Primary 4 Mathematics Fractions Quiz

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Primary 4 Mathematics Quiz - Fractions

Name: ___________________________
Class: Primary 4 _______
Date: _______________
Score: _______ / 40

Duration: 45 minutes
Total Marks: 40

Instructions:

1. Answer all questions.
2. Show your working clearly in the space provided.
3. Write your answers in the spaces provided.
4. For multiple-choice questions, write the letter (A, B, C, or D) in the bracket provided.

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Section A: Multiple-Choice Questions (10 × 1 mark = 10 marks)

1. Which of the following fractions is equivalent to $\frac{3}{5}$?
A) $\frac{6}{15}$
B) $\frac{9}{15}$
C) $\frac{12}{25}$
D) $\frac{15}{20}$

Answer: (____)

2. Express $\frac{17}{6}$ as a mixed number.
A) $2\frac{5}{6}$
B) $2\frac{1}{6}$
C) $3\frac{1}{6}$
D) $3\frac{5}{6}$

Answer: (____)

3. Which of the following fractions is the smallest?
A) $\frac{3}{8}$
B) $\frac{5}{12}$
C) $\frac{7}{16}$
D) $\frac{1}{2}$

Answer: (____)

4. Find the value of $\frac{5}{12} + \frac{1}{4}$.
A) $\frac{6}{16}$
B) $\frac{8}{12}$
C) $\frac{2}{3}$
D) $\frac{3}{4}$

Answer: (____)

5. Subtract $\frac{3}{10}$ from $\frac{7}{8}$.
A) $\frac{23}{40}$
B) $\frac{17}{40}$
C) $\frac{11}{40}$
D) $\frac{7}{40}$

Answer: (____)

6. A ribbon is $\frac{5}{6}$ m long. Mei Ling cuts off $\frac{1}{3}$ m. What is the length of the remaining ribbon?
A) $\frac{1}{2}$ m
B) $\frac{1}{3}$ m
C) $\frac{2}{3}$ m
D) $\frac{4}{6}$ m

Answer: (____)

7. Which of the following is an improper fraction?
A) $\frac{4}{9}$
B) $\frac{7}{7}$
C) $\frac{5}{12}$
D) $\frac{2}{5}$

Answer: (____)

8. Arrange the following fractions from the smallest to the greatest:
$\frac{2}{5}$, $\frac{3}{10}$, $\frac{1}{2}$
A) $\frac{1}{2}$, $\frac{2}{5}$, $\frac{3}{10}$
B) $\frac{3}{10}$, $\frac{2}{5}$, $\frac{1}{2}$
C) $\frac{2}{5}$, $\frac{3}{10}$, $\frac{1}{2}$
D) $\frac{3}{10}$, $\frac{1}{2}$, $\frac{2}{5}$

Answer: (____)

9. What is the missing fraction in the box?
$\frac{5}{8} + \boxed{} = 1\frac{1}{4}$
A) $\frac{3}{8}$
B) $\frac{5}{8}$
C) $\frac{7}{8}$
D) $\frac{1}{2}$

Answer: (____)

10. Mr Tan bought $2\frac{1}{2}$ kg of rice. He used $\frac{3}{4}$ kg to cook dinner. How much rice had he left?
A) $1\frac{1}{4}$ kg
B) $1\frac{3}{4}$ kg
C) $2\frac{1}{4}$ kg
D) $2\frac{3}{4}$ kg

Answer: (____)

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Section B: Short-Answer Questions (5 × 2 marks = 10 marks)

11. Express $\frac{24}{36}$ in its simplest form.

Answer: _____________________ [2]

12. Convert $4\frac{2}{7}$ to an improper fraction.

Answer: _____________________ [2]

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

Answer: _____________________ [2]

14. A cake was cut into 12 equal slices. John ate $\frac{1}{3}$ of the cake and Mary ate $\frac{1}{4}$ of the cake. What fraction of the cake was left?

Answer: _____________________ [2]

15. The sum of two fractions is $\frac{7}{8}$. One of the fractions is $\frac{1}{4}$. What is the other fraction?

Answer: _____________________ [2]

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Section C: Structured / Word Problems (5 × 4 marks = 20 marks)

16. Siti has a piece of string $\frac{7}{8}$ m long. She cuts it into 2 pieces. The first piece is $\frac{1}{4}$ m long.
(a) What is the length of the second piece?
(b) She then cuts the second piece into 3 equal shorter pieces. What is the length of each shorter piece?

Answer: (a) _____________________ [2]
(b) _____________________ [2]

17. A tank is $\frac{3}{5}$ full of water. After 12 litres of water are poured into the tank, it becomes $\frac{7}{10}$ full. What is the capacity of the tank?

Answer: _____________________ [4]

18. In a class of 40 pupils, $\frac{3}{8}$ of them are boys. $\frac{2}{5}$ of the boys wear glasses.
(a) How many boys are there in the class?
(b) How many boys wear glasses?

Answer: (a) _____________________ [2]
(b) _____________________ [2]

19. Mrs Lim baked some cookies. She gave $\frac{2}{5}$ of the cookies to her neighbour and $\frac{1}{3}$ of the remaining cookies to her colleague. She had 24 cookies left. How many cookies did she bake at first?

Answer: _____________________ [4]

20. The figure below shows a rectangle divided into equal parts.

Generated diagram for Q20.

(a) What fraction of the rectangle is shaded? Express your answer in its simplest form.
(b) How many more parts must be shaded so that $\frac{3}{4}$ of the rectangle is shaded?

Answer: (a) _____________________ [2]
(b) _____________________ [2]

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End of Quiz

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Primary 4 Mathematics Quiz - Fractions (Answer Key)

Total Marks: 40

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Section A: Multiple-Choice Questions (10 × 1 mark = 10 marks)

1. Answer: B
Explanation: To find an equivalent fraction, multiply both numerator and denominator by the same number. $\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}$.

• A) $\frac{6}{15} = \frac{2}{5}$ (incorrect)
• B) $\frac{9}{15} = \frac{3}{5}$ ✓
• C) $\frac{12}{25}$ cannot simplify to $\frac{3}{5}$
• D) $\frac{15}{20} = \frac{3}{4}$ (incorrect)

2. Answer: A
Explanation: Divide 17 by 6. $17 \div 6 = 2$ remainder 5. So $\frac{17}{6} = 2\frac{5}{6}$.
Check: $2 \times 6 + 5 = 12 + 5 = 17$. ✓

3. Answer: A
Explanation: Compare by finding a common denominator (LCM of 8, 12, 16, 2 = 48):

• $\frac{3}{8} = \frac{18}{48}$
• $\frac{5}{12} = \frac{20}{48}$
• $\frac{7}{16} = \frac{21}{48}$
• $\frac{1}{2} = \frac{24}{48}$
  Smallest is $\frac{18}{48} = \frac{3}{8}$.

4. Answer: C
Explanation: $\frac{5}{12} + \frac{1}{4} = \frac{5}{12} + \frac{3}{12} = \frac{8}{12} = \frac{2}{3}$ (simplest form).
Common mistake: Adding denominators to get $\frac{6}{16}$ (Option A).

5. Answer: A
Explanation: $\frac{7}{8} - \frac{3}{10} = \frac{35}{40} - \frac{12}{40} = \frac{23}{40}$.
Common denominator = 40 (LCM of 8 and 10).

6. Answer: A
Explanation: $\frac{5}{6} - \frac{1}{3} = \frac{5}{6} - \frac{2}{6} = \frac{3}{6} = \frac{1}{2}$ m.
Option D ($\frac{4}{6}$) is not in simplest form.

7. Answer: B
Explanation: An improper fraction has numerator ≥ denominator.

• A) $\frac{4}{9}$: proper (4 < 9)
• B) $\frac{7}{7}$: improper (7 = 7) ✓
• C) $\frac{5}{12}$: proper (5 < 12)
• D) $\frac{2}{5}$: proper (2 < 5)

8. Answer: B
Explanation: Convert to common denominator 10:

• $\frac{2}{5} = \frac{4}{10}$
• $\frac{3}{10} = \frac{3}{10}$
• $\frac{1}{2} = \frac{5}{10}$
  Order: $\frac{3}{10} < \frac{4}{10} < \frac{5}{10}$ → $\frac{3}{10}, \frac{2}{5}, \frac{1}{2}$.

9. Answer: B
Explanation: $1\frac{1}{4} = \frac{5}{4} = \frac{10}{8}$.
$\frac{10}{8} - \frac{5}{8} = \frac{5}{8}$.
Check: $\frac{5}{8} + \frac{5}{8} = \frac{10}{8} = 1\frac{1}{4}$. ✓

10. Answer: B
Explanation: $2\frac{1}{2} - \frac{3}{4} = \frac{5}{2} - \frac{3}{4} = \frac{10}{4} - \frac{3}{4} = \frac{7}{4} = 1\frac{3}{4}$ kg.

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Section B: Short-Answer Questions (5 × 2 marks = 10 marks)

11. Answer: $\frac{2}{3}$ [2]
Working:
$\frac{24}{36} = \frac{24 \div 12}{36 \div 12} = \frac{2}{3}$
(Divide by HCF = 12)
Marking: 1 mark for correct method (dividing by common factor), 1 mark for correct simplest form.

12. Answer: $\frac{30}{7}$ [2]
Working:
$4\frac{2}{7} = \frac{4 \times 7 + 2}{7} = \frac{28 + 2}{7} = \frac{30}{7}$
Marking: 1 mark for correct method (whole × denominator + numerator), 1 mark for correct answer.

13. Answer: $1\frac{3}{10}$ [2]
Working:
$\frac{3}{5} + \frac{7}{10} = \frac{6}{10} + \frac{7}{10} = \frac{13}{10} = 1\frac{3}{10}$
Marking: 1 mark for common denominator and addition, 1 mark for correct mixed number in simplest form.

14. Answer: $\frac{5}{12}$ [2]
Working:
Fraction eaten = $\frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12}$
Fraction left = $1 - \frac{7}{12} = \frac{5}{12}$
Alternative: 12 slices total. John: $\frac{1}{3} \times 12 = 4$ slices. Mary: $\frac{1}{4} \times 12 = 3$ slices. Left: $12 - 7 = 5$ slices = $\frac{5}{12}$.
Marking: 1 mark for finding fraction eaten/total eaten, 1 mark for correct fraction left.

15. Answer: $\frac{5}{8}$ [2]
Working:
$\frac{7}{8} - \frac{1}{4} = \frac{7}{8} - \frac{2}{8} = \frac{5}{8}$
Marking: 1 mark for common denominator, 1 mark for correct subtraction and answer.

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Section C: Structured / Word Problems (5 × 4 marks = 20 marks)

16. (a) Answer: $\frac{5}{8}$ m [2]
Working:
$\frac{7}{8} - \frac{1}{4} = \frac{7}{8} - \frac{2}{8} = \frac{5}{8}$ m
Marking: 1 mark for common denominator, 1 mark for correct answer with unit.

(b) Answer: $\frac{5}{24}$ m [2]
Working:
$\frac{5}{8} \div 3 = \frac{5}{8} \times \frac{1}{3} = \frac{5}{24}$ m
Marking: 1 mark for correct division method (multiply by reciprocal), 1 mark for correct answer with unit.
Common mistake: Forgetting to multiply by reciprocal, or answering $\frac{5}{8} \div 3 = \frac{5}{24}$ without showing method.

17. Answer: 80 litres [4]
Working:
Difference in fraction = $\frac{7}{10} - \frac{3}{5} = \frac{7}{10} - \frac{6}{10} = \frac{1}{10}$
$\frac{1}{10}$ of tank = 12 litres
Capacity of tank = $12 \times 10 = 120$ litres
Wait, let me recheck:
$\frac{3}{5} = \frac{6}{10}$, so $\frac{7}{10} - \frac{6}{10} = \frac{1}{10}$.
$\frac{1}{10}$ of capacity = 12 L → Capacity = 120 L.
Correction: The answer should be 120 litres, not 80. Let me fix this.
Correct Answer: 120 litres [4]
Marking:

• 1 mark for finding difference in fractions ($\frac{1}{10}$)
• 1 mark for understanding this difference = 12 L
• 1 mark for correct operation (12 ÷ $\frac{1}{10}$ or 12 × 10)
• 1 mark for correct answer with unit

18. (a) Answer: 15 boys [2]
Working:
$\frac{3}{8} \times 40 = 15$ boys
Marking: 1 mark for correct method (fraction × total), 1 mark for correct answer.

(b) Answer: 6 boys [2]
Working:
$\frac{2}{5} \times 15 = 6$ boys
Marking: 1 mark for correct method (fraction × number of boys), 1 mark for correct answer.
Note: Must use answer from (a) even if (a) was wrong (follow-through marking).

19. Answer: 60 cookies [4]
Working:
Let total cookies = 1 whole.
Given to neighbour = $\frac{2}{5}$
Remaining = $1 - \frac{2}{5} = \frac{3}{5}$
Given to colleague = $\frac{1}{3} \times \frac{3}{5} = \frac{1}{5}$
Left = $\frac{3}{5} - \frac{1}{5} = \frac{2}{5}$
$\frac{2}{5}$ of total = 24 cookies
$\frac{1}{5}$ of total = 12 cookies
Total = $12 \times 5 = 60$ cookies
Check: Neighbour: $\frac{2}{5} \times 60 = 24$. Remaining: 36. Colleague: $\frac{1}{3} \times 36 = 12$. Left: $36 - 12 = 24$. ✓
Marking:

• 1 mark for finding fraction remaining after neighbour ($\frac{3}{5}$)
• 1 mark for finding fraction given to colleague ($\frac{1}{5}$)
• 1 mark for finding fraction left ($\frac{2}{5}$)
• 1 mark for correct total with working

20. (a) Answer: $\frac{5}{12}$ [2]
Working:
Total parts = 12, Shaded parts = 5
Fraction shaded = $\frac{5}{12}$ (already in simplest form)
Marking: 1 mark for correct fraction, 1 mark for simplest form (or stating it is already simplest).

(b) Answer: 4 more parts [2]
Working:
$\frac{3}{4}$ of rectangle = $\frac{3}{4} \times 12 = 9$ parts
Already shaded = 5 parts
More parts needed = $9 - 5 = 4$ parts
Marking: 1 mark for finding $\frac{3}{4}$ of 12 = 9 parts, 1 mark for correct difference.
Alternative: $\frac{3}{4} - \frac{5}{12} = \frac{9}{12} - \frac{5}{12} = \frac{4}{12} = \frac{1}{3}$ of rectangle. $\frac{1}{3} \times 12 = 4$ parts.

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Common Mistakes to Watch For:

1. Adding/subtracting denominators instead of finding common denominators.
2. Not simplifying fractions to simplest form.
3. Confusing mixed numbers and improper fractions in conversion.
4. Forgetting units in word problems (m, kg, litres, etc.).
5. In multi-step problems, using the original total instead of the remaining amount for subsequent fractions.
6. In Q17, incorrectly calculating the fraction difference (e.g., $\frac{7}{10} - \frac{3}{5} = \frac{4}{5}$ instead of $\frac{1}{10}$).

Teaching Notes:

• Equivalent fractions: Multiply/divide numerator and denominator by the same number.
• Mixed number ↔ Improper fraction: Whole × denominator + numerator = new numerator.
• Addition/Subtraction: Must have common denominator. Use LCM.
• Fraction of a quantity: Fraction × quantity.
• Fraction of a remainder: First find the remainder, then take the fraction of that remainder.
• Simplest form: Divide numerator and denominator by their HCF.