When two fractions refer to the same whole, subtract the smaller fraction from the larger one. Match that fractional difference to the number given, find the value of one equal part, then scale up to the whole.
The MOE Primary Mathematics syllabus covers fractions of a set and subtraction of unlike fractions. This PSLE Mathematics guide shows how to link a difference in fractions to a difference in the number of objects.
- Check that both fractions describe the same original total.
- Rewrite them with a common denominator.
- Match the difference in parts to the difference in objects.
- Find one part, then multiply by the number of parts in the whole.
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Start by naming the whole
If two fractions both describe the original number of tokens, they share one whole. Draw one bar for that whole and divide it into parts small enough to show both fractions.
For 1/3 and 1/4, use 12 equal parts. One third is four parts and one quarter is three parts. Their difference is one part of the same bar.
If the second fraction describes what remains after the first action, it has a different whole. Check the exact words before subtracting.
CHAPTER 2 OF 4 · Back to contents
Worked example | A difference of nine tokens
Of the tokens in a box, 1/3 are red and 1/4 are blue. There are nine more red tokens than blue tokens. How many tokens are in the box altogether?
| Quantity | Fraction of all tokens | Equal parts |
|---|---|---|
| Red | 1/3 = 4/12 | 4 |
| Blue | 1/4 = 3/12 | 3 |
| Difference | 1/12 | 1 |
| All tokens | 12/12 | 12 |
One part represents nine tokens. All 12 parts represent 12 × 9 = 108 tokens.
Check forwards. One third of 108 is 36 and one quarter is 27. The difference is 36 − 27 = 9, matching the question.
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CHAPTER 3 OF 4 · Back to contents
Practise when the gap covers several parts
Each card in a set has one colour. Two fifths of the cards are yellow and one quarter are green. There are 18 more yellow cards than green cards. Both fractions refer to the whole set. Find the total number of cards.
Use 20 equal parts. Yellow covers 8 parts and green covers 5. Their difference of 3 parts is 18 cards, so one part is 6 cards. The whole set has 20 × 6 = 120 cards.
If the next part asks how many cards are neither yellow nor green, use the fact that each card has one colour. Together they occupy 13 parts, leaving 7 parts or 42 cards.
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CHAPTER 4 OF 4 · Back to contents
Frequently asked questions
Why do I divide by three in the second example?
The 18 cards represent three equal parts. Dividing finds how many cards are in one part.
Must I use the smallest common denominator?
Any common denominator gives the same result when the parts are handled consistently. The smallest one often gives simpler numbers.
What can a parent check before looking at the answer?
Ask the pupil to point to the part of the bar that represents the given difference, then to the whole bar.
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Sources and next reading
SEAB PSLE Mathematics examination syllabus, applicable from 2026