Primary 6 PSLE Mathematics Fractions Quiz

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Primary 6 PSLE Mathematics Quiz - Fractions

Name: ___________________________
Class: Primary 6 _______
Date: _______________
Score: _______ / 50

Duration: 60 minutes
Total Marks: 50

Instructions:

1. Answer all questions.
2. Show your working clearly in the space provided.
3. Write your answers in the spaces provided.
4. For questions requiring units, give your answers in the units stated.
5. The use of calculators is NOT allowed.

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Section A: Multiple-Choice Questions (10 marks)

Questions 1 to 5 carry 2 marks each. Choose the correct answer and write its number (1, 2, 3 or 4) in the brackets provided.

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

(1) $\frac{5}{24}$
(2) $\frac{20}{6}$
(3) $\frac{5}{10}$
(4) $\frac{1}{24}$

Answer: (_____)

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

(1) $\frac{2}{15}$
(2) $1\frac{1}{2}$
(3) $7\frac{1}{2}$
(4) $\frac{6}{5}$

Answer: (_____)

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

(1) 16
(2) 35
(3) 49
(4) 56

Answer: (_____)

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

(1) $\frac{1}{8}$ m
(2) $\frac{1}{5}$ m
(3) $\frac{5}{40}$ m
(4) $\frac{25}{8}$ m

Answer: (_____)

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

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

Answer: (_____)

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Section B: Short-Answer Questions (20 marks)

Questions 6 to 15 carry 2 marks each. Show your working clearly and write your answers in the spaces provided. Give your answers in the units stated and in their simplest form where necessary.

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

Working:

Answer: _______________

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

Working:

Answer: _______________

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

Working:

Answer: _______________

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]

Working:

Answer: _______________ litres

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]

Working:

Answer: _______________ cookies

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

Working:

Answer: _______________

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]

Working:

Answer: _______________ pieces

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]

Working:

Answer: $_______________

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]

Working:

Answer: _______________ times

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]

Working:

Answer: _______________ cup

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Section C: Long-Answer Questions (20 marks)

Questions 16 to 20 carry 4 marks each. Show your working clearly and write your answers in the spaces provided.

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]

Working:

Answer: _______________ marbles

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]

Working:

Answer: _______________ litres

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]

Working:

Answer: $_______________

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]

Working:

Answer: _______________ marbles

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]

Working:

Answer: _______________ minutes

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End of Quiz

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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