Primary 5 Mathematics Fractions Quiz

Primary 5 Mathematics Quiz - Fractions

Answer Key

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Section A: Understanding Fractions (Questions 1–5)

1. $\frac{3}{5} = \frac{\boxed{12}}{20}$

Working: $20 \div 5 = 4$, so multiply numerator by 4: $3 \times 4 = 12$.

Answer: 12 ✅ [2 marks]

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2. $\frac{1}{4},\quad \frac{2}{3},\quad \frac{3}{4},\quad \frac{5}{6}$

Working: Convert to equivalent fractions with denominator 12:

• $\frac{1}{4} = \frac{3}{12}$
• $\frac{2}{3} = \frac{8}{12}$
• $\frac{3}{4} = \frac{9}{12}$
• $\frac{5}{6} = \frac{10}{12}$

Order: $\frac{3}{12} < \frac{8}{12} < \frac{9}{12} < \frac{10}{12}$

Answer: $\frac{1}{4},\ \frac{2}{3},\ \frac{3}{4},\ \frac{5}{6}$ ✅ [2 marks]

Common mistake: Students may compare numerators without finding a common denominator first.

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3. $\frac{19}{6} = 3\frac{1}{6}$

Working: $19 \div 6 = 3$ remainder $1$, so $\frac{19}{6} = 3\frac{1}{6}$.

Answer: $3\frac{1}{6}$ ✅ [2 marks]

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4. $\frac{2}{7} + \frac{3}{7} = \frac{5}{7}$

Working: Same denominator, add numerators: $2 + 3 = 5$. Answer is $\frac{5}{7}$, already in simplest form.

Answer: $\frac{5}{7}$ ✅ [2 marks]

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5. $\frac{5}{8} - \frac{1}{4} = \frac{5}{8} - \frac{2}{8} = \frac{3}{8}$

Working: Convert $\frac{1}{4}$ to $\frac{2}{8}$ (LCM of 8 and 4 is 8). Then subtract: $5 - 2 = 3$.

Answer: $\frac{3}{8}$ ✅ [2 marks]

Common mistake: Forgetting to convert to a common denominator before subtracting.

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Section B: Fraction Operations (Questions 6–10)

6. $\frac{3}{5} + \frac{1}{3} = \frac{9}{15} + \frac{5}{15} = \frac{14}{15}$

Working: LCM of 5 and 3 is 15. $\frac{3}{5} = \frac{9}{15}$, $\frac{1}{3} = \frac{5}{15}$. Add: $9 + 5 = 14$.

Answer: $\frac{14}{15}$ ✅ [2 marks]

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7. $\frac{7}{9} - \frac{2}{3} = \frac{7}{9} - \frac{6}{9} = \frac{1}{9}$

Working: LCM of 9 and 3 is 9. $\frac{2}{3} = \frac{6}{9}$. Subtract: $7 - 6 = 1$.

Answer: $\frac{1}{9}$ ✅ [2 marks]

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8. $\frac{2}{3} \times \frac{3}{8} = \frac{6}{24} = \frac{1}{4}$

Working: Multiply numerators: $2 \times 3 = 6$. Multiply denominators: $3 \times 8 = 24$. Simplify $\frac{6}{24}$ by dividing numerator and denominator by 6: $\frac{1}{4}$.

Answer: $\frac{1}{4}$ ✅ [2 marks]

Tip: Students can also cancel before multiplying: $\frac{\cancel{2}^1}{\cancel{3}_1} \times \frac{\cancel{3}^1}{\cancel{8}_4} = \frac{1}{4}$.

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9. $\frac{4}{5} \div 2 = \frac{4}{5} \times \frac{1}{2} = \frac{4}{10} = \frac{2}{5}$

Working: Dividing by 2 is the same as multiplying by $\frac{1}{2}$. $\frac{4}{5} \times \frac{1}{2} = \frac{4}{10} = \frac{2}{5}$.

Answer: $\frac{2}{5}$ ✅ [2 marks]

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10. $1\frac{1}{4} \times \frac{2}{5} = \frac{5}{4} \times \frac{2}{5} = \frac{10}{20} = \frac{1}{2}$

Working: Convert $1\frac{1}{4}$ to improper fraction: $\frac{5}{4}$. Multiply: $\frac{5}{4} \times \frac{2}{5} = \frac{10}{20} = \frac{1}{2}$.

Answer: $\frac{1}{2}$ ✅ [2 marks]

Common mistake: Forgetting to convert the mixed number to an improper fraction before multiplying.

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Section C: Word Problems — Fraction of a Quantity (Questions 11–15)

11. $\frac{2}{7} + \frac{3}{7} = \frac{5}{7}$

Working: Same denominator, add numerators: $2 + 3 = 5$.

Answer: She read $\frac{5}{7}$ of the book altogether. ✅ [2 marks]

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12. $60 \times \frac{3}{5} = \frac{180}{5} = 36$ cm

Working: Find $\frac{3}{5}$ of 60 cm. $60 \div 5 = 12$, then $12 \times 3 = 36$.

Answer: 36 cm ✅ [2 marks]

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13. Blue marbles: $48 \times \frac{5}{8} = 30$. Red marbles: $48 - 30 = 18$.

Working: Find blue marbles first: $\frac{5}{8} \times 48 = 30$. Then subtract from total: $48 - 30 = 18$.

Answer: 18 red marbles ✅ [2 marks]

Alternative: Fraction that is red = $1 - \frac{5}{8} = \frac{3}{8}$. Red marbles: $\frac{3}{8} \times 48 = 18$.

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14. Spent: $\frac{3}{10} + \frac{1}{2} = \frac{3}{10} + \frac{5}{10} = \frac{8}{10} = \frac{4}{5}$

Left: $1 - \frac{4}{5} = \frac{1}{5}$

Working: Convert $\frac{1}{2}$ to $\frac{5}{10}$. Add: $\frac{3}{10} + \frac{5}{10} = \frac{8}{10} = \frac{4}{5}$. Fraction left: $1 - \frac{4}{5} = \frac{1}{5}$.

Answer: She spent $\frac{4}{5}$ of her pocket money. $\frac{1}{5}$ was left. ✅ [2 marks]

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15. Roosters: $200 \times \frac{2}{5} = 80$. Hens: $200 - 80 = 120$. Hens sold: $120 \times \frac{1}{4} = 30$.

Working: Find roosters: $\frac{2}{5} \times 200 = 80$. Hens: $200 - 80 = 120$. Hens sold: $\frac{1}{4} \times 120 = 30$.

Answer: He sells 30 hens. ✅ [2 marks]

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Section D: Multi-Step Word Problems (Questions 16–20)

16. Working backwards:

After giving $\frac{1}{4}$ to Ben, Ali has $\frac{3}{4}$ left. He gave $\frac{1}{3}$ of the remainder to Carl, so he kept $\frac{2}{3}$ of the remainder. $\frac{2}{3} \times \frac{3}{4} = \frac{6}{12} = \frac{1}{2}$ of the original.

$\frac{1}{2}$ of original = 30 Original = $30 \times 2 = 60$

Answer: Ali had 60 stamps at first. ✅ [2 marks]

Model method: Draw a bar divided into 4 equal parts. Shade 1 part for Ben. Divide the remaining 3 parts into 3 equal smaller parts each (12 small units total). Carl gets 1 small unit from each of the 3 remaining large parts = 3 small units. Ali keeps 6 small units = 30 stamps. So 1 small unit = 5 stamps. Total = $12 \times 5 = 60$.

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17. $\frac{2}{3} - \frac{1}{4} = \frac{8}{12} - \frac{3}{12} = \frac{5}{12}$

$\frac{5}{12}$ of capacity = 24 litres $\frac{1}{12}$ of capacity = $24 \div 5 = 4.8$ litres Total capacity = $4.8 \times 12 = 57.6$ litres

Working: The difference between $\frac{2}{3}$ full and $\frac{1}{4}$ full is $\frac{5}{12}$, which equals 24 litres. Find 1 unit: $24 \div 5 = 4.8$. Total capacity = $4.8 \times 12 = 57.6$ litres.

Answer: 57.6 litres ✅ [2 marks]

Alternative (fraction method): $\frac{5}{12} \times \text{Capacity} = 24$. Capacity = $24 \div \frac{5}{12} = 24 \times \frac{12}{5} = \frac{288}{5} = 57.6$ litres.

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18. After spending $\frac{2}{5}$ on the dress, Priya has $\frac{3}{5}$ left. She spent $\frac{1}{2}$ of the remaining on shoes, so she has $\frac{1}{2}$ of $\frac{3}{5}$ left. $\frac{1}{2} \times \frac{3}{5} = \frac{3}{10}$ of original money = $36

$\frac{1}{10}$ of original = $36 \div 3 = 12$ Original = $12 \times 10 = 120$

Answer: She had $120 at first. ✅ [2 marks]

Working backwards: $36 is half of what remained after buying the dress. So after the dress, she had$36 \times 2 = 72$. This$\frac{3}{5}$of original =$72. Original = $72 \div \frac{3}{5} = 72 \times \frac{5}{3} = 120$.

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19. Fraction that are girls: $1 - \frac{3}{8} = \frac{5}{8}$

$\frac{2}{5}$ of girls wear glasses = 120 girls All girls: $120 \div \frac{2}{5} = 120 \times \frac{5}{2} = 300$ girls

Girls = $\frac{5}{8}$ of total pupils = 300 Total pupils: $300 \div \frac{5}{8} = 300 \times \frac{8}{5} = 480$

Answer: There are 480 pupils in the school. ✅ [2 marks]

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20. Morning: Sold $\frac{5}{9} \times 360 = 200$ muffins. Remaining: $360 - 200 = 160$.

Afternoon: Sold $\frac{1}{4} \times 160 = 40$ muffins. Remaining: $160 - 40 = 120$.

Working: Morning sales: $\frac{5}{9} \times 360 = 200$. Left after morning: $360 - 200 = 160$. Afternoon sales: $\frac{1}{4} \times 160 = 40$. Final remaining: $160 - 40 = 120$.

Answer: He had 120 muffins left at the end of the day. ✅ [2 marks]

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Marking Notes Summary

Section	Questions	Marks per Q	Section Total
A: Understanding Fractions	1–5	2	10
B: Fraction Operations	6–10	2	10
C: Word Problems (Single/Multi-step)	11–15	2	10
D: Multi-Step Word Problems	16–20	2	10
Total	20	—	40

Awarding marks:

• Award full marks (2) for correct answer with clear working.
• Award 1 mark for correct method but arithmetic error (method mark).
• Award 0 marks for no working or completely incorrect approach.
• For questions requiring units (cm, litres, etc.), deduct ½ mark if the unit is missing but the numerical answer is correct (at teacher's discretion).