Percentage increase/decrease | Year 8

01 / LEARN

The idea, step by step

Choose the original amount

A percentage change describes the change as a fraction of the starting amount. First identify what represents 100%. A rise from 80 to 92 is a change of 12, so its percentage increase is measured against 80, not 92.

To increase an amount by 15%, keep its original 100% and add 15%, giving 115% altogether. To decrease it by 15%, keep 85%. These give the multipliers 1.15 and 0.85.

percentage change = \frac{change}{original amount} \times 100 %

Use and check a multiplier

Multiply the starting amount by the percentage that remains, written as a decimal. Estimate first: a 10% reduction should leave a result slightly below the original. A multiplier above 1 gives an increase; one between 0 and 1 gives a decrease.

For successive changes, apply the second percentage to the new amount. An increase followed by the same percentage decrease does not usually return to the start because the second whole has changed.

A common trap

An increase of 20% and then a decrease of 20% cancel out.

Instead: The second change uses a different starting amount: $100 \times 1.2 \times 0.8 = 96$ .

02 / WORKED EXAMPLES

See the thinking

Example 1

Find a percentage increase

A club grows from 80 to 92 members. Find the percentage increase.

The increase is $92 - 80 = 12$ members.
The fraction of the original is $12 \div 80 = 0.15$ .
Convert to a percentage: $0.15 \times 100 % = 15 %$ .

15%

Example 2

Apply a decrease

A 240 AUD bicycle is reduced by 15%. Find its new price.

The remaining percentage is $100 % - 15 % = 85 %$ .
Use the multiplier $0.85$ .
$240 \times 0.85 = 204$ . A 36 AUD reduction is reasonable because 10% is 24 AUD and 5% is 12 AUD.

204 AUD

Check your understanding

Increase 60 by 25%.

Show answer

$25 %$ of 60 is 15, so $60 + 15 = 75$ ; equivalently $60 \times 1.25 = 75$ .

03 / WORKSHEET

Your turn

6 questions · 13 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Increase 80 by 10%.
2 marks
Decrease 150 by 20%.
2 marks
A quantity rises from 50 to 65. Find the percentage increase.
2 marks
A fare falls from 40 AUD to 34 AUD. Find the percentage decrease.
2 marks
Increase 160 by 12.5%.
2 marks
A 100 AUD price rises by 20%, then falls by 20%. Find the final price and explain why it is not 100 AUD.
3 marks

Read the worked solutions

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

Increase 80 by 10%.
2 marks
$10 % \times 80 = 8$ .
$80 + 8 = 88$ .
88
Decrease 150 by 20%.
2 marks
The multiplier is $0.80$ .
$150 \times 0.80 = 120$ .
120
A quantity rises from 50 to 65. Find the percentage increase.
2 marks
The change is $65 - 50 = 15$ .
$15 \div 50 \times 100 % = 30 %$ .
30%
A fare falls from 40 AUD to 34 AUD. Find the percentage decrease.
2 marks
The reduction is $40 - 34 = 6$ AUD.
$6 \div 40 \times 100 % = 15 %$ .
15%
Increase 160 by 12.5%.
2 marks
$12.5 % = \frac{1}{8}$ .
$160 \div 8 = 20$ , so $160 + 20 = 180$ .
180
A 100 AUD price rises by 20%, then falls by 20%. Find the final price and explain why it is not 100 AUD.
3 marks
The increased price is $100 \times 1.2 = 120$ .
The reduced price is $120 \times 0.8 = 96$ .
The rise is 20 AUD but the reduction is 24 AUD.
96 AUD; the reduction uses 120 AUD as its whole.

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum

Percentage increase/decrease; finding an original amount; discounts and mark-ups; percentage comparisons; budgets and purchase decisions; modelling and checking financial problems with digital tools. Simple interest can be offered here as a school-dependent application and developed in Year 9.

Official curriculum source ↗

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