Primary 5 Maths: Fractions
Why P5 Fractions is the hardest jump in upper primary Maths, the mistakes most children make, and worked examples of the question types that appear in year-end exams.
Most schools typically cover this topic in Term 1, around weeks 2–5 — though every school sets its own sequence.
Ask any upper primary Maths teacher which P5 topic separates confident students from struggling ones, and the answer is almost always the same: fractions. In Primary 5, fractions stop being about shading parts of a circle. Your child now adds and subtracts unlike fractions, multiplies fractions by fractions, works with mixed numbers, and — the real test — solves multi-step fraction word problems where the fraction refers to a remainder, not the whole.
This topic feeds directly into P6 Fractions, Ratio, and Percentage. A gap here doesn't stay here; it compounds.
P5 Fractions: the mistakes to watch for
- Adding denominators. Under time pressure, 1/3 + 1/4 becomes 2/7. Your child knows the rule; the error appears when working speed matters. That's a fluency gap, not a knowledge gap — and it shows up in Paper 1, where no calculator is allowed.
- "Of the remainder" read as "of the whole". In word problems, "She gave away 1/4 of her stickers, then 2/5 of the remainder…" trips more P5 students than any other phrasing. If your child multiplies 2/5 by the original amount, they've missed the remainder concept.
- Multiplying fractions like adding them. 3/5 × 2/7 answered as 5/12 (adding across) instead of 6/35 (multiplying numerators and denominators separately).
- Mixed numbers left unconverted. Multiplying 2 1/2 × 3/5 without converting to 5/2 first.
P5 Fractions: bar models for the remainder structure
P5 Fractions: unlike-denominator warm-ups
Easy: adding unlike fractions
Find 1/3 + 1/4.
Show the worked solution
Common denominator 12: 1/3 = 4/12, and 1/4 = 3/12.
4/12 + 3/12 = 7/12.
Easy: subtracting unlike fractions
Find 2/3 − 1/5.
Show the worked solution
Common denominator 15: 2/3 = 10/15, and 1/5 = 3/15.
10/15 − 3/15 = 7/15.
Easy: multiplying two fractions
Find 3/5 × 2/7.
Show the worked solution
Multiply numerators: 3 × 2 = 6. Multiply denominators: 5 × 7 = 35.
3/5 × 2/7 = 6/35.
Easy: multiplying and simplifying
Find 1/2 × 2/3, giving your answer in its simplest form.
Show the worked solution
1/2 × 2/3 = 2/6.
Simplify by dividing top and bottom by 2: 1/3.
P5 Fractions: exam-style word problems
Exam: dividing a fraction by a whole number
A 3/4-litre bottle of juice is poured equally into 6 cups. How much juice is in each cup?
Show the worked solution
3/4 ÷ 6 means splitting 3/4 into 6 equal parts.
3/4 ÷ 6 = 3/4 × 1/6 = 3/24 = 1/8 litre in each cup.
Sense check: each cup must hold much less than the whole 3/4 litre — 1/8 is reasonable; 8 litres would not be.
Exam: fraction of a fraction
A garden is 5/6 of a hectare. 3/10 of the garden is planted with flowers. What fraction of a hectare is planted with flowers?
Show the worked solution
"3/10 of the garden" means 3/10 × 5/6.
3/10 × 5/6 = 15/60 = 1/4 hectare.
Exam: adding unlike fractions in context
Jun read 2/5 of a book on Monday and 1/4 of the book on Tuesday. What fraction of the book has she read so far?
Show the worked solution
Common denominator 20: 2/5 = 8/20, and 1/4 = 5/20.
8/20 + 5/20 = 13/20 of the book.
Exam: scaling a recipe
A recipe needs 3/4 cup of sugar. Ben wants to make only 2/3 of the recipe. How much sugar does he need?
Show the worked solution
3/4 × 2/3 = 6/12.
Simplify: 1/2 cup.
Exam: subtracting unlike fractions in context
A ribbon 7/8 m long has a piece 1/3 m long cut off. How much ribbon remains?
Show the worked solution
Common denominator 24: 7/8 = 21/24, and 1/3 = 8/24.
21/24 − 8/24 = 13/24 m.
P5 Fractions: PSLE-challenge questions
PSLE challenge: fraction of a remainder
Mrs Lim baked some muffins. She gave 1/4 of them to her neighbour and 2/5 of the remainder to her sister. She had 27 muffins left. How many muffins did she bake?
Show the worked solution
After giving 1/4 away, the remainder is 3/4 of the muffins.
Her sister received 2/5 of that remainder, so 3/5 of the remainder was left:
3/5 × 3/4 = 9/20 of all the muffins = 27 muffins left.
So 9/20 of the muffins is 27, meaning 1/20 is 27 ÷ 9 = 3, and the whole batch = 20 × 3 = 60 muffins.
Check: 60 → neighbour gets 15, remainder 45 → sister gets 18 → 27 left. ✓
PSLE challenge: working backwards through two remainders
Mei spent 1/3 of her money on a toy, then 3/5 of what remained on a book. She had $16 left. How much money did she start with?
Show the worked solution
After the toy, the remainder is 2/3 of her money.
She spent 3/5 of that remainder on the book, so 2/5 of the remainder was left:
2/5 × 2/3 = 4/15 of her money = $16.
Money at first = 16 × 15/4 = $60.
Check: $60 → toy $20, remainder $40 → book $24, left $16. ✓
PSLE challenge: two fraction operations in one tank
A tank is 5/8 full of water. 2/5 of the water in the tank is used for cleaning. What fraction of the tank's full capacity is left?
Show the worked solution
Water used = 2/5 of the water present = 2/5 × 5/8 = 10/40 = 1/4 of the tank's capacity.
Water left = 5/8 − 1/4 = 5/8 − 2/8 = 3/8 of the tank's capacity.
P5 Fractions: how to practise this topic
Fraction skills fade quickly if they're not revisited — a child who could add unlike fractions in March may fumble them by August. Two things matter: practising the remainder structure until the bar model is automatic, and coming back to the topic after a gap to check it stuck. A short focused set every few days beats one long weekend session.
What this topic covers
In the MOE Primary Mathematics syllabus, Primary 5 Fractions includes the concepts below. (P5-M-02 is Test Paper's own topic code, not an MOE reference.)
- Addition of unlike fractions
- Subtraction of unlike fractions
- Multiplication of fractions
- Division of fractions
- Operations on mixed numbers
- Converting between mixed numbers and improper fractions
- Fraction of a set of items
- Fraction word problems
Before this topic
These topics feed into Fractions — if this one wobbles, check them first: Primary 4 Fractions.
Where to go next
Is Fractions actually solid?
A 15-minute check-up maps exactly which concepts your child has mastered — and re-tests them days later to prove the fixes stuck. Free.
Start the free check-up