Primary 4 Mathematics Fractions Quiz

Primary 4 Mathematics Quiz - Fractions (Answer Key)

Total Marks: 40

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.

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.

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.

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.