Practical quantities | Year 6

01 / LEARN

Understand the idea.

Find one share first

To find a fraction of a quantity, use the denominator to share the whole into equal groups. This finds one share. Then multiply that share by the numerator to take the required number of groups.

For $\frac{3}{5}$ of $40$ , one fifth is $40 \div 5 = 8$ and three fifths is $3 \times 8 = 24$ . Keep the unit attached: a fraction of a length remains a length, while a fraction of a class counts students.

Work back to the whole

A reverse problem gives a share and asks for the whole. If one quarter of a length is six centimetres, four equal quarters make the whole. Multiply the known one-quarter length by four, rather than dividing it again.

If several shares are known, first find one. When two thirds contain fourteen objects, each third contains seven, and all three thirds contain twenty-one. Equal-group reasoning makes clear which division and multiplication are needed.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Worked example 1

Three fifths of a class of 30 bring lunch from home. How many students is that?

Five equal groups of six students
Group	Students	Bring lunch from home
1	6	Yes
2	6	Yes
3	6	Yes
4	6	No
5	6	No

Worked solution

1
Find one fifth of the class.
$30 \div 5 = 6 students$
The denominator divides the class into five equal groups.
2
Take three of those groups.
$3 \times 6 = 18 students$
The numerator tells us to select three fifths.
3
Check against the class size.
$18 < 30$
Three fifths is less than the whole class, so 18 students is a sensible count.

Answer

18 students.

EXAMPLE 02

Worked example 2

One quarter of a walking track is 350 metres long. Find the whole length.

Worked solution

1
Identify how many quarters make the whole.
$\frac{4}{4} = 1$
The full track contains four equal quarters.
2
Combine four lengths of 350 metres.
$4 \times 350 = 1.400 m$
Each quarter has the given length, so four quarters give the full track.
3
Check the given share.
$1.400 \div 4 = 350 m$
A quarter of the calculated whole matches the length supplied.

Answer

1,400 metres.

03 / YOUR TURN

Try it yourself.

Check your understanding

What is $\frac{3}{4}$ of 28 apples?

Show answer & reasoning

21 apples.

One quarter is $28 \div 4 = 7$ apples. Three quarters is $3 \times 7 = 21$ apples.

Keep practising

6 worksheet questions · 12 marks

Open worksheet Worked solutions

Read the questions online

Find $\frac{2}{5}$ of 35 counters.
2 marks
Find $\frac{3}{8}$ of 64 centimetres.
2 marks
A tank holds 48 litres. It is $\frac{5}{6}$ full. How much water is in it?
2 marks
One third of a number is 9. Find the number.
2 marks
A 24-kilometre journey is $\frac{3}{4}$ complete. How much further remains?
2 marks
A baker has 20 equal rolls and sells $\frac{3}{5}$ of them. How many remain?
2 marks

Read the worked solutions

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

Find $\frac{2}{5}$ of 35 counters.
2 marks
$35 \div 5 = 7$ ; $2 \times 7 = 14$ .
14 counters.
Find $\frac{3}{8}$ of 64 centimetres.
2 marks
$64 \div 8 = 8$ ; $3 \times 8 = 24$ .
24 cm.
A tank holds 48 litres. It is $\frac{5}{6}$ full. How much water is in it?
2 marks
$48 \div 6 = 8$ ; $5 \times 8 = 40$ .
40 L.
One third of a number is 9. Find the number.
2 marks
Three equal thirds make $3 \times 9 = 27$ .
27.
A 24-kilometre journey is $\frac{3}{4}$ complete. How much further remains?
2 marks
One quarter remains: $24 \div 4 = 6$ .
6 km.
A baker has 20 equal rolls and sells $\frac{3}{5}$ of them. How many remain?
2 marks
$\frac{3}{5}$ of 20 is 12; $20 - 12 = 8$ .
8 rolls.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Equivalence; comparing/ordering; addition/subtraction; practical quantities.

Official curriculum source ↗

In this lesson

Understand the idea.

Find one share first

Work back to the whole

See the method in action.

Worked example 1

Find one fifth of the class.

Take three of those groups.

Check against the class size.

Worked example 2

Identify how many quarters make the whole.

Combine four lengths of 350 metres.

Check the given share.

Try it yourself.

Check your understanding

Keep practising