Fraction/decimal/percentage quantities | Year 6

01 / LEARN

Understand the method.

THE CORE RULE

40 % = \frac{40}{100} = \frac{2}{5} = 0.4

Percent means out of one hundred. Each form describes the same proportion.

Three names for the same part

40% means 40 out of 100. As a fraction, that is $\frac{40}{100} = \frac{2}{5}$ . As a decimal, it is 0.4.

Use the same whole when you compare the forms. Half of one class is not necessarily the same number of students as half of another class.

\begin{aligned} \frac{1}{2} & = 0.5 = 50 % \\ \frac{1}{4} & = 0.25 = 25 % \end{aligned}

Find a useful part first

For 10%, divide the amount by 10. Build 20%, 30% or 40% from that answer.

For 25%, divide by 4. For 50%, divide by 2. Keep the unit in your answer: counters, students or litres.

40 % of 80 = 4 \times (80 \div 10) = 32

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Find 40% of a quantity

Find 40% of 80 counters.

Worked solution

1
Find 10% first.
$80 \div 10 = 8$
Ten percent is one tenth of the whole, so 10% is 8 counters.
2
Build four lots of 10%.
$4 \times 8 = 32$
Forty percent is four lots of ten percent.
3
Check with a fraction.
$\frac{2}{5} \times 80 = 32$
The fraction gives the same result. Since 40% is less than 100%, the answer is smaller than 80.

Answer

32 counters.

EXAMPLE 02

Connect the forms, then find the amount

Three quarters of 60 students join a game. Write the proportion as a decimal and percentage, then find the number of students.

Worked solution

1
Rename three quarters as hundredths.
$\frac{3}{4} = \frac{75}{100} = 0.75 = 75 %$
The fraction, decimal and percentage all describe the same proportion.
2
Find one quarter of the students.
$60 \div 4 = 15$
One quarter of 60 is 15 students.
3
Take three of those equal parts.
$3 \times 15 = 45$
Three quarters contains three of the four equal groups.

Answer

0.75; 75%; 45 students.

03 / YOUR TURN

Try it yourself.

Calculate, explain, then apply.

CHECK 01

Your turn

Write 0.6 as a percentage and a simple fraction.

Show answer & reasoning

$60 %$ and $\frac{3}{5}$ .

$0.6 = \frac{6}{10} = \frac{60}{100} = 60 %$ . Simplify $\frac{6}{10}$ by dividing both numbers by 2 to get $\frac{3}{5}$ .

Keep practising

6 worksheet questions · 11 marks

Open worksheet Worked solutions

Read the questions online

Write $\frac{7}{10}$ as a decimal and a percentage.
2 marks
Find $20 %$ of 45 metres.
2 marks
Find $60 %$ of 30 counters.
2 marks
Find $\frac{1}{8}$ of 56 litres, then name this fraction as a percentage.
2 marks
Sixteen of 40 library books are about animals. What percentage is that?
2 marks
Find $25 %$ of 28 students.
1 mark

Read the worked solutions

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

Write $\frac{7}{10}$ as a decimal and a percentage.
2 marks
$\frac{7}{10} = \frac{70}{100}$ .
0.7 and $70 %$ .
Find $20 %$ of 45 metres.
2 marks
$10 %$ is 4.5 m; twice that is 9 m.
9 m.
Find $60 %$ of 30 counters.
2 marks
$10 %$ is 3 counters; $6 \times 3 = 18$ .
18 counters.
Find $\frac{1}{8}$ of 56 litres, then name this fraction as a percentage.
2 marks
$56 \div 8 = 7$ ; $\frac{1}{8}$ is half of $\frac{1}{4}$ , so half of $25 %$ is $12.5 %$ .
7 L; $12.5 %$ .
Sixteen of 40 library books are about animals. What percentage is that?
2 marks
$\frac{16}{40} = \frac{4}{10} = \frac{40}{100}$ .
$40 %$ .
Find $25 %$ of 28 students.
1 mark
$25 % = \frac{1}{4}$ and $28 \div 4 = 7$ .
7 students.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Fraction/decimal/percentage quantities; discounts; budgets/cost predictions; comparing choices, risks and consequences.

Official curriculum source ↗

Fractions, decimals and percentages

In this lesson

Understand the method.

Three names for the same part

Find a useful part first

See the method in action.

Find 40% of a quantity

Find 10% first.

Build four lots of 10%.

Check with a fraction.

Connect the forms, then find the amount

Rename three quarters as hundredths.

Find one quarter of the students.

Take three of those equal parts.

Try it yourself.

Your turn

Keep practising