Primary 6 Maths: Fractions
P6 Fractions extends division to fraction-by-fraction and powers the hardest PSLE word problems. Key structures, common errors, and worked examples.
Most schools typically cover this topic in Term 1, around weeks 2–4 — though every school sets its own sequence.
By Primary 6, your child has met every fraction operation. What P6 adds is the last missing piece — dividing by a fraction — and then raises the stakes: fractions embedded inside multi-step PSLE problems, mixed with ratio, percentage and even circle measurements, under time pressure.
The conceptual heart of P6 Fractions is the question "how many quarters fit inside three and a half?" A child who can picture that (14, because each litre holds 4 quarter-litres) owns the topic. A child who only remembers "flip and multiply" will pass drills and fail transfers.
P6 Fractions: the mistakes to watch for
- Dividing the wrong way round. 1/2 ÷ 4 and 4 ÷ 1/2 give different answers (1/8 and 8). Children who blur them are pattern-matching, not reasoning — and PSLE questions are written to catch exactly that.
- Remainder problems re-emerging. The P5 "fraction of the remainder" structure returns in P6 with more steps. If it wasn't solid last year, it resurfaces here — usually in the last questions of Paper 2.
- Not sense-checking magnitude. Dividing by a fraction less than 1 makes the answer bigger. A child who gets 14 cups from 3 1/2 litres shouldn't doubt it — and a child who gets 0.875 cups should.
- Losing track when ratio or percentage joins in. A PSLE question that mixes fractions with ratio units or a percentage step fails not because any one operation is hard, but because the child loses the thread between steps.
P6 Fractions: bar models for fraction division
P6 Fractions: dividing fractions warm-ups
Easy: dividing by a fraction
A drinks stall has 3 1/2 litres of lime juice. The juice is poured into cups of 1/4 litre each. How many full cups can be poured?
Show the worked solution
Ask: how many 1/4-litres fit into 3 1/2 litres?
3 1/2 ÷ 1/4 = 7/2 × 4 = 14 cups.
Sense check: each litre fills 4 cups, so 3 litres fills 12, and the extra half-litre fills 2 more. 14. ✓
Easy: dividing a fraction by a fraction
Find 2/3 ÷ 1/6.
Show the worked solution
Dividing by 1/6 is the same as multiplying by 6.
2/3 × 6 = 12/3 = 4.
Easy: dividing a mixed number
Find 3 1/2 ÷ 1/2.
Show the worked solution
3 1/2 = 7/2. Dividing by 1/2 means multiplying by 2.
7/2 × 2 = 7.
Easy: dividing and leaving a mixed number
Find 5/6 ÷ 2/3, giving your answer as a mixed number.
Show the worked solution
5/6 ÷ 2/3 = 5/6 × 3/2 = 15/12.
Simplify: 15/12 = 1 1/4.
P6 Fractions: exam-style multi-step problems
Exam: dividing a length of cloth
A tailor has 4 1/2 m of cloth and uses 3/4 m for each shirt. How many complete shirts can be made?
Show the worked solution
4 1/2 ÷ 3/4 = 9/2 × 4/3 = 36/6 = 6 shirts.
Exam: fraction combined with percentage
3/5 of a class of 40 students passed with distinction. What percentage of the class did not get distinction?
Show the worked solution
Passed with distinction: 3/5 × 40 = 24 students.
Did not: 40 − 24 = 16 students.
As a percentage: 16/40 × 100% = 40%.
Exam: fraction combined with ratio
The ratio of boys to girls in a class is 3 : 5. There are 24 boys. If 3/5 of the girls wear spectacles, how many girls wear spectacles?
Show the worked solution
3 units = 24 boys, so 1 unit = 8.
Girls = 5 units = 5 × 8 = 40.
Girls wearing spectacles = 3/5 × 40 = 24 girls.
Exam: dividing a length with no remainder
A rope of length 6 1/4 m is cut into pieces of 5/8 m each. How many complete pieces can be cut, and is there any rope left over?
Show the worked solution
6 1/4 ÷ 5/8 = 25/4 × 8/5 = 200/20 = 10 pieces, with no rope left over.
Exam: fraction of a fraction removed
A photographer's memory card was 5/8 full. After she deleted 1/5 of the used space, what fraction of the card is now full?
Show the worked solution
Space deleted = 1/5 of the used 5/8 = 1/5 × 5/8 = 1/8.
Space still used = 5/8 − 1/8 = 1/2 of the card.
P6 Fractions: PSLE-challenge questions
PSLE challenge: two-step remainder
Meiling spent 1/3 of her money on a book and 3/4 of the remainder on a bag. She had $12 left. How much money did she have at first?
Show the worked solution
After the book, the remainder = 2/3 of her money.
She spent 3/4 of that remainder on the bag, so 1/4 of the remainder was left:
1/4 × 2/3 = 1/6 of her money = $12.
Money at first = 6 × $12 = $72.
Check: book $24, remainder $48, bag $36, left $12. ✓
PSLE challenge: fraction, ratio and percentage together
Rui Feng and Wei Jie shared a sum of money in the ratio 5 : 3. Rui Feng spent 2/5 of his share and had $180 left. How much money did Wei Jie get, and what percentage of the total sum was Wei Jie's share?
Show the worked solution
Rui Feng had 3/5 of his share left, so 3/5 of his share = $180, meaning his full share = $300.
His share is 5 units, so 1 unit = $60. Wei Jie's share = 3 units = $180.
Total sum = 8 units = $480. Wei Jie's percentage of the total = 180/480 × 100% = 37.5%.
PSLE challenge: fraction, percentage and a fixed amount
A tank is 3/4 full of water. 40% of the water in the tank is poured out, and then 5 litres of water is added, making the tank exactly 1/2 full. What is the capacity of the tank?
Show the worked solution
Let the capacity be C. Water at first = 3/4 C.
After pouring out 40%, water left = 60% × 3/4 C = 9/20 C.
Adding 5 L brings it to 1/2 C: 9/20 C + 5 = 10/20 C, so 5 = 1/20 C.
C = 5 × 20 = 100 litres.
Check: 3/4 × 100 = 75 L; 40% of 75 = 30 L poured out, leaving 45 L; +5 L = 50 L = 1/2 × 100. ✓
P6 Fractions: how to practise this topic
P6 fraction skills need to be retained, not just relearned — PSLE is months after the topic is taught, and the skill quietly decays in between. The most valuable practice is spaced: revisit fraction division and remainder problems weeks after they were last correct, and treat any slip as a signal to re-practise now rather than during the final revision crunch.
What this topic covers
In the MOE Primary Mathematics syllabus, Primary 6 Fractions includes the concepts below. (P6-M-02 is Test Paper's own topic code, not an MOE reference.)
- Four operations on fractions
- Fraction of a set/quantity
- Fraction word problems
- Conversion between fractions and decimals
- Conversion between fractions and percentages
- Mixed numbers and improper fractions
Before this topic
These topics feed into Fractions — if this one wobbles, check them first: Primary 5 Fractions · Primary 5 Decimals · Primary 5 Percentage.
Where to go next
Is Fractions actually solid?
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