2 marks
.
.
12% - A jacket costs AUD 108 after a 25% discount. Find the original price.2 marks
.
.
AUD 144.00 - AUD 500 increases 10%, then decreases 10%. Find the final value and overall change.2 marks
.
.
AUD 495.00;1% decrease - Add 8% tax to a tax-exclusive price of AUD 225. Find tax and total.2 marks
.
.
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 ↗