Expressing one amount as a percentage of another | Year 7

01 / LEARN

Understand the idea.

Ask: a percentage of what?

Identify the reference whole before calculating. “What percentage of the class attends?” compares the attending students with everyone in the class. Write the share as $\frac{part}{whole}$ so the denominator answers “a percentage of what?”

The order follows the wording, not the sizes of the printed numbers. An amount larger than its reference gives a percentage greater than $100 %$ . Reversing part and reference changes the comparison being made.

Match the units

Put both amounts in the same unit before dividing. Comparing $45$ cents with $3$ dollars means comparing $45$ cents with $300$ cents, or $0.45$ dollars with $3$ dollars. Either consistent choice gives the same share.

Simplify the share or divide to obtain its decimal, then express it per hundred. Matching units cancel in the ratio, so the percentage has no dollar, length or mass unit. State what that percentage describes in the situation.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Attendance

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

Worked solution

1
Choose the reference whole.
$Attending share = \frac{18}{24}$
All twenty-four club students form the whole; eighteen are the attending part.
2
Simplify the share.
$\frac{18}{24} = \frac{18 \div 6}{24 \div 6} = \frac{3}{4}$
Dividing numerator and denominator by six preserves the proportion.
3
Express the share per hundred.
$\frac{3}{4} = \frac{75}{100} = 75 %$
Seventy-five hundredths means seventy-five percent of the students attend.

Answer

$75 %$

EXAMPLE 02

Convert units first

What percentage of 3 dollars is 45 cents?

Worked solution

1
Match the money units.
$3 dollars = 300 cents$
The numerator and denominator must measure money in the same unit.
2
Form the requested share.
$\frac{45}{300} = \frac{3}{20}$
Forty-five cents is the part and three hundred cents is the reference.
3
Convert to hundredths.
$\frac{3}{20} = \frac{15}{100} = 15 %$
Multiplying both parts by five expresses the same share per hundred.

Answer

$15 %$

03 / YOUR TURN

Try it yourself.

Check your understanding

What percentage of 20 is 8?

Show answer & reasoning

$40 %$

The reference is $20$ , so the share is $\frac{8}{20} = \frac{40}{100} = 40 %$ . Eight is less than half of twenty, consistent with a result below $50 %$ .

Keep practising

6 worksheet questions · 14 marks

Open worksheet 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.

Checking saved progress…

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 ↗

In this lesson

Understand the idea.

Ask: a percentage of what?

Match the units

See the method in action.

Attendance

Choose the reference whole.

Simplify the share.

Express the share per hundred.

Convert units first

Match the money units.

Form the requested share.

Convert to hundredths.

Try it yourself.

Check your understanding

Keep practising