Primary 4 Mathematics Fractions Quiz

Primary 4 Mathematics Quiz - Fractions (Answer Key)

Section A: Multiple Choice (1 mark each)

1. Answer: B) $\frac{9}{12}$

• To find equivalent fractions, multiply or divide numerator and denominator by the same number.
• $\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$ ✓
• Check others: A) $\frac{6}{10} = \frac{3}{5}$ ✗; C) $\frac{12}{16} = \frac{3}{4}$ ✓ but not listed as correct; D) $\frac{15}{20} = \frac{3}{4}$ ✓ but not listed as correct.
• Wait: C and D are also equivalent. Rechecking: The question asks which is equivalent. B is definitely equivalent. C ($\frac{12}{16} = \frac{3}{4}$) and D ($\frac{15}{20} = \frac{3}{4}$) are also equivalent. However, standard practice expects one best answer. If multiple are equivalent, B is the simplest form transformation.
• Clarification: All B, C, D are mathematically equivalent to $\frac{3}{4}$. In a well-constructed MCQ, only one should be equivalent. C should read $\frac{12}{18}$ or D should read $\frac{15}{25}$. Assuming the question as stated, B is the intended answer as the most straightforward equivalent using multiplication by 3.

Marking note: Accept B. If test construction allows, verify C and D are non-equivalent in final version. For this key, B is correct.

2. Answer: A) $\frac{3}{5}$, $\frac{2}{3}$, $\frac{5}{6}$

• Convert to common denominator: LCD of 3, 5, 6 = 30.
• $\frac{2}{3} = \frac{20}{30}$; $\frac{3}{5} = \frac{18}{30}$; $\frac{5}{6} = \frac{25}{30}$
• Ascending order: $\frac{18}{30} < \frac{20}{30} < \frac{25}{30}$, so $\frac{3}{5} < \frac{2}{3} < \frac{5}{6}$

3. Answer: C) $\frac{7}{8}$

• Convert to like fractions: $\frac{1}{4} = \frac{2}{8}$
• $\frac{5}{8} + \frac{2}{8} = \frac{7}{8}$

4. Answer: C) $\frac{2}{5}$ m or B) $\frac{1}{5}$ m — rechecking:

• $\frac{7}{10} - \frac{1}{2} = \frac{7}{10} - \frac{5}{10} = \frac{2}{10} = \frac{1}{5}$ m
• Answer: D) $\frac{3}{10}$ m is wrong. C) $\frac{2}{5}$ m = $\frac{4}{10}$ is wrong. The calculation gives $\frac{1}{5}$ m.
• Correct answer: B) $\frac{1}{5}$ m

5. Answer: A) $\frac{17}{6}$

• Convert mixed to improper: whole number × denominator + numerator, over denominator.
• $2\frac{5}{6} = \frac{2 \times 6 + 5}{6} = \frac{12 + 5}{6} = \frac{17}{6}$

Section B: Short Answer (2 marks each)

6. Answer: $4\frac{3}{5}$

• Method: Divide numerator by denominator. $23 \div 5 = 4$ remainder $3$
• So $\frac{23}{5} = 4\frac{3}{5}$
• Marking: [1] for correct whole number 4, [1] for correct fraction $\frac{3}{5}$

7. Answer: $\frac{30}{7}$

• Method: $4 \times 7 + 2 = 28 + 2 = 30$, keep denominator 7.
• Marking: [2] for correct answer, [1] if method shown but arithmetic error

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

• Convert to like fractions: LCD of 12 and 3 is 12.
• $\frac{1}{3} = \frac{4}{12}$
• $\frac{7}{12} - \frac{4}{12} = \frac{3}{12} = \frac{1}{4}$
• Marking: [1] for correct conversion, [1] for correct subtraction and simplification

9. Answer: 28

• $\frac{4}{5} \times 35 = \frac{4 \times 35}{5} = \frac{140}{5} = 28$
• Or: $35 \div 5 = 7$, then $7 \times 4 = 28$
• Marking: [1] for correct method, [1] for correct answer

10. Answer: 18 cookies

• $\frac{3}{8} \times 48 = \frac{3 \times 48}{8} = \frac{144}{8} = 18$
• Or: $48 \div 8 = 6$, then $6 \times 3 = 18$
• Marking: [1] for correct method, [1] for correct answer with unit

11. Answer: $\frac{5}{6} > \frac{7}{9}$ (or $\frac{7}{9} < \frac{5}{6}$)

• LCD of 9 and 6 is 18.
• $\frac{7}{9} = \frac{14}{18}$; $\frac{5}{6} = \frac{15}{18}$
• Since $\frac{15}{18} > \frac{14}{18}$, we have $\frac{5}{6} > \frac{7}{9}$
• Marking: [1] for correct common denominator, [1] for correct comparison symbol

12. Answer: 20

• Equivalent fraction: $\frac{5}{8} = \frac{?}{32}$
• Denominator multiplied by 4 ($8 \times 4 = 32$), so numerator also multiplied by 4.
• $5 \times 4 = 20$
• Marking: [2] for correct answer, [1] if method partially correct

13. Answer: $\frac{7}{12}$

• Convert to like fractions: LCD of 3 and 4 is 12.
• $\frac{1}{3} = \frac{4}{12}$; $\frac{1}{4} = \frac{3}{12}$
• Total: $\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$
• Marking: [1] for correct conversion, [1] for correct addition

14. Answer: $\frac{1}{6}$ litre

• $\frac{5}{6} \div 5 = \frac{5}{6} \times \frac{1}{5} = \frac{5}{30} = \frac{1}{6}$
• Or: $\frac{5}{6}$ divided into 5 equal parts = $\frac{1}{6}$ each (since 5 ÷ 5 = 1)
• Marking: [1] for correct method, [1] for correct answer with unit

15. Answer: 12

• $\frac{2}{3} \times 18 = \frac{2 \times 18}{3} = \frac{36}{3} = 12$
• Or: $18 \div 3 = 6$, then $6 \times 2 = 12$
• Marking: [1] for correct method, [1] for correct answer

Section C: Problem Solving (4 marks each)

16. (a) Answer: $\frac{3}{4}$ kg

• Convert to like fractions: LCD of 2 and 4 is 4.
• $\frac{1}{2} = \frac{2}{4}$; keep $\frac{1}{4} = \frac{1}{4}$
• Total used: $\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$ kg
• [2 marks]: [1] for correct conversion/method, [1] for correct answer with unit

(b) Answer: $\frac{1}{8}$ kg

• Flour left = initial − used = $\frac{7}{8} - \frac{3}{4} = \frac{7}{8} - \frac{6}{8} = \frac{1}{8}$ kg
• [2 marks]: [1] for setting up correct subtraction, [1] for correct answer with unit

17. (a) Answer: $\frac{3}{10}$ m

• $\frac{9}{10} \div 3 = \frac{9}{10} \times \frac{1}{3} = \frac{9}{30} = \frac{3}{10}$ m
• Or: 9 tenths ÷ 3 = 3 tenths = $\frac{3}{10}$ m
• [2 marks]: [1] for correct method, [1] for correct answer with unit

(b) Answer: $\frac{3}{5}$ m

• 2 pieces: $\frac{3}{10} \times 2 = \frac{6}{10} = \frac{3}{5}$ m
• Or: $\frac{3}{10} + \frac{3}{10} = \frac{6}{10} = \frac{3}{5}$ m
• [2 marks]: [1] for correct method, [1] for correct answer with unit

18. (a) Answer: 24 adults

• $\frac{2}{5} \times 60 = \frac{2 \times 60}{5} = \frac{120}{5} = 24$
• [2 marks]: [1] for correct method, [1] for correct answer with unit

(b) Answer: 9 girls

• Children = $60 - 24 = 36$ or $\frac{3}{5} \times 60 = 36$
• Boys: $\frac{3}{4} \times 36 = 27$
• Girls: $36 - 27 = 9$ or $\frac{1}{4} \times 36 = 9$
• [2 marks]: [1] for finding number of children correctly, [1] for correct number of girls

19. (a) Answer: $1\frac{7}{12}$ km or $\frac{19}{12}$ km

• LCD of 4 and 6 is 12.
• $\frac{3}{4} = \frac{9}{12}$; $\frac{5}{6} = \frac{10}{12}$
• Total: $\frac{9}{12} + \frac{10}{12} = \frac{19}{12} = 1\frac{7}{12}$ km
• [2 marks]: [1] for correct common denominator and addition, [1] for correct answer with unit

(b) Answer: $1\frac{1}{4}$ km or $\frac{5}{4}$ km

• Outward journey = $\frac{19}{12}$ km
• Shortcut shorter by $\frac{1}{3}$ km = $\frac{4}{12}$ km
• Return: $\frac{19}{12} - \frac{4}{12} = \frac{15}{12} = \frac{5}{4} = 1\frac{1}{4}$ km
• [2 marks]: [1] for correct setup, [1] for correct answer with unit

20. (a) Answer: $\frac{1}{2}$

• Water used = initial − final = $\frac{5}{6} - \frac{1}{3} = \frac{5}{6} - \frac{2}{6} = \frac{3}{6} = \frac{1}{2}$
• [2 marks]: [1] for correct setup, [1] for correct simplified answer

(b) Answer: 36 litres

• $\frac{1}{2} \times 72 = 36$ litres
• Or verify: full = 72, so $\frac{5}{6}$ full = 60 litres, $\frac{1}{3}$ full = 24 litres, used = $60 - 24 = 36$ litres
• [2 marks]: [1] for correct method, [1] for correct answer with unit

Common Mistakes to Flag

• Forgetting to simplify final answers (e.g., leaving $\frac{3}{12}$ instead of $\frac{1}{4}$)
• Adding numerators and denominators directly: $\frac{1}{2} + \frac{1}{4} \neq \frac{2}{6}$
• Confusing "of" with division — "of" means multiplication
• Finding common denominators when multiplying fractions (unnecessary step, leads to errors)
• Dividing by a whole number: students may multiply instead, or divide denominator only

Total Marks: 40