Fractions of Quantities, Grouping & Sharing

Finding a fraction of an amount, working backwards from a fraction to the whole, and the grouping and sharing word problems that carry the marks in exams — worked examples, a worksheet with memo and a quiz.

This is where fractions meet real life — and where most of the exam marks sit. Every question below is really the same skill dressed in different words, so learn to spot which of the three types you are looking at.

1Type 1: Finding a fraction of an amount

A bar model: split the whole into equal parts, find one part, then take as many as you need.

'of' means ×. The quickest route: divide by the bottom, multiply by the top.

Worked ExampleCalculate 34 of R60

1
Divide by the denominator: 60 ÷ 4 = 15.
This finds one quarter.
2
Multiply by the numerator: 15 × 3 = 45.
Three quarters is three of those.
3
Answer: R45.
Always keep the unit in the answer.

Worked ExampleThere are 32 learners in a class and 58 walk to school. How many walk?

1
58 of 32: divide by 8 → 32 ÷ 8 = 4.
One eighth of the class is 4 learners.
2
Multiply by 5 → 4 × 5 = 20.
3
20 learners walk to school.
Answer in words — this earns the final mark.

2Type 2: Working backwards to the whole

Sometimes the exam gives you the part and asks for the whole. Reverse the process: multiply by the bottom, divide by the top.

Worked Example23 of a number is 18. What is the number?

1
If 23 is 18, then 13 is 18 ÷ 2 = 9.
Work out one part first.
2
The whole is 3 thirds: 9 × 3 = 27.
3
The number is 27.
Check: 23 of 27 = 18. ✓

💡

Always check backwards on this type: put your answer into the original sentence. It takes five seconds and catches almost every mistake.

3Type 3: Grouping — how many pieces fit?

When a question asks how many small pieces fit into a bigger amount, that is a division.

Worked ExampleHow many 34-metre pieces of ribbon can be cut from 6 metres?

1
This is 6 ÷ 34.
'How many fit into' means divide.
2
Flip and multiply: 6 × 43 = 243.
Dividing by a fraction means multiplying by its reciprocal.
3
= 8 pieces.

4Type 4: Sharing what is left

Worked ExampleThabo spends 13 of his money on airtime and 14 on lunch. What fraction is left?

1
Add what he spent: 13 + 14.
Combine the two parts first.
2
LCD 12: 412 + 312 = 712.
3
Left over: 1 − 712 = 1212 − 712 = 512.
The whole amount is 1, written as 1212.
4
512 of his money is left.

⚠️

In 'what is left' questions the whole must be written as a fraction with the same denominator before subtracting — here 1 became 1212. Forgetting this step is the most common error in the whole topic.

Practice exercises

Work each one out, then click to reveal the answer.

📄 Worksheet ✅ Memo 📝 Exam paper 🗝️ Marking guide

1
Find 34 of 60.
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60 ÷ 4 × 3 = 45
2
Find ⅖ of R150.
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150 ÷ 5 × 2 = R60
3
Find 58 of 48.
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48 ÷ 8 × 5 = 30
4
There are 45 learners and 13 play sport. How many play sport?
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45 ÷ 3 = 15 learners
5
34 of a number is 24. What is the number?
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14 = 24 ÷ 3 = 8, so the number is 8 × 4 = 32
6
⅖ of a number is 30. What is the number?
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⅕ = 30 ÷ 2 = 15, so the number is 15 × 5 = 75
7
How many 12-litre bottles can be filled from 7 litres?
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7 ÷ 12 = 7 × 2 = 14 bottles
8
How many 23-metre pieces can be cut from 8 metres?
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8 ÷ 23 = 8 × 32 = 12 pieces
9
Sipho spends 14 of his money on a book and 13 on food. What fraction is left?
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14 + 13 = 312 + 412 = 712; left = 1212 − 712 = 512
10
A tank is ⅗ full and holds 45 litres when full. How many litres are in it?
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45 ÷ 5 × 3 = 27 litres