Percentages of quantities | Year 7

01 / LEARN

The idea, step by step

Build a percentage from useful parts

Ten percent is one tenth, five percent is half of ten percent, and one percent is one hundredth. You can combine these pieces to find percentages such as 15 or 12 percent without a calculator.

Common fraction equivalents provide another route: 25 percent is a quarter, 50 percent is half, and 75 percent is three quarters. Choose a method that fits the numbers.

A general multiplication method

For any percentage p, take p hundredths of the starting quantity. Multiplying by the decimal form gives the same result. Keep the unit: a percentage of 80 dollars produces dollars, while a percentage of 80 students produces a student count.

Check the size. A percentage below 100 of a positive amount must be smaller than that amount. If a population count is required, consider whether the given data can produce a whole number exactly.

p % of A = \frac{p}{100} \times A

A common trap

Finding a percentage means subtracting that printed number.

Instead: A percentage is a proportion of the given amount. Fifteen percent of 80 is 12, not 80 minus 15.

02 / WORKED EXAMPLES

See the thinking

Example 1

Build from ten and five percent

Find $15 %$ of 80 dollars.

10 percent of 80 is 8 dollars.
5 percent is half of 8, or 4 dollars.
Add 8 + 4 to obtain 12 dollars.

12 dollars

Example 2

Use a familiar fraction

Find $37.5 %$ of 64 cm.

$37.5 % = \frac{3}{8}$ .
One eighth of 64 cm is 8 cm.
Three eighths is 3 times 8 cm.

24 cm

Check your understanding

Find $25 %$ of 68.

Show answer

One quarter of 68 is 17.

03 / WORKSHEET

Your turn

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

Worksheet PDF Worked solutions

Read the questions online

Find $10 %$ of 240.
2 marks
Find $25 %$ of 84.
2 marks
Find $5 %$ of 360 dollars.
2 marks
Find $12 %$ of 150 m.
2 marks
Find $35 %$ of 80.
2 marks
A class has 48 students. Exactly $62.5 %$ choose a museum visit. How many is that?
3 marks

Read the worked solutions

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

Find $10 %$ of 240.
2 marks
Divide 240 by 10.
24
Find $25 %$ of 84.
2 marks
Divide 84 by 4.
21
Find $5 %$ of 360 dollars.
2 marks
Ten percent is 36 dollars; halve it.
18 dollars
Find $12 %$ of 150 m.
2 marks
10 percent is 15 m and 2 percent is 3 m; add.
18 m
Find $35 %$ of 80.
2 marks
30 percent is 24 and 5 percent is 4.
28
A class has 48 students. Exactly $62.5 %$ choose a museum visit. How many is that?
3 marks
$62.5 % = \frac{5}{8}$ ; one eighth of 48 is 6, so five eighths is 30.
30 students

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Fractions–decimals–percentages; percentages of quantities; expressing one amount as a percentage of another; discounts and sale prices; practical spending/budget comparisons; choosing and explaining a financial model.

Official curriculum source ↗

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