Expressing one amount as a percentage of another | Year 7

01 / LEARN

The idea, step by step

Ask: a percentage of what?

The reference whole belongs in the denominator. If 18 out of 24 students attend, the attendance share is eighteen twenty-fourths. Simplifying or dividing turns that share into a percentage.

The words matter. A question about the percentage of students attending uses all students as the whole, not just those absent. Draw a part-whole bar or write part divided by whole before inserting numbers.

Match the units

Both amounts must use the same unit. Comparing 45 cents with 3 dollars requires either converting 3 dollars to 300 cents or converting 45 cents to 0.45 dollars.

Multiply the part-to-whole ratio by 100 to express it per hundred. The ratio itself has no unit because matching units cancel. Then interpret the resulting percentage in the original situation.

A common trap

The smaller of the two printed numbers must always be the numerator.

Instead: Use the requested part as numerator and the stated reference as denominator. The result may exceed 100 percent if the compared amount is larger than its reference.

02 / WORKED EXAMPLES

See the thinking

Example 1

Attendance

18 of 24 students attend a club. What percentage attend?

The whole is 24 students, so the share is $\frac{18}{24} = \frac{3}{4}$ .
$\frac{3}{4} = 0.75 = 75 %$ .

75 %

Example 2

Convert units first

What percentage of 3 dollars is 45 cents?

Convert 3 dollars to 300 cents.
$\frac{45}{300} = 0.15$ .
$0.15 \times 100 % = 15 %$ .

15 %

Check your understanding

What percentage of 20 is 8?

Show answer

$40 %$

$\frac{8}{20} = 0.4$ , which is 40 per hundred.

03 / WORKSHEET

Your turn

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

Worksheet PDF Worked solutions

Read the questions online

Express 8 as a percentage of 20.
2 marks
Express 27 as a percentage of 45.
2 marks
A team wins 14 of its 40 games. What percentage does it win?
2 marks
What percentage of 1.2 km is 18 m?
3 marks
Twelve of 15 classmates have a ticket. What percentage have a ticket?
2 marks
Group A has 7 correct answers out of 10. Group B has 9 out of 15. Which has the higher percentage correct?
3 marks

Read the worked solutions

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

Express 8 as a percentage of 20.
2 marks
$\frac{8}{20} \times 100 % = 40 %$ .
$40 %$
Express 27 as a percentage of 45.
2 marks
$\frac{27}{45} = \frac{3}{5} = 60 %$ .
$60 %$
A team wins 14 of its 40 games. What percentage does it win?
2 marks
$\frac{14}{40} = \frac{35}{100}$ .
$35 %$
What percentage of 1.2 km is 18 m?
3 marks
1.2 km = 1200 m.
$\frac{18}{1200} \times 100 % = 1.5 %$ .
$1.5 %$
Twelve of 15 classmates have a ticket. What percentage have a ticket?
2 marks
$\frac{12}{15} = \frac{4}{5} = 80 %$ .
$80 %$
Group A has 7 correct answers out of 10. Group B has 9 out of 15. Which has the higher percentage correct?
3 marks
$\frac{7}{10} = 70 %$ and $\frac{9}{15} = 60 %$ .
Comparing only 7 and 9 ignores the different totals.
Group A: $70 %$ , compared with $60 %$ for Group B.

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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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