Percentage comparisons | Year 8

01 / LEARN

The idea, step by step

Compare shares, not just counts

Two groups may have different totals. A count of 18 successful attempts is not automatically a better success rate than 12 successes. Divide each success count by its own total and express the share as a percentage.

Before comparing, ask whether the groups measured the same thing in comparable conditions. A percentage makes totals easier to compare but does not remove bias, different task difficulty or an unfair sampling method.

A percentage-point difference is not a percentage increase

When a rate rises from 30% to 36%, the difference is 6 percentage points. Relative to the original rate, the increase is $6 \div 30 = 0.2$ , or 20%. These are two different descriptions of the same change.

A larger percentage discount does not always mean more dollars saved: it depends on the original price. State whether you are comparing proportions, dollar changes or final prices.

A common trap

The difference between 30% and 36% is always called a 6% increase.

Instead: It is a 6-percentage-point rise, but a 20% relative increase from the original 30%.

02 / WORKED EXAMPLES

See the thinking

Example 1

Different group totals

Team A makes 12 of 40 shots. Team B makes 18 of 75 shots. Compare their success rates.

Team A: $\frac{12}{40} \times 100 % = 30 %$ .
Team B: $\frac{18}{75} \times 100 % = 24 %$ .
Team A has the higher rate by 6 percentage points, even though Team B made more shots.

A: 30%; B: 24%; Team A has the higher success rate.

Example 2

Two ways to describe a rise

A survey result rises from 30% to 36%. Find the percentage-point rise and relative percentage increase.

Percentage-point rise: $36 - 30 = 6$ .
Relative rise: $6 \div 30 \times 100 % = 20 %$ .
The reference for the relative rise is the old percentage, 30%.

6 percentage points; 20% relative increase.

Check your understanding

Which is greater: 8 successes out of 20, or 15 out of 50?

Show answer

8 out of 20.

The rates are 40% and 30%.

03 / WORKSHEET

Your turn

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

Worksheet PDF Worked solutions

Read the questions online

Write 18 out of 60 as a percentage.
2 marks
Compare 14 out of 20 with 18 out of 30. Which rate is higher?
2 marks
A rate rises from 40% to 50%. Find the difference in percentage points.
2 marks
For the rise from 40% to 50%, find the relative percentage increase.
2 marks
Shop A takes 15% off a 200 AUD item. Shop B takes 20% off an 80 AUD item. Which discount saves more dollars?
3 marks
A class of 25 has 20 completed projects; another class of 40 has 30. Compare completion rates. Give one reason the rates alone cannot prove which class worked harder.
3 marks

Read the worked solutions

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

Write 18 out of 60 as a percentage.
2 marks
$18 \div 60 \times 100 % = 30 %$ .
30%
Compare 14 out of 20 with 18 out of 30. Which rate is higher?
2 marks
$14 \div 20 = 0.7$ .
$18 \div 30 = 0.6$ .
14 out of 20: 70%, compared with 60%.
A rate rises from 40% to 50%. Find the difference in percentage points.
2 marks
$50 - 40 = 10$ percentage points.
10 percentage points
For the rise from 40% to 50%, find the relative percentage increase.
2 marks
The change is 10 percentage points.
$10 \div 40 \times 100 % = 25 %$ .
25%
Shop A takes 15% off a 200 AUD item. Shop B takes 20% off an 80 AUD item. Which discount saves more dollars?
3 marks
Shop A: $0.15 \times 200 = 30$ .
Shop B: $0.20 \times 80 = 16$ .
Shop B has the larger percentage, but Shop A saves more dollars.
Shop A saves 30 AUD; Shop B saves 16 AUD.
A class of 25 has 20 completed projects; another class of 40 has 30. Compare completion rates. Give one reason the rates alone cannot prove which class worked harder.
3 marks
$20 \div 25 \times 100 % = 80 %$ .
$30 \div 40 \times 100 % = 75 %$ .
Rates compare completed shares, not effort directly.
80% and 75%; the first rate is higher, but task difficulty, time or support may differ.

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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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