Primary 6 PSLE Mathematics Multiplication Division Quiz

Primary 6 PSLE Mathematics Quiz - Answer Key

Multiplication Division

Total Marks: 40

---

Section A: Short Answer (1 mark each)

---

Q1. Calculate $4 \times \frac{3}{8}$

Answer: $1\frac{1}{2}$ or $\frac{3}{2}$

Working:

• When multiplying a whole number by a fraction, treat the whole number as having denominator 1: $4 = \frac{4}{1}$
• $4 \times \frac{3}{8} = \frac{4}{1} \times \frac{3}{8} = \frac{12}{8}$
• Simplify by dividing numerator and denominator by 4: $\frac{12 \div 4}{8 \div 4} = \frac{3}{2} = 1\frac{1}{2}$

Teaching note: A common mistake is to multiply whole number with denominator instead of numerator. Remember: whole number × numerator, keep the denominator, then simplify.

---

Q2. Find the value of $\frac{5}{6} \times 9$

Answer: $7\frac{1}{2}$ or $\frac{15}{2}$

Working:

• $\frac{5}{6} \times 9 = \frac{5}{6} \times \frac{9}{1} = \frac{45}{6}$
• Simplify: divide numerator and denominator by 3: $\frac{15}{2} = 7\frac{1}{2}$

Alternative method: Simplify before multiplying — $\frac{5}{\cancel{6}_2} \times \frac{\cancel{9}^3}{1} = \frac{5 \times 3}{2} = \frac{15}{2}$

---

Q3. What is $7 \div \frac{1}{4}$?

Answer: 28

Working:

• Dividing by a fraction = multiplying by its reciprocal
• Reciprocal of $\frac{1}{4}$ is $\frac{4}{1}$ = 4
• $7 \div \frac{1}{4} = 7 \times 4 = 28$

Teaching note: Think practically: "How many quarters are in 7 wholes?" Since there are 4 quarters in 1 whole, there are $7 \times 4 = 28$ quarters in 7 wholes.

---

Q4. Calculate $\frac{2}{3} \div 4$

Answer: $\frac{1}{6}$

Working:

• Dividing by whole number 4 = multiplying by reciprocal $\frac{1}{4}$
• $\frac{2}{3} \div 4 = \frac{2}{3} \times \frac{1}{4} = \frac{2}{12} = \frac{1}{6}$

Common mistake: Students sometimes write $\frac{2}{3 \div 4} = \frac{2}{0.75}$ which is incorrect. Always convert to multiplication by reciprocal.

---

Q5. Find the value of $\frac{3}{4} \div \frac{1}{8}$

Answer: 6

Working:

• Reciprocal of $\frac{1}{8}$ is $\frac{8}{1}$ = 8
• $\frac{3}{4} \div \frac{1}{8} = \frac{3}{4} \times 8 = \frac{3 \times 8}{4} = \frac{24}{4} = 6$

Teaching note: "How many eighths fit into three-quarters?" Since $\frac{1}{8} \times 6 = \frac{6}{8} = \frac{3}{4}$, the answer is 6.

---

Q6. A packet of biscuits weighs $\frac{3}{5}$ kg. What is the total weight of 8 such packets?

Answer: $4\frac{4}{5}$ kg or $\frac{24}{5}$ kg

Working:

• $\frac{3}{5} \times 8 = \frac{3 \times 8}{5} = \frac{24}{5} = 4\frac{4}{5}$ kg

---

Q7. How many $\frac{1}{6}$ m pieces can be cut from a string that is 5 m long?

Answer: 30

Working:

• Number of pieces = total length ÷ length of each piece
• $5 \div \frac{1}{6} = 5 \times 6 = 30$

Teaching note: This is a "how many fit into" question — classic division by fraction context.

---

Q8. Calculate $2\frac{1}{4} \times \frac{2}{3}$. Give your answer as a mixed number.

Answer: $1\frac{1}{2}$

Working:

• Convert mixed number to improper fraction: $2\frac{1}{4} = \frac{9}{4}$
• $\frac{9}{4} \times \frac{2}{3} = \frac{18}{12} = \frac{3}{2} = 1\frac{1}{2}$

Common mistake: Multiplying whole and fraction parts separately: $(2 \times \frac{2}{3}) + (\frac{1}{4} \times \frac{2}{3})$ — this distributive approach works but is more complex and error-prone. Always convert to improper fraction first for safer calculation.

---

Q9. Find the value of $3\frac{1}{2} \div 1\frac{3}{4}$

Answer: 2

Working:

• Convert both to improper fractions: $3\frac{1}{2} = \frac{7}{2}$ and $1\frac{3}{4} = \frac{7}{4}$
• $\frac{7}{2} \div \frac{7}{4} = \frac{7}{2} \times \frac{4}{7} = \frac{28}{14} = 2$

Teaching note: Notice the cancellation opportunity: $\frac{\cancel{7}}{2} \times \frac{4}{\cancel{7}} = \frac{4}{2} = 2$

---

Q10. $\frac{5}{8}$ of a number is 40. What is the number?

Answer: 64

Working:

• Let the number be $n$
• $\frac{5}{8} \times n = 40$
• $n = 40 \div \frac{5}{8} = 40 \times \frac{8}{5} = \frac{320}{5} = 64$

Verification: $\frac{5}{8} \times 64 = \frac{320}{8} = 40$ ✓

---

Section B: Structured Problems (3 marks each)

---

Q11. Rectangular tank with base area $\frac{7}{10}$ m² and water height $\frac{5}{6}$ m

(a) Volume of water [2 marks]

Answer: $\frac{7}{12}$ m³

Working:

• Volume = base area × height
• $V = \frac{7}{10} \times \frac{5}{6} = \frac{35}{60} = \frac{7}{12}$ m³

Marking: [1] for correct formula/method, [1] for correct answer with simplification

(b) Remaining volume after pouring out $\frac{3}{5}$ [1 mark]

Answer: $\frac{7}{30}$ m³

Working:

• Fraction remaining = $1 - \frac{3}{5} = \frac{2}{5}$
• Remaining volume = $\frac{7}{12} \times \frac{2}{5} = \frac{14}{60} = \frac{7}{30}$ m³

Marking: [1] for correct answer (method may be implied)

---

Q12. Mrs Tan's flour

(a) Flour used [2 marks]

Answer: $\frac{3}{5}$ kg

Working:

• Flour used = $\frac{9}{10} \times \frac{2}{3} = \frac{18}{30} = \frac{3}{5}$ kg

Marking: [1] for correct multiplication setup, [1] for correct simplified answer

(b) Flour left [1 mark]

Answer: $\frac{3}{10}$ kg

Working:

• Flour left = $\frac{9}{10} - \frac{3}{5} = \frac{9}{10} - \frac{6}{10} = \frac{3}{10}$ kg
• Or: $\frac{9}{10} \times \frac{1}{3} = \frac{9}{30} = \frac{3}{10}$ kg (since $\frac{2}{3}$ used means $\frac{1}{3}$ left)

---

Q13. Pipe cutting

(a) Number of complete pieces [2 marks]

Answer: 10

Working:

• Pipe length = $\frac{15}{2}$ m = 7.5 m; each piece = $\frac{3}{4}$ m = 0.75 m
• Number = $\frac{15}{2} \div \frac{3}{4} = \frac{15}{2} \times \frac{4}{3} = \frac{60}{6} = 10$

Marking: [1] for correct division setup, [1] for answer

(b) Length of remaining piece [1 mark]

Answer: 0 m (or no remainder)

Working:

• Since $\frac{15}{2} \div \frac{3}{4} = 10$ exactly, there is no remainder.
• Check: $10 \times \frac{3}{4} = \frac{30}{4} = \frac{15}{2}$ ✓

Teaching note: This exact division is designed to show students that not all division problems have remainders — a common assumption after working with whole number division.

---

Q14. Raj's stickers

(a) To brother [1 mark]

Answer: 144 stickers

Working:

• $\frac{2}{5} \times 360 = \frac{720}{5} = 144$

(b) To sister [1 mark]

Answer: 72 stickers

Working:

• Remainder after giving to brother: $360 - 144 = 216$
• To sister: $\frac{1}{3} \times 216 = 72$

(c) Left [1 mark]

Answer: 144 stickers

Working:

• Left: $216 - 72 = 144$
• Or: $\frac{2}{3} \times 216 = 144$ (since $\frac{1}{3}$ given away, $\frac{2}{3}$ remains)

Teaching note: This is a classic "fraction of remainder" problem. The key trap is applying $\frac{1}{3}$ to the original 360 instead of the remainder 216.

---

Q15. Recipe milk

(a) Milk for 1 cupcake [1 mark]

Answer: $\frac{1}{8}$ cup

Working:

• $\frac{3}{4} \div 6 = \frac{3}{4} \times \frac{1}{6} = \frac{3}{24} = \frac{1}{8}$ cup

(b) Milk for 15 cupcakes [2 marks]

Answer: $1\frac{7}{8}$ cups or $\frac{15}{8}$ cups

Working:

• Method 1: $\frac{1}{8} \times 15 = \frac{15}{8} = 1\frac{7}{8}$ cups
• Method 2: $\frac{3}{4} \times \frac{15}{6} = \frac{3}{4} \times \frac{5}{2} = \frac{15}{8}$ cups (scaling factor approach)

Marking: [1] for correct method, [1] for correct final answer

---

Q16. Composite L-shaped garden plot

Key visual features expected from image placeholder:

• Large rectangle: 2¼ m × 1½ m
• Small removed rectangle at top-right: ¾ m × ½ m

(a) Area of large rectangle [1 mark]

Answer: $\frac{27}{8}$ m² or $3\frac{3}{8}$ m²

Working:

• $2\frac{1}{4} \times 1\frac{1}{2} = \frac{9}{4} \times \frac{3}{2} = \frac{27}{8} = 3\frac{3}{8}$ m²

(b) Area of small rectangle [1 mark]

Answer: $\frac{3}{8}$ m²

Working:

• $\frac{3}{4} \times \frac{1}{2} = \frac{3}{8}$ m²

(c) Area of garden plot [1 mark]

Answer: 3 m²

Working:

• Garden area = large area − small area
• $\frac{27}{8} - \frac{3}{8} = \frac{24}{8} = 3$ m²

Teaching note: This demonstrates subtraction of fractions with common denominators — a simpler case than finding common denominators first.

---

Q17. School pupils

(a) Number of boys [1 mark]

Answer: 315 boys

Working:

• $\frac{3}{8} \times 840 = \frac{2520}{8} = 315$

(b) Number of girls [1 mark]

Answer: 525 girls

Working:

• $840 - 315 = 525$
• Or: $\frac{5}{8} \times 840 = 525$

(c) Girls who wear spectacles [1 mark]

Answer: 210 girls

Working:

• $\frac{2}{5} \times 525 = \frac{1050}{5} = 210$

---

Q18. Tank and bottles

(a) Water in each bottle [2 marks]

Answer: $\frac{3}{4}$ litre

Working:

• $4\frac{1}{2} \div 6 = \frac{9}{2} \div 6 = \frac{9}{2} \times \frac{1}{6} = \frac{9}{12} = \frac{3}{4}$ litre

Marking: [1] for correct conversion to improper fraction and division setup, [1] for correct simplification

(b) Water in jug [1 mark]

Answer: $1\frac{1}{2}$ litres

Working:

• $2 \times \frac{3}{4} = \frac{6}{4} = 1\frac{1}{2}$ litres

---

Q19. Sulin's money (Fraction of remainder problem)

(a) Fraction left after book [1 mark]

Answer: $\frac{3}{5}$

Working:

• $1 - \frac{2}{5} = \frac{3}{5}$

(b) Fraction left after both items [1 mark]

Answer: $\frac{2}{5}$

Working:

• After book: $\frac{3}{5}$ remains
• Spent $\frac{1}{3}$ of remainder on pen, so $\frac{2}{3}$ of remainder left
• Fraction left: $\frac{3}{5} \times \frac{2}{3} = \frac{6}{15} = \frac{2}{5}$

(c) Original amount [1 mark]

Answer: $60

Working:

• $\frac{2}{5}$ of original = $24
• Original = $24 \div \frac{2}{5} = 24 \times \frac{5}{2} = \frac{120}{2} = 60$

Verification:

• Book: $\frac{2}{5} \times 60 = 24$, remaining 36
• Pen: $\frac{1}{3} \times 36 = 12$, remaining 24 ✓

Teaching note: This is a PSLE-style fraction-of-remainder problem. The critical step is recognizing that $\frac{1}{3}$ applies to the remainder, not the original. Drawing a bar model is highly recommended: [whole] → [2/5 spent|3/5 remains] → [1/3 of 3/5 spent|2/3 of 3/5 left].

---

Q20. Pizza sharing

(a) Ben's fraction [1 mark]

Answer: $\frac{1}{2}$

Working:

• After Andy: $1 - \frac{1}{4} = \frac{3}{4}$ remains
• Ben ate $\frac{2}{3}$ of $\frac{3}{4} = \frac{2}{3} \times \frac{3}{4} = \frac{6}{12} = \frac{1}{2}$

(b) Caleb's fraction [1 mark]

Answer: $\frac{1}{4}$

Working:

• Caleb's fraction = $1 - \frac{1}{4} - \frac{1}{2} = \frac{1}{4}$
• Or: After Ben, remaining = $\frac{3}{4} - \frac{1}{2} = \frac{3}{4} - \frac{2}{4} = \frac{1}{4}$ (Caleb ate all that remained)

(c) Caleb's slices [1 mark]

Answer: 6 slices

Working:

• $\frac{1}{4} \times 24 = 6$ slices

---

END OF ANSWER KEY