Percentage change consolidation | Year 9

01 / LEARN

The idea, step by step

A percentage is relative to a base

A 15% discount means subtracting 15% of the original price. Equivalently, pay 85% of that price, using multiplier $0.85$ . An increase of 15% uses multiplier $1.15$ . Write the original amount and multiplier before calculating.

To find percentage change, divide the change by the original amount, then multiply by 100%. If a price rises from 80 to 92 dollars, the increase is 12 dollars and $12 / 80 = 0.15$ , so the rise is 15%.

Reverse by division

If a price after a 10% discount is 81 dollars, then $0.9 P = 81$ . Divide by $0.9$ to obtain the original price, $P = 90$ . Adding 10% to the sale price uses the wrong base and gives a different amount.

Successive changes use a new base each time. Increasing 100 dollars by 10% gives 110 dollars; decreasing that by 10% gives 99 dollars. Equal percentage increases and decreases do not generally cancel.

A common trap

Use the new price as the denominator for percentage change.

Instead: The comparison is with the original price, so divide by the original amount.

02 / WORKED EXAMPLES

See the thinking

Example 1

Worked example

A 160-dollar jacket is discounted by 15%. Find the sale price.

Pay $100 % - 15 % = 85 %$ of the original.
$160 \times 0.85 = 136$ .
The discount is $24$ , and $160 - 24 = 136$ .

AUD 136.00

Example 2

Worked example

A fee rises from 80 to 92 dollars. Find its percentage increase.

Increase $= 92 - 80 = 12$ dollars.
Use the original fee as the base: $12 / 80 = 0.15$ .
$0.15 \times 100 % = 15 %$ .

15%

Check your understanding

A 50-dollar item rises by 8%. What is the new price?

Show answer

AUD 54.00

$50 \times 1.08 = 54$ .

03 / WORKSHEET

Your turn

6 questions · 14 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Find 10% of 240 dollars.
2 marks
Increase 72 dollars by 25%.
2 marks
A 180-dollar item is discounted by 20%. Find its sale price.
2 marks
A price falls from 150 to 120 dollars. Find the percentage decrease.
2 marks
An item costs 81 dollars after a 10% discount. Find its original price.
3 marks
A 100-dollar price increases by 10%, then decreases by 10%. Find the final price and explain why it is not 100 dollars.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Find 10% of 240 dollars.
2 marks
$0.10 \times 240 = 24$ .
AUD 24.00
Increase 72 dollars by 25%.
2 marks
$72 \times 1.25 = 90$ .
AUD 90.00
A 180-dollar item is discounted by 20%. Find its sale price.
2 marks
$180 \times 0.80 = 144$ .
AUD 144.00
A price falls from 150 to 120 dollars. Find the percentage decrease.
2 marks
Decrease $= 30$ dollars.
$30 / 150 = 0.2 = 20 %$ .
20%
An item costs 81 dollars after a 10% discount. Find its original price.
3 marks
$0.9 P = 81$ , so $P = 81 / 0.9 = 90$ .
AUD 90.00
A 100-dollar price increases by 10%, then decreases by 10%. Find the final price and explain why it is not 100 dollars.
3 marks
$100 \times 1.10 \times 0.90 = 99$ .
The decrease is calculated from the new base of 110 dollars.
AUD 99.00

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Year 9 financial modelling within AC9M9A05 and AC9M9M05; supplied hypothetical rates and costs, not financial advice.

Official curriculum source ↗

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