Primary 6 PSLE Mathematics Fractions Quiz

Primary 6 PSLE Mathematics Quiz - Fractions (Answer Key)

Total Marks: 50

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Section A: Multiple-Choice Questions (10 marks)

1. Express $\frac{5}{6} \div 4$ in its simplest form. [2]

Answer: (1) $\frac{5}{24}$

Working: $\frac{5}{6} \div 4 = \frac{5}{6} \times \frac{1}{4} = \frac{5}{24}$

Explanation: Dividing by a whole number is the same as multiplying by its reciprocal. The reciprocal of 4 is $\frac{1}{4}$. Multiply the fractions: $\frac{5 \times 1}{6 \times 4} = \frac{5}{24}$. The fraction is already in simplest form.

Common mistake: Multiplying by 4 instead of dividing, giving $\frac{20}{6}$ (Option 2).

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2. Find the value of $3 \div \frac{2}{5}$. [2]

Answer: (3) $7\frac{1}{2}$

Working: $3 \div \frac{2}{5} = 3 \times \frac{5}{2} = \frac{15}{2} = 7\frac{1}{2}$

Explanation: Dividing by a fraction means multiplying by its reciprocal. The reciprocal of $\frac{2}{5}$ is $\frac{5}{2}$. $3 \times \frac{5}{2} = \frac{15}{2} = 7\frac{1}{2}$.

Common mistake: Multiplying by $\frac{2}{5}$ instead of its reciprocal, giving $\frac{6}{5}$ (Option 4).

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3. $\frac{4}{7}$ of a number is 28. What is the number? [2]

Answer: (3) 49

Working: Let the number be $x$. $\frac{4}{7} \times x = 28$ $x = 28 \div \frac{4}{7} = 28 \times \frac{7}{4} = 7 \times 7 = 49$

Explanation: "Of" means multiply. To find the original number, divide 28 by $\frac{4}{7}$, which is the same as multiplying by $\frac{7}{4}$. $28 \times \frac{7}{4} = 7 \times 7 = 49$.

Check: $\frac{4}{7} \times 49 = 4 \times 7 = 28$. ✓

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4. A ribbon is $\frac{5}{8}$ m long. It is cut into 5 equal pieces. What is the length of each piece? [2]

Answer: (1) $\frac{1}{8}$ m

Working: Length of each piece = $\frac{5}{8} \div 5 = \frac{5}{8} \times \frac{1}{5} = \frac{1}{8}$ m

Explanation: Dividing the total length by the number of pieces gives the length of each piece. $\frac{5}{8} \div 5 = \frac{5}{8} \times \frac{1}{5} = \frac{1}{8}$.

Common mistake: Multiplying $\frac{5}{8} \times 5 = \frac{25}{8}$ (Option 4).

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5. Which of the following is equivalent to $\frac{3}{4} \div \frac{5}{8}$? [2]

Answer: (2) $\frac{3}{4} \times \frac{8}{5}$

Explanation: Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of $\frac{5}{8}$ is $\frac{8}{5}$. So $\frac{3}{4} \div \frac{5}{8} = \frac{3}{4} \times \frac{8}{5}$.

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Section B: Short-Answer Questions (20 marks)

6. Find the value of $\frac{7}{9} \div 3$. Express your answer as a fraction in its simplest form. [2]

Answer: $\frac{7}{27}$

Working: $\frac{7}{9} \div 3 = \frac{7}{9} \times \frac{1}{3} = \frac{7}{27}$

Marking: 1 mark for correct method (multiply by reciprocal), 1 mark for correct answer in simplest form.

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7. Find the value of $5 \div \frac{3}{10}$. Express your answer as a mixed number in its simplest form. [2]

Answer: $16\frac{2}{3}$

Working: $5 \div \frac{3}{10} = 5 \times \frac{10}{3} = \frac{50}{3} = 16\frac{2}{3}$

Marking: 1 mark for correct method (multiply by reciprocal), 1 mark for correct mixed number in simplest form.

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8. $\frac{2}{5}$ of a number is 18. Find the number. [2]

Answer: 45

Working: Number = $18 \div \frac{2}{5} = 18 \times \frac{5}{2} = 9 \times 5 = 45$

Check: $\frac{2}{5} \times 45 = 2 \times 9 = 18$. ✓

Marking: 1 mark for correct method (divide by fraction = multiply by reciprocal), 1 mark for correct answer.

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9. A tank is $\frac{3}{7}$ full of water. After 12 litres of water are poured in, the tank becomes $\frac{5}{7}$ full. What is the capacity of the tank? [2]

Answer: 42 litres

Working: Increase in fraction = $\frac{5}{7} - \frac{3}{7} = \frac{2}{7}$ $\frac{2}{7}$ of capacity = 12 litres Capacity = $12 \div \frac{2}{7} = 12 \times \frac{7}{2} = 6 \times 7 = 42$ litres

Marking: 1 mark for finding the fraction increase ($\frac{2}{7}$), 1 mark for correct capacity.

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10. Mrs Tan baked some cookies. She gave $\frac{3}{8}$ of them to her neighbour and $\frac{1}{4}$ of the remainder to her friend. She had 45 cookies left. How many cookies did she bake at first? [2]

Answer: 96 cookies

Working: Fraction given to neighbour = $\frac{3}{8}$ Remainder = $1 - \frac{3}{8} = \frac{5}{8}$ Fraction given to friend = $\frac{1}{4} \times \frac{5}{8} = \frac{5}{32}$ Fraction left = $\frac{5}{8} - \frac{5}{32} = \frac{20}{32} - \frac{5}{32} = \frac{15}{32}$ $\frac{15}{32}$ of total = 45 Total = $45 \div \frac{15}{32} = 45 \times \frac{32}{15} = 3 \times 32 = 96$

Alternative (Model method): Total = 32 units Neighbour = 12 units (3/8) Remainder = 20 units Friend = 5 units (1/4 of 20) Left = 15 units = 45 cookies 1 unit = 3 cookies Total = 32 × 3 = 96 cookies

Marking: 1 mark for correct fraction left ($\frac{15}{32}$ or 15 units), 1 mark for correct total.

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11. Find the value of $\frac{5}{6} \div \frac{2}{3}$. Express your answer as a mixed number in its simplest form. [2]

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

Working: $\frac{5}{6} \div \frac{2}{3} = \frac{5}{6} \times \frac{3}{2} = \frac{15}{12} = \frac{5}{4} = 1\frac{1}{4}$

Marking: 1 mark for correct method (multiply by reciprocal), 1 mark for correct mixed number in simplest form.

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12. A piece of string is $\frac{4}{5}$ m long. It is cut into pieces each $\frac{1}{10}$ m long. How many pieces are there? [2]

Answer: 8 pieces

Working: Number of pieces = $\frac{4}{5} \div \frac{1}{10} = \frac{4}{5} \times 10 = 4 \times 2 = 8$

Marking: 1 mark for correct method (divide total length by piece length), 1 mark for correct answer.

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13. Peter spent $\frac{2}{5}$ of his money on a book and $\frac{1}{3}$ of the remainder on a pen. He had $24 left. How much money did he have at first? [2]

Answer: $60

Working: Fraction spent on book = $\frac{2}{5}$ Remainder after book = $1 - \frac{2}{5} = \frac{3}{5}$ Fraction spent on pen = $\frac{1}{3} \times \frac{3}{5} = \frac{1}{5}$ Fraction left = $\frac{3}{5} - \frac{1}{5} = \frac{2}{5}$ $\frac{2}{5}$ of money = $24 Money at first =$24 \div \frac{2}{5} = 24 \times \frac{5}{2} = 12 \times 5 = $60

Marking: 1 mark for correct fraction left ($\frac{2}{5}$), 1 mark for correct answer.

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14. The mass of a box of apples is $\frac{7}{8}$ kg. The mass of a box of oranges is $\frac{3}{4}$ kg. How many times the mass of the box of oranges is the mass of the box of apples? Express your answer as a mixed number in its simplest form. [2]

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

Working: Times = $\frac{7}{8} \div \frac{3}{4} = \frac{7}{8} \times \frac{4}{3} = \frac{28}{24} = \frac{7}{6} = 1\frac{1}{6}$

Marking: 1 mark for correct method (divide mass of apples by mass of oranges), 1 mark for correct mixed number in simplest form.

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15. A recipe requires $\frac{3}{4}$ cup of flour. If Jane wants to make $\frac{2}{3}$ of the recipe, how much flour does she need? Express your answer as a fraction in its simplest form. [2]

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

Working: Flour needed = $\frac{2}{3} \times \frac{3}{4} = \frac{6}{12} = \frac{1}{2}$ cup

Marking: 1 mark for correct method (multiply fraction of recipe by flour amount), 1 mark for correct answer in simplest form.

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Section C: Long-Answer Questions (20 marks)

16. Alan and Ben had a total of 360 marbles. Alan gave $\frac{2}{5}$ of his marbles to Ben. Then Ben gave $\frac{1}{4}$ of his marbles to Alan. In the end, they had an equal number of marbles. How many marbles did Alan have at first? [4]

Answer: 200 marbles

Working: Let Alan have $A$ marbles at first, Ben have $B$ marbles. $A + B = 360$ ...(1)

After Alan gives $\frac{2}{5}A$ to Ben: Alan has: $A - \frac{2}{5}A = \frac{3}{5}A$ Ben has: $B + \frac{2}{5}A$

Then Ben gives $\frac{1}{4}$ of his marbles to Alan: Ben gives: $\frac{1}{4}(B + \frac{2}{5}A)$ Ben finally has: $\frac{3}{4}(B + \frac{2}{5}A)$ Alan finally has: $\frac{3}{5}A + \frac{1}{4}(B + \frac{2}{5}A)$

In the end, they have equal marbles: $\frac{3}{5}A + \frac{1}{4}(B + \frac{2}{5}A) = \frac{3}{4}(B + \frac{2}{5}A)$

Multiply by 20: $12A + 5(B + \frac{2}{5}A) = 15(B + \frac{2}{5}A)$ $12A + 5B + 2A = 15B + 6A$ $14A + 5B = 15B + 6A$ $8A = 10B$ $4A = 5B$ $B = \frac{4}{5}A$

Substitute into (1): $A + \frac{4}{5}A = 360$ $\frac{9}{5}A = 360$ $A = 360 \times \frac{5}{9} = 40 \times 5 = 200$

Check: Alan: 200, Ben: 160 Alan gives $\frac{2}{5} \times 200 = 80$ to Ben Alan: 120, Ben: 240 Ben gives $\frac{1}{4} \times 240 = 60$ to Alan Alan: 180, Ben: 180 ✓ Equal!

Marking:

• 1 mark for setting up correct equations/expressions for each stage
• 1 mark for equating final amounts correctly
• 1 mark for solving to find $A = 200$
• 1 mark for correct final answer with unit

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17. A container is $\frac{2}{5}$ full of water. When 18 litres of water are added, it becomes $\frac{7}{10}$ full. What is the capacity of the container? [4]

Answer: 36 litres

Working: Increase in fraction = $\frac{7}{10} - \frac{2}{5} = \frac{7}{10} - \frac{4}{10} = \frac{3}{10}$ $\frac{3}{10}$ of capacity = 18 litres Capacity = $18 \div \frac{3}{10} = 18 \times \frac{10}{3} = 6 \times 10 = 36$ litres

Alternative (Unit method): Let capacity = 10 units Initially: $\frac{2}{5} \times 10 = 4$ units Finally: $\frac{7}{10} \times 10 = 7$ units Increase = 3 units = 18 litres 1 unit = 6 litres Capacity = 10 units = 60 litres? Wait, let me recheck.

Actually: $\frac{2}{5} = \frac{4}{10}$, so increase is $\frac{3}{10}$. 3 units = 18 L, 1 unit = 6 L, 10 units = 60 L? No, 18 ÷ 3 = 6, 6 × 10 = 60. But earlier I got 36. Let me recalculate.

$18 \div \frac{3}{10} = 18 \times \frac{10}{3} = 60$. Yes, 60 litres.

Wait, the question says "When 18 litres of water are added, it becomes $\frac{7}{10}$ full." $\frac{7}{10} - \frac{2}{5} = \frac{7}{10} - \frac{4}{10} = \frac{3}{10}$. $\frac{3}{10}$ of capacity = 18 L. Capacity = $18 \times \frac{10}{3} = 60$ L.

My first calculation had an error: $18 \times \frac{10}{3} = 60$, not 36. Let me correct.

Correct Answer: 60 litres

Working (corrected): Increase in fraction = $\frac{7}{10} - \frac{2}{5} = \frac{7}{10} - \frac{4}{10} = \frac{3}{10}$ $\frac{3}{10}$ of capacity = 18 litres Capacity = $18 \div \frac{3}{10} = 18 \times \frac{10}{3} = 6 \times 10 = 60$ litres

Marking:

• 1 mark for finding the increase in fraction ($\frac{3}{10}$)
• 1 mark for correct method (divide added volume by fraction increase)
• 1 mark for correct calculation
• 1 mark for correct answer with unit

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18. Mrs Lim had some money. She spent $\frac{3}{7}$ of it on a dress and $\frac{2}{5}$ of the remainder on a pair of shoes. She had $48 left. How much money did she have at first? [4]

Answer: $140

Working: Fraction spent on dress = $\frac{3}{7}$ Remainder after dress = $1 - \frac{3}{7} = \frac{4}{7}$ Fraction spent on shoes = $\frac{2}{5} \times \frac{4}{7} = \frac{8}{35}$ Fraction left = $\frac{4}{7} - \frac{8}{35} = \frac{20}{35} - \frac{8}{35} = \frac{12}{35}$ $\frac{12}{35}$ of money = $48 Money at first =$48 \div \frac{12}{35} = 48 \times \frac{35}{12} = 4 \times 35 = $140

Alternative (Unit method): Let total = 35 units Dress = $\frac{3}{7} \times 35 = 15$ units Remainder = 20 units Shoes = $\frac{2}{5} \times 20 = 8$ units Left = 12 units = $48 1 unit =$4 Total = 35 × $4 =$140

Check: Dress: $\frac{3}{7} \times 140 =$60 Remainder: $80 Shoes:$\frac{2}{5} \times 80 = $32 Left:$80 - $32 =$48 ✓

Marking:

• 1 mark for correct remainder after dress ($\frac{4}{7}$ or 20 units)
• 1 mark for correct fraction spent on shoes ($\frac{8}{35}$ or 8 units)
• 1 mark for correct fraction left ($\frac{12}{35}$ or 12 units)
• 1 mark for correct final answer with unit

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19. There are some red and blue marbles in a box. $\frac{3}{8}$ of the marbles are red. After 24 red marbles are added and 12 blue marbles are removed, $\frac{1}{2}$ of the marbles are red. How many marbles were in the box at first? [4]

Answer: 144 marbles

Working: Let total marbles at first = $x$ Red at first = $\frac{3}{8}x$ Blue at first = $\frac{5}{8}x$

After changes: Red = $\frac{3}{8}x + 24$ Blue = $\frac{5}{8}x - 12$ Total = $x + 24 - 12 = x + 12$

Given: Red = $\frac{1}{2}$ of total $\frac{3}{8}x + 24 = \frac{1}{2}(x + 12)$ $\frac{3}{8}x + 24 = \frac{1}{2}x + 6$ $24 - 6 = \frac{1}{2}x - \frac{3}{8}x$ $18 = \frac{4}{8}x - \frac{3}{8}x$ $18 = \frac{1}{8}x$ $x = 18 \times 8 = 144$

Check: At first: Red = $\frac{3}{8} \times 144 = 54$, Blue = 90 After: Red = 54 + 24 = 78, Blue = 90 - 12 = 78 Total = 156, Red = 78 = $\frac{1}{2}$ ✓

Marking:

• 1 mark for correct expressions for red and blue at first
• 1 mark for correct expressions after changes
• 1 mark for setting up correct equation
• 1 mark for correct final answer with unit

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20. A tank measuring 40 cm by 30 cm by 20 cm is $\frac{3}{8}$ filled with water. Water flows into the tank at a rate of 2 litres per minute. How long will it take to fill the tank completely? Express your answer in minutes. [4]

Answer: 105 minutes

Working: Volume of tank = $40 \times 30 \times 20 = 24,000$ cm³ = 24 litres (1 litre = 1000 cm³)

Fraction filled = $\frac{3}{8}$ Fraction empty = $1 - \frac{3}{8} = \frac{5}{8}$ Volume to fill = $\frac{5}{8} \times 24 = 15$ litres

Rate = 2 litres/min Time = $15 \div 2 = 7.5$ minutes? Wait, let me recheck.

Volume of tank = 40 × 30 × 20 = 24,000 cm³ = 24 litres. Yes. $\frac{3}{8}$ filled = 9 litres. Remaining = 15 litres. At 2 L/min, time = 15 ÷ 2 = 7.5 minutes.

But the question says "Express your answer in minutes." 7.5 minutes or 7½ minutes.

Wait, let me double-check the volume calculation. 40 × 30 = 1200 1200 × 20 = 24,000 cm³ = 24 litres. Correct. $\frac{3}{8} \times 24 = 9$ litres filled. $24 - 9 = 15$ litres to fill. 15 ÷ 2 = 7.5 minutes.

Answer: 7.5 minutes (or 7½ minutes)

Marking:

• 1 mark for correct volume of tank (24 litres or 24,000 cm³)
• 1 mark for correct volume to fill (15 litres or $\frac{5}{8}$ of tank)
• 1 mark for correct method (divide volume by rate)
• 1 mark for correct answer with unit

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End of Answer Key