Primary 6 PSLE Mathematics Multiplication Division Quiz

Primary 6 PSLE Mathematics Quiz - Multiplication Division: ANSWER KEY

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Section A: Direct Computation (2 marks each)

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1. Calculate $24 \times 37$

Method: Use standard long multiplication or distributive property.

• $24 \times 37 = 24 \times (30 + 7)$
• $= 24 \times 30 + 24 \times 7$
• $= 720 + 168$
• $= 888$

Or by long multiplication:

   24
 × 37
 ----
  168  (7 × 24)
  720  (30 × 24)
 ----
  888

Answer: 888 [2 marks]

Common mistake: Forgetting to add a zero when multiplying by the tens digit.

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2. Calculate $576 \div 8$

Method: Use short division or split the number.

• $576 \div 8 = (560 + 16) \div 8$
• $= 560 \div 8 + 16 \div 8$
• $= 70 + 2$
• $= 72$

Or by short division: 8 into 57 goes 7 remainder 1; 8 into 16 goes 2.

Answer: 72 [2 marks]

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3. Find the value of $15 \times 28 \times 4$

Method: Use commutative property to simplify first.

• $15 \times 28 \times 4 = 15 \times 4 \times 28$
• $= 60 \times 28$
• $= 60 \times (30 - 2)$
• $= 1800 - 120$
• $= 1680$

Answer: 1680 [2 marks]

Teaching note: Look for friendly number pairs. $15 \times 4 = 60$ is easier than $15 \times 28$.

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4. Calculate $903 \div 7$

Method: Use short division.

• $903 \div 7$: 7 into 9 goes 1 remainder 2
• 7 into 20 goes 2 remainder 6
• 7 into 63 goes 9

Answer: 129 [2 marks]

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5. Find the value of $125 \times 32 \times 25$

Method: Group friendly numbers using associative property.

• $125 \times 32 \times 25 = 125 \times 8 \times 4 \times 25$
• $= (125 \times 8) \times (4 \times 25)$ [Key step: $125 \times 8 = 1000$ and $4 \times 25 = 100$]
• $= 1000 \times 100$
• $= 100000$

Answer: 100 000 [2 marks]

PSLE heuristic: Recognize $125 \times 8 = 1000$ and $25 \times 4 = 100$ as common "magic pairs."

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6. Calculate $\frac{3}{4} \times \frac{8}{9}$

Method: Multiply numerators and denominators, then simplify; or cancel first.

• $\frac{3}{4} \times \frac{8}{9} = \frac{3 \times 8}{4 \times 9}$
• Cancel common factors: 3 and 9 share 3; 4 and 8 share 4
• $= \frac{1 \times 2}{1 \times 3}$
• $= \frac{2}{3}$

Answer: $\frac{2}{3}$ [2 marks]

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7. Calculate $\frac{5}{6} \div \frac{15}{24}$

Method: Multiply by the reciprocal of the divisor.

• $\frac{5}{6} \div \frac{15}{24} = \frac{5}{6} \times \frac{24}{15}$ [Key concept: dividing by fraction = multiplying by reciprocal]
• Cancel: 5 and 15 share 5; 6 and 24 share 6
• $= \frac{1 \times 4}{1 \times 3}$
• $= \frac{4}{3}$ or $1\frac{1}{3}$

Answer: $\frac{4}{3}$ or $1\frac{1}{3}$ [2 marks]

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8. Find the value of $2\frac{1}{3} \times 1\frac{4}{5}$

Method: Convert to improper fractions first.

• $2\frac{1}{3} = \frac{7}{3}$
• $1\frac{4}{5} = \frac{9}{5}$
• $\frac{7}{3} \times \frac{9}{5} = \frac{7 \times 9}{3 \times 5}$
• Cancel: 3 and 9 share 3
• $= \frac{7 \times 3}{1 \times 5} = \frac{21}{5}$
• Convert to mixed number: $4\frac{1}{5}$

Answer: $4\frac{1}{5}$ [2 marks]

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Section B: Problem Solving (2 marks each)

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9. A baker packs 288 cupcakes into boxes of 12. How many boxes does she need?

Method: Division finds how many groups of 12 fit into 288.

• Number of boxes $= 288 \div 12$
• $= 24$

Answer: 24 boxes [2 marks]

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10. Mr Lim buys 15 boxes of pencils. Each box contains 24 pencils. He repackages the pencils into packets of 8. How many packets can he make?

Method: Two-step problem: multiply then divide.

• Total pencils $= 15 \times 24 = 360$
• Number of packets $= 360 \div 8 = 45$

Answer: 45 packets [2 marks]

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11. A school has 840 students. $\frac{3}{7}$ of them are girls. How many boys are there?

Method: Find fraction that are boys, then calculate.

• Fraction of boys $= 1 - \frac{3}{7} = \frac{4}{7}$
• Number of boys $= \frac{4}{7} \times 840$
• $= 4 \times 120 = 480$

Alternative: Number of girls $= \frac{3}{7} \times 840 = 360$; Boys $= 840 - 360 = 480$

Answer: 480 boys [2 marks]

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12. Siti had $\frac{9}{10}$ m of ribbon. She cut it into pieces of $\frac{3}{20}$ m each. How many pieces did she get?

Method: Division of fractions—how many $\frac{3}{20}$ fit into $\frac{9}{10}$?

• Number of pieces $= \frac{9}{10} \div \frac{3}{20}$
• $= \frac{9}{10} \times \frac{20}{3}$
• $= \frac{9 \times 20}{10 \times 3} = \frac{180}{30} = 6$

Answer: 6 pieces [2 marks]

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13. A rectangular tank measures 25 cm by 18 cm by 12 cm. It is filled with water to a height of 8 cm. How much water is in the tank?

Method: Volume of water = length × breadth × height of water (not full tank height).

• Volume $= 25 \times 18 \times 8$
• $= 25 \times 144$
• $= 3600 \text{ cm}^3$
• $= 3600 \text{ ml}$ (since $1 \text{ cm}^3 = 1 \text{ ml}$)

Common mistake: Using 12 cm instead of 8 cm.

Answer: 3600 ml (or 3600 cm³) [2 marks]

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14. A bag contains red and blue beads in the ratio $5:3$. There are 240 blue beads. How many red beads are there?

Method: Use ratio units.

• 3 units = 240 blue beads
• 1 unit $= 240 \div 3 = 80$
• Red beads = 5 units $= 5 \times 80 = 400$

Answer: 400 red beads [2 marks]

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15. A shop sold 450 T-shirts over three days. On Monday, it sold $\frac{2}{5}$ of the T-shirts. On Tuesday, it sold $\frac{3}{4}$ of the remainder. How many T-shirts were sold on Wednesday?

Method: Multi-step fraction of remainder.

• Monday: $\frac{2}{5} \times 450 = 180$
• Remainder after Monday: $450 - 180 = 270$
• Tuesday: $\frac{3}{4} \times 270 = 202.5$ → let me recalculate: $\frac{3}{4} \times 270 = \frac{810}{4} = 202.5$

Rechecking with cleaner numbers: Let me verify: $\frac{3}{4} \times 270 = 202.5$. This gives a decimal, so let me recheck the problem. Actually this works: $270 \times \frac{3}{4} = 202.5$, but T-shirts should be whole numbers. Let me recalculate: $270 \div 4 = 67.5$, times 3 = 202.5.

Actually, let me use the intended clean answer: $270 \times \frac{3}{4}$ - this does give 202.5 which is problematic. The original design should have used cleaner numbers. However, following standard PSLE format where such problems do work out, let me recheck: if remainder is 270, then $\frac{3}{4}$ of 270 = 202.5. This suggests I should have used different numbers.

Given the question as stated, I'll proceed: This is a teaching point about careful problem design. For the answer key, I'll note that in practice this would be adjusted, but students should show the method.

• Tuesday: $\frac{3}{4} \times 270 = 202.5$ → Problem note: This should be 202 or 203, or original numbers needed adjustment. In actual PSLE, numbers are chosen to avoid this.

Let me provide the straightforward calculation:

• Remainder after Tuesday: $270 \times \frac{1}{4} = 67.5$

Actually, rechecking: let me use the intended pedagogical approach. I'll note this as a case where students should identify that the final answer represents Wednesday's sales as the final remainder.

• Wednesday: $270 - 202.5 = 67.5$ or directly $\frac{1}{4} \times 270 = 67.5$

Given this is non-ideal, I'll provide the mathematically correct answer and note rounding, though in reality PSLE would use numbers giving whole answers.

Revised clean approach for answer key: The method is what matters.

• Remainder after Monday: $450 \times \frac{3}{5} = 270$
• Fraction left after Tuesday: $1 - \frac{3}{4} = \frac{1}{4}$
• Wednesday: $\frac{1}{4} \times 270 = 67.5$

Given this is 67.5, I'll present: Answer: 67 or 68 T-shirts (with note that PSLE problems typically use numbers giving whole answers). For marking: [2 marks] for correct method.

Actually, let me be more careful. Let me redo: if the problem was intended with 480 shirts:

• Monday: $\frac{2}{5} \times 480 = 192$, remainder 288
• Tuesday: $\frac{3}{4} \times 288 = 216$, remainder 72. This gives clean numbers.

But with 450 as stated: The answer key should reflect the question as written.

Method as stated:

• Monday: $\frac{2}{5} \times 450 = 180$ sold, 270 remainder
• Tuesday: $\frac{3}{4} \times 270 = 202.5$ sold from remainder
• Wednesday: $270 - 202.5 = 67.5$

Answer: 67.5 T-shirts, or 67 or 68 if rounding to nearest whole [2 marks]

Marking note: Award full marks for correct method even if student rounds; the question has a slight design flaw that teachers should note for future revision to use 480 or 360 T-shirts.

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16. A number multiplied by 15 gives 720. What is the number when it is divided by 8?

Method: Two-step: find the number, then divide.

• Number $\times 15 = 720$
• Number $= 720 \div 15 = 48$
• Number divided by 8: $48 \div 8 = 6$

Answer: 6 [2 marks]

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Section C: Applied Reasoning (4 marks each)

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17. Raju had $840. He spent$\frac{2}{7}$of his money on a bicycle and$\frac{3}{8}$ of the remainder on a video game. How much money did he have left?

Method: Same template as Q15—fraction of remainder problem.

Step 1: Find bicycle cost and remainder [1 mark]

• Bicycle: $\frac{2}{7} \times 840 = 240$
• Remainder: $840 - 240 = 600$

Step 2: Find video game cost [1 mark]

• Video game: $\frac{3}{8} \times 600 = 225$

Step 3: Find final amount [1 mark]

• Money left: $600 - 225 = 375$

Or directly: $\frac{5}{8} \times 600 = 375$

Step 4: Verify or present clearly [1 mark]

Answer: $375 [4 marks]

Common error: Taking $\frac{3}{8}$ of $840 instead of the remainder.

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18. [Cross-reference the table visual] A factory produces 480 toy cars in 6 hours using 8 machines. How many toy cars can 5 machines produce in 10 hours if all machines work at the same rate?

Method: Find unit rate, then scale.

Step 1: Find rate per machine per hour [2 marks]

• 8 machines → 6 hours → 480 cars
• 8 machines → 1 hour → $480 \div 6 = 80$ cars
• 1 machine → 1 hour → $80 \div 8 = 10$ cars per machine per hour

Step 2: Calculate for 5 machines, 10 hours [2 marks]

• 5 machines → 1 hour → $5 \times 10 = 50$ cars
• 5 machines → 10 hours → $50 \times 10 = 500$ cars

Alternative (combined method):

• Total machine-hours for first case: $8 \times 6 = 48$ machine-hours → 480 cars
• So 1 machine-hour → 10 cars
• Total machine-hours for new case: $5 \times 10 = 50$ machine-hours
• Cars produced: $50 \times 10 = 500$ cars

Expected visual from image_placeholder Q18-fig1: A table with:

• Row 1: 8 machines, 6 hours, 480 cars
• Row 2: 1 machine, 1 hour, 10 cars (derived)
• Row 3: 5 machines, 10 hours, 500 cars

Answer: 500 toy cars [4 marks]

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19. The length of a rectangle is $3\frac{1}{4}$ times its breadth. The perimeter of the rectangle is 102 cm. Find the area of the rectangle.

Method: Use units/ratio approach with algebra.

Step 1: Set up relationship [1 mark]

• Let breadth = 4 units (choosing 4 to match the fraction denominator)
• Length = $3\frac{1}{4} \times 4 = 13$ units

Step 2: Use perimeter to find unit value [2 marks]

• Perimeter = $2 \times (\text{length} + \text{breadth})$
• $102 = 2 \times (13 + 4)$ units $= 2 \times 17$ units $= 34$ units
• 1 unit $= 102 \div 34 = 3$ cm

Step 3: Find dimensions and area [1 mark]

• Breadth: $4 \times 3 = 12$ cm
• Length: $13 \times 3 = 39$ cm
• Area = $39 \times 12 = 468$ cm²

Verification: Perimeter = $2 \times (39 + 12) = 2 \times 51 = 102$ ✓

Answer: 468 cm² [4 marks]

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20. Mrs Tan bought some apples and oranges. For every 5 apples, she bought 3 oranges. She bought 24 more apples than oranges. How many fruits did she buy altogether?

Method: Ratio with difference.

Step 1: Express as ratio [1 mark]

• Apples : Oranges = $5 : 3$

Step 2: Find difference in ratio units [1 mark]

• Difference: $5 - 3 = 2$ units
• 2 units = 24 fruits

Step 3: Find total fruits [2 marks]

• 1 unit $= 24 \div 2 = 12$
• Total units = $5 + 3 = 8$ units
• Total fruits = $8 \times 12 = 96$

Alternative:

• Apples: $5 \times 12 = 60$; Oranges: $3 \times 12 = 36$
• Check: $60 - 36 = 24$ ✓
• Total: $60 + 36 = 96$

Answer: 96 fruits [4 marks]

Common error: Thinking $5 - 3 = 2$ means the '2' is the actual number rather than units; or setting up equation incorrectly as $5x + 3x = 24$.