Percentage change consolidation | Year 9

01 / LEARN

Understand the idea.

A percentage is relative to a base

A percentage change compares the increase or decrease with the original amount. Find the dollar change first, divide by the original amount, and express that fraction as a percentage. The original amount is the reference base.

For a known percentage change, use a multiplier. A $15 %$ discount leaves $85 %$ , so multiply by $0.85$ ; a $15 %$ increase leaves $115 %$ , so multiply by $1.15$ . Distinguish the change from the final amount.

Reverse by division

To reverse a percentage change, divide the final amount by its multiplier. If a price becomes $81$ dollars after a $10 %$ discount, $0.9 P = 81$ , so the original was $P = 90$ dollars.

Successive changes act on successive bases, so multiply their factors. An increase of $10 %$ followed by a decrease of $10 %$ uses $1.1 \times 0.9 = 0.99$ : the final amount is $99 %$ of the original, rather than unchanged.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Worked example

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

Worked solution

1
Find the percentage still payable.
$100 % - 15 % = 85 %$
A discount removes part of the original price.
2
Convert to a multiplier and calculate.
$160 \times \frac{85}{100} = 160 \times 0.85 = 136$
The sale price is 85 percent of the original 160 dollars.
3
Check using the discount amount.
$\begin{aligned} 160 \times 0.15 & = 24 \\ 160 - 24 & = 136 \end{aligned}$
Subtracting the discount independently confirms a sale price of AUD 136.00.

Answer

AUD 136.00

EXAMPLE 02

Worked example

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

Worked solution

1
Find the increase in dollars.
$92 - 80 = 12$
Percentage increase measures the change relative to the starting fee.
2
Divide by the original fee.
$\frac{12}{80} = 0.15$
The original 80 dollars is the correct reference base.
3
Express the fraction as a percentage.
$0.15 \times 100 % = 15 %$
A decimal fraction is converted to a percentage by multiplying by 100 percent.

Answer

15%

03 / YOUR TURN

Try it yourself.

Check your understanding

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

Show answer & reasoning

AUD 54.00

An $8 %$ increase uses multiplier $1.08$ , so $50 \times 1.08 = 54$ . Equivalently, the increase is $50 \times 0.08 = 4$ dollars and the new price is AUD 54.00.

Keep practising

6 worksheet questions · 14 marks

Open worksheet 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.
$\frac{30}{150} = 0.2 = 20 %$ .
20%
An item costs 81 dollars after a 10% discount. Find its original price.
3 marks
$0.9 P = 81$ , so $P = \frac{81}{0.9} = 90$ .
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 ↗

In this lesson

Understand the idea.

A percentage is relative to a base

Reverse by division

See the method in action.

Worked example

Find the percentage still payable.

Convert to a multiplier and calculate.

Check using the discount amount.

Worked example

Find the increase in dollars.

Divide by the original fee.

Express the fraction as a percentage.

Try it yourself.

Check your understanding

Keep practising