Primary 4 Mathematics Fractions Quiz

Primary 4 Mathematics Quiz - Fractions

Answer Key

Section A: Equivalent Fractions and Simplest Form (5 marks)

1. (c) $\dfrac{8}{12}$ [1]

Explanation: $\dfrac{2}{3} = \dfrac{2 \times 4}{3 \times 4} = \dfrac{8}{12}$. The other options do not simplify or scale to $\dfrac{2}{3}$.

Common mistake: Students may choose (a) $\dfrac{4}{9}$, thinking that doubling the numerator doubles the fraction. Remind students to multiply both numerator and denominator by the same number.

2. (a) $\dfrac{2}{3}$ [1]

Explanation: $\dfrac{12}{18} = \dfrac{12 \div 6}{18 \div 6} = \dfrac{2}{3}$. The greatest common factor of 12 and 18 is 6.

Common mistake: Students may choose (c) $\dfrac{4}{6}$ or (d) $\dfrac{6}{9}$, which are equivalent but not in simplest form. Remind students that simplest form means the numerator and denominator share no common factor other than 1.

3. (b) $\dfrac{15}{24}$ [1]

Explanation: $\dfrac{5}{8} = \dfrac{5 \times 3}{8 \times 3} = \dfrac{15}{24}$.

Common mistake: Students may choose (a) $\dfrac{10}{14}$ because both numerator and denominator are doubled from $\dfrac{5}{7}$, not $\dfrac{5}{8}$. Check by cross-multiplication: $5 \times 24 = 120$ and $8 \times 15 = 120$ ✓.

4. (c) $\dfrac{4}{5}$ [1]

Explanation: $\dfrac{16}{20} = \dfrac{16 \div 4}{20 \div 4} = \dfrac{4}{5}$.

Common mistake: Students may choose (d) $\dfrac{8}{10}$, which is equivalent but not fully simplified.

5. (d) $\dfrac{12}{25}$ [1]

Explanation: $\dfrac{3}{5} = \dfrac{12}{20}$, not $\dfrac{12}{25}$. Check: $3 \times 25 = 75$ but $5 \times 12 = 60$. Since $75 \neq 60$, the fractions are not equivalent.

Common mistake: Students may overlook that the numerator and denominator must be multiplied by the same number.

Section B: Comparing and Ordering Fractions (10 marks)

6. $\dfrac{1}{2}$ < $\dfrac{2}{3}$ < $\dfrac{3}{4}$ [2]

Working:

• Convert to a common denominator (LCM of 4, 2, 3 = 12):
  • $\dfrac{3}{4} = \dfrac{9}{12}$
  • $\dfrac{1}{2} = \dfrac{6}{12}$
  • $\dfrac{2}{3} = \dfrac{8}{12}$
• Compare: $\dfrac{6}{12} < \dfrac{8}{12} < \dfrac{9}{12}$

Marking: Award [1] for correct common denominator conversion. Award [1] for correct order.

7. $\dfrac{7}{8}$ is greater. [2]

Working:

• LCM of 6 and 8 = 24.
• $\dfrac{5}{6} = \dfrac{20}{24}$
• $\dfrac{7}{8} = \dfrac{21}{24}$
• Since $\dfrac{21}{24} > \dfrac{20}{24}$, $\dfrac{7}{8} > \dfrac{5}{6}$.

Marking: Award [1] for correct conversion to common denominator. Award [1] for correct comparison and conclusion.

8. $\dfrac{3}{5}$ (accept any fraction between $\dfrac{2}{5}$ and $\dfrac{4}{5}$, e.g. $\dfrac{1}{2}$, $\dfrac{3}{5}$) [2]

Working:

• $\dfrac{2}{5} = \dfrac{4}{10}$ and $\dfrac{4}{5} = \dfrac{8}{10}$
• $\dfrac{5}{10} = \dfrac{1}{2}$ or $\dfrac{6}{10} = \dfrac{3}{5}$ both lie between them.

Marking: Award [2] for any correct fraction strictly between $\dfrac{2}{5}$ and $\dfrac{4}{5}$. Award [1] if the student shows correct conversion but gives a borderline answer.

9. Jerry ate more. [2]

Working:

• LCM of 8 and 5 = 40.
• Tom: $\dfrac{3}{8} = \dfrac{15}{40}$
• Jerry: $\dfrac{2}{5} = \dfrac{16}{40}$
• Since $\dfrac{16}{40} > \dfrac{15}{40}$, Jerry ate more.

Marking: Award [1] for correct conversion. Award [1] for correct comparison and naming Jerry.

10. $\dfrac{7}{10}$ > $\dfrac{3}{5}$ > $\dfrac{1}{2}$ [2]

Working:

• Convert to a common denominator (LCM of 10, 5, 2 = 10):
  • $\dfrac{7}{10} = \dfrac{7}{10}$
  • $\dfrac{3}{5} = \dfrac{6}{10}$
  • $\dfrac{1}{2} = \dfrac{5}{10}$
• Compare: $\dfrac{7}{10} > \dfrac{6}{10} > \dfrac{5}{10}$

Marking: Award [1] for correct conversion. Award [1] for correct order (largest to smallest).

Section C: Addition and Subtraction of Fractions (10 marks)

11. $\dfrac{5}{7}$ [2]

Working:

• Same denominator: add the numerators.
• $\dfrac{2}{7} + \dfrac{3}{7} = \dfrac{2+3}{7} = \dfrac{5}{7}$

Marking: Award [2] for correct answer. Award [1] if the student writes $\dfrac{5}{14}$ (common mistake of adding denominators).

Common mistake: Adding both numerator and denominator. Remind students: same denominator → add numerators only.

12. $\dfrac{4}{6} = \dfrac{2}{3}$ [2]

Working:

• $\dfrac{5}{6} - \dfrac{1}{6} = \dfrac{5-1}{6} = \dfrac{4}{6} = \dfrac{2}{3}$

Marking: Award [2] for $\dfrac{2}{3}$ or unsimplified $\dfrac{4}{6}$. Award [1] for $\dfrac{4}{6}$ if not simplified (accept at P4 level, but note simplification is expected).

13. $\dfrac{4}{8} = \dfrac{1}{2}$ (or $\dfrac{2}{4}$) [2]

Working:

• Simplify $\dfrac{2}{8} = \dfrac{1}{4}$
• $\dfrac{1}{4} + \dfrac{1}{4} = \dfrac{2}{4} = \dfrac{1}{2}$

Alternative: Convert to denominator 8: $\dfrac{1}{4} = \dfrac{2}{8}$, so $\dfrac{2}{8} + \dfrac{2}{8} = \dfrac{4}{8} = \dfrac{1}{2}$.

Marking: Award [2] for correct answer. Award [1] for correct conversion but arithmetic error.

14. $\dfrac{3}{10}$ [2]

Working:

• Convert $\dfrac{2}{5}$ to tenths: $\dfrac{2}{5} = \dfrac{4}{10}$
• $\dfrac{7}{10} - \dfrac{4}{10} = \dfrac{3}{10}$

Marking: Award [2] for correct answer. Award [1] for correct conversion but subtraction error.

15. $\dfrac{5}{8}$ kg [2]

Working:

• Convert $\dfrac{1}{4}$ to eighths: $\dfrac{1}{4} = \dfrac{2}{8}$
• $\dfrac{3}{8} + \dfrac{2}{8} = \dfrac{5}{8}$

Marking: Award [1] for correct conversion. Award [1] for correct addition and answer with unit.

Section D: Mixed Numbers, Improper Fractions and Application (11 marks)

16. $2\dfrac{3}{4}$ [2]

Working:

• $11 \div 4 = 2$ remainder $3$
• So $\dfrac{11}{4} = 2\dfrac{3}{4}$

Marking: Award [2] for correct answer. Award [1] if the student shows correct division but writes the remainder incorrectly.

17. $\dfrac{13}{5}$ [2]

Working:

• $2\dfrac{3}{5} = \dfrac{(2 \times 5) + 3}{5} = \dfrac{10 + 3}{5} = \dfrac{13}{5}$

Marking: Award [2] for correct answer. Award [1] for correct method with arithmetic error.

18. $12$ [2]

Working:

• $20 \div 5 = 4$, so multiply numerator by 4: $3 \times 4 = 12$
• $\dfrac{3}{5} = \dfrac{12}{20}$

Marking: Award [2] for correct answer. Award [1] for identifying the scale factor of 4.

19. $1\dfrac{3}{4}$ litres [3]

Working:

• Convert $2\dfrac{1}{2}$ to an improper fraction: $2\dfrac{1}{2} = \dfrac{5}{2}$
• Convert to quarters: $\dfrac{5}{2} = \dfrac{10}{4}$
• Subtract: $\dfrac{10}{4} - \dfrac{3}{4} = \dfrac{7}{4}$
• Convert to mixed number: $\dfrac{7}{4} = 1\dfrac{3}{4}$

Marking: Award [1] for correct conversion of mixed number to improper fraction. Award [1] for correct subtraction. Award [1] for correct final answer as a mixed number with unit.

Common mistake: Students may try to subtract without converting to a common denominator first, or may forget to borrow when the fractional part is smaller.

20.

(a) $1$ metre [2]

Working:

• Convert $\dfrac{7}{3}$ to a mixed number: $\dfrac{7}{3} = 2\dfrac{1}{3}$
• Convert $1\dfrac{1}{3}$ to an improper fraction: $1\dfrac{1}{3} = \dfrac{4}{3}$
• Subtract: $\dfrac{7}{3} - \dfrac{4}{3} = \dfrac{3}{3} = 1$

Marking: Award [1] for correct conversion. Award [1] for correct subtraction and answer.

(b) Both pieces are the same length. The difference is $0$ m. [1]

Working:

• First piece = $1\dfrac{1}{3}$ m = $\dfrac{4}{3}$ m
• Second piece = $1$ m = $\dfrac{3}{3}$ m
• Difference: $\dfrac{4}{3} - \dfrac{3}{3} = \dfrac{1}{3}$ m

Correction: The first piece ($1\dfrac{1}{3}$ m) is longer than the second piece ($1$ m) by $\dfrac{1}{3}$ m.

Marking: Award [1] for correct comparison and difference.

Mark Summary

Note: Questions 16, 17, 18 carry 2 marks each (6 marks). Question 19 carries 3 marks. Question 20 carries 3 marks (2+1). Section D total = 11 marks. Overall total = 5 + 10 + 10 + 5 = 30 marks.

— End of Answer Key —