Percentage increase/decrease | Year 8

01 / LEARN

Understand the idea.

Choose the original amount

A percentage change compares the change with the original amount, which represents $100 %$ . First subtract to find how much the quantity changed, then divide by the starting amount. Using the final amount would describe a different comparison.

To increase by $15 %$ , keep the original $100 %$ and add $15 %$ : the multiplier is $1.15$ . To decrease by $15 %$ , retain $85 %$ : the multiplier is $0.85$ . Distinguish the amount removed from the amount remaining.

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

Use and check a multiplier

Apply the multiplier to the original amount, then check the direction and size. An increase has multiplier above one; a decrease of less than $100 %$ has multiplier between zero and one. Estimate a familiar percentage to catch unreasonable results.

For successive changes, the next percentage uses the new amount as its whole. An increase followed by an equal percentage decrease therefore does not cancel: $100 \times 1.2 \times 0.8 = 96$ . The second $20 %$ acts on $120$ , not $100$ .

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Find a percentage increase

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

Worked solution

1
Find the change in membership.
$92 - 80 = 12 members$
Percentage increase measures the added members relative to the original club.
2
Compare with the original amount.
$\frac{12}{80} = 0.15$
Eighty members represents the original whole, or one hundred percent.
3
Convert the fraction to a percentage.
$0.15 \times 100 % = 15 %$
Multiplying the fractional change by one hundred percent gives the percentage increase.

Answer

15%

EXAMPLE 02

Apply a decrease

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

Worked solution

1
Find the percentage remaining.
$100 % - 15 % = 85 % = 0.85$
A reduction removes fifteen percent but leaves eighty-five percent to pay.
2
Apply the remaining-price multiplier.
$240 \times 0.85 = 204 AUD$
The new price is eighty-five percent of the original two hundred and forty dollars.
3
Check the saving.
$\begin{aligned} 240 \times 0.15 & = 36 AUD \\ 240 - 36 & = 204 AUD \end{aligned}$
Calculating the amount removed independently confirms the remaining price.

Answer

204 AUD

03 / YOUR TURN

Try it yourself.

Check your understanding

Increase 60 by 25%.

Show answer & reasoning

A quarter of $60$ is $15$ , so increasing by $25 %$ gives $60 + 15 = 75$ . Equivalently, multiply $60$ by $1.25$ .

Keep practising

6 worksheet questions · 13 marks

Open worksheet 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 ↗

In this lesson

Understand the idea.

Choose the original amount

Use and check a multiplier

See the method in action.

Find a percentage increase

Find the change in membership.

Compare with the original amount.

Convert the fraction to a percentage.

Apply a decrease

Find the percentage remaining.

Apply the remaining-price multiplier.

Check the saving.

Try it yourself.

Check your understanding

Keep practising