YEAR 7 · PERCENTAGES AND MONEY · 15 MIN

Percentages of quantities

Find a percentage of a quantity using familiar fractions or efficient mental steps.

In this lesson

Choose a mental or decimal method
Interpret a percentage amount with its unit

Before you start

Fraction of a quantity
Percentage equivalents

01 / LEARN

Understand the idea.

Build a percentage from useful parts

Find useful benchmark percentages first. Ten percent is one tenth of an amount, five percent is half of that result, and one percent is one hundredth. Combine these amounts to build percentages such as $15 %$ or $12 %$ .

Fraction equivalents can shorten the calculation: $25 % = \frac{1}{4}$ , $50 % = \frac{1}{2}$ and $75 % = \frac{3}{4}$ . Choose the representation that makes the particular quantity easy to divide, rather than using the same method for every question.

A general multiplication method

To find $p %$ of a quantity $A$ , multiply $A$ by $\frac{p}{100}$ or its equivalent decimal. “Of” means multiplication here. This calculates the requested share of $A$ ; it does not subtract $p$ from $A$ .

Keep the original unit in the answer. For a positive amount, a share between $0 %$ and $100 %$ lies between zero and the whole. An exact count of people must also be a whole number; a fractional result may signal rounded data.

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

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Build from ten and five percent

Find $15 %$ of 80 dollars.

Worked solution

1
Find ten percent.
$\frac{10}{100} \times 80 = 8 dollars$
Ten percent is one tenth of the starting amount.
2
Halve that amount for five percent.
$8 \div 2 = 4 dollars$
Five percent is half of ten percent of the same whole.
3
Combine the two shares.
$15 % of 80 = 8 + 4 = 12 dollars$
The disjoint ten-percent and five-percent shares make fifteen percent.

Answer

12 dollars

EXAMPLE 02

Use a familiar fraction

Find $37.5 %$ of 64 cm.

Worked solution

1
Convert to an exact fraction.
$37.5 % = 0.375 = \frac{375}{1000} = \frac{3}{8}$
The decimal and fraction express the same share of one whole.
2
Find one eighth of the length.
$64 \div 8 = 8 cm$
The denominator divides the whole into eight equal parts.
3
Take three of those parts.
$3 \times 8 = 24 cm$
The numerator specifies three equal eighths.

Answer

24 cm

03 / YOUR TURN

Try it yourself.

Check your understanding

Find $25 %$ of 68.

Show answer & reasoning

Since $25 % = \frac{1}{4}$ , divide the whole into four equal parts: $68 \div 4 = 17$ . This is reasonable because a quarter is smaller than the whole.

Keep practising

6 worksheet questions · 13 marks

Open worksheet 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 ↗

In this lesson

Understand the idea.

Build a percentage from useful parts

A general multiplication method

See the method in action.

Build from ten and five percent

Find ten percent.

Halve that amount for five percent.

Combine the two shares.

Use a familiar fraction

Convert to an exact fraction.

Find one eighth of the length.

Take three of those parts.

Try it yourself.

Check your understanding

Keep practising