The idea, step by step
Find one share first
To find 3/5 of 40, share 40 into five equal groups. One fifth is 8; three fifths is 3×8=24. The denominator tells you how many equal shares make the whole, and the numerator tells you how many shares to take.
Keep the unit in the answer. A fraction of a length is a length; a fraction of a class is a count of students. Check whether the actual objects can be split.
Work back to the whole
If one quarter of a length is 6 centimetres, the whole contains four such equal parts, so its length is 24 centimetres. Draw equal shares when a reverse problem is difficult to picture.
When several shares are known, find one share before finding all of them. If two thirds of a collection contain 14 objects, one third contains 7 and the whole contains 21.
A common trap
To find 2/3 of 24, divide by 2 and multiply by 3.
Instead: The denominator 3 gives the number of equal shares: 24÷3=8. Take two shares, giving 16.
See the thinking
Worked example 1
Three fifths of a class of 30 bring lunch from home. How many students is that?
| Group | Students | Bring lunch from home |
|---|---|---|
| 1 | 6 | Yes |
| 2 | 6 | Yes |
| 3 | 6 | Yes |
| 4 | 6 | No |
| 5 | 6 | No |
- One fifth is 30÷5=6 students.
- Three fifths is 3×6=18 students.
Worked example 2
One quarter of a walking track is 350 metres long. Find the whole length.
- There are four equal quarters in the whole track.
- 4×350=1,400 metres.
Check your understanding
What is of 28 apples?
Show answer
21 apples.
One quarter is 28÷4=7; three quarters is 3×7=21.
Your turn
6 questions · 12 marks · Work at your own pace.
Read the questions online
- Find of 35 counters.2 marks
- Find of 64 centimetres.2 marks
- A tank holds 48 litres. It is 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 complete. How much further remains?2 marks
- A baker has 20 equal rolls and sells of them. How many remain?2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Find of 35 counters.2 marks
35÷5=7; 2×7=14.
14 counters. - Find of 64 centimetres.2 marks
64÷8=8; 3×8=24.
24 cm. - A tank holds 48 litres. It is full. How much water is in it?2 marks
48÷6=8; 5×8=40.
40 L. - One third of a number is 9. Find the number.2 marks
Three equal thirds make 3×9=27.
27. - A 24-kilometre journey is complete. How much further remains?2 marks
One quarter remains: 24÷4=6.
6 km. - A baker has 20 equal rolls and sells of them. How many remain?2 marks
3/5 of 20 is 12; 20−12=8.
8 rolls.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum Mathematics
Equivalence; comparing/ordering; addition/subtraction; practical quantities.
Official curriculum source ↗