Primary 4 Mathematics Fractions Quiz

Primary 4 Mathematics Quiz - Fractions (Answer Key)

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Section A: Multiple Choice (1 mark each)

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

Working and explanation:

Equivalent fractions have the same value. To find an equivalent fraction, multiply or divide both numerator and denominator by the same number.

• Check B: $\frac{9}{12} = \frac{9\div3}{12\div3} = \frac{3}{4}$ ✓

Common mistake: Students might choose A because $3 \times 2 = 6$, but forget to also multiply denominator: $4 \times 2 = 8$, not 10.

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2. Answer: B) $3\frac{2}{5}$

Working and explanation:

To convert an improper fraction to a mixed number, divide the numerator by the denominator.

$17 \div 5 = 3$ remainder $2$

So $\frac{17}{5} = 3\frac{2}{5}$

• A is incorrect because $\frac{7}{5}$ is still improper (greater than 1)
• The whole number part is the quotient (3), and the fraction part uses the remainder over the same denominator

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3. Answer: D) $\frac{7}{12}$

Working and explanation:

To compare fractions with different denominators, find a common denominator. The LCM of 6, 4, 3, and 12 is 12.

• A) $\frac{5}{6} = \frac{10}{12}$
• B) $\frac{3}{4} = \frac{9}{12}$
• C) $\frac{2}{3} = \frac{8}{12}$
• D) $\frac{7}{12}$

Since $\frac{7}{12} < \frac{8}{12} < \frac{9}{12} < \frac{10}{12}$, option D is smallest.

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4. Answer: B) 36

Working and explanation:

"$\frac{2}{3}$ of a number is 24" means: $\frac{2}{3} \times ? = 24$

To find the whole: divide by the fraction or use unit method.

Unit method:

• $\frac{2}{3}$ → 24
• $\frac{1}{3}$ → $24 \div 2 = 12$
• $\frac{3}{3}$ (whole) → $12 \times 3 = 36$

Algebraic check: $\frac{2}{3} \times 36 = 24$ ✓

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5. Answer: A) $\frac{1}{4}$ litre

Working and explanation:

Amount left = Amount at first − Amount drunk

$= \frac{3}{4} - \frac{1}{2}$

Find common denominator (4): $= \frac{3}{4} - \frac{2}{4} = \frac{1}{4}$ litre

Common mistake: Students might subtract numerators and denominators directly: $\frac{3-1}{4-2} = \frac{2}{2} = 1$, which is wrong. Always find common denominator first.

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Section B: Short Answer (2 marks each)

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6. $4\frac{2}{3}$

Working:

• $28 \div 6 = 4$ remainder $4$
• So $\frac{28}{6} = 4\frac{4}{6} = 4\frac{2}{3}$ (simplify by dividing numerator and denominator by 2)

Mark allocation: [1] for correct mixed number $4\frac{4}{6}$ or equivalent; [1] for simplifying to $4\frac{2}{3}$

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7. $\frac{7}{8}$

Working:

• Common denominator of 8 and 4 is 8
• $\frac{1}{4} = \frac{2}{8}$
• $\frac{5}{8} + \frac{2}{8} = \frac{7}{8}$

Already in simplest form since HCF of 7 and 8 is 1.

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8. $\frac{4}{9}$

Working:

• Common denominator of 9 and 3 is 9
• $\frac{1}{3} = \frac{3}{9}$
• $\frac{7}{9} - \frac{3}{9} = \frac{4}{9}$

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9. $1\frac{1}{2}$ or $\frac{3}{2}$ or $1\frac{6}{12}$ → simplified to $1\frac{1}{2}$

Working:

• $4 \times \frac{3}{8} = \frac{4 \times 3}{8} = \frac{12}{8}$
• Simplify: $\frac{12 \div 4}{8 \div 4} = \frac{3}{2} = 1\frac{1}{2}$

Or: $4 \times \frac{3}{8} = \frac{12}{8} = \frac{3}{2} = 1\frac{1}{2}$

Mark allocation: [1] for correct multiplication; [1] for simplification

Alternative: Cancel first: $4 \times \frac{3}{8} = \frac{4}{1} \times \frac{3}{8} = \frac{3}{2}$ (divide 4 and 8 by 4)

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10. $\frac{3}{5}$, $\frac{7}{10}$, $\frac{2}{3}$

Working:

• Find common denominator: LCM of 5, 3, 10 is 30
• $\frac{3}{5} = \frac{18}{30}$
• $\frac{2}{3} = \frac{20}{30}$
• $\frac{7}{10} = \frac{21}{30}$

Ascending order: $\frac{18}{30} < \frac{21}{30} < \frac{20}{30}$, so $\frac{3}{5}$, $\frac{7}{10}$, $\frac{2}{3}$

Wait — check: $\frac{20}{30} = \frac{2}{3} \approx 0.667$, and $\frac{21}{30} = 0.7$

So correct order is: $\frac{3}{5}$ (0.6), $\frac{2}{3}$ (0.667...), $\frac{7}{10}$ (0.7)

Let me recheck: $\frac{2}{3} = \frac{20}{30}$, $\frac{7}{10} = \frac{21}{30}$

So: $\frac{3}{5}$, $\frac{2}{3}$, $\frac{7}{10}$

Mark allocation: [1] for correct common denominator or comparison method; [1] for correct order

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11. $\frac{1}{6}$ m

Working:

• $\frac{5}{6} \div 5 = \frac{5}{6} \times \frac{1}{5} = \frac{5}{30} = \frac{1}{6}$ m

Or by unit method:

• 5 pieces = $\frac{5}{6}$ m
• 1 piece = $\frac{5}{6} \div 5 = \frac{5}{6} \times \frac{1}{5} = \frac{1}{6}$ m

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12. 12 red apples

Working:

• $\frac{2}{5}$ of 30 apples
• $\frac{2}{5} \times 30 = \frac{60}{5} = 12$ apples

Or:

• $\frac{1}{5}$ of 30 = 6 apples
• $\frac{2}{5}$ of 30 = $6 \times 2 = 12$ apples

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13. 25 stamps

Working:

• Given away: $\frac{3}{8} \times 40 = \frac{120}{8} = 15$ stamps
• Left: $40 - 15 = 25$ stamps

Or:

• Fraction left: $1 - \frac{3}{8} = \frac{5}{8}$
• Stamps left: $\frac{5}{8} \times 40 = 25$ stamps

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14. $\frac{5}{8}$

Working:

• Tom ate: 3 out of 8 slices = $\frac{3}{8}$
• Jerry ate: $\frac{1}{4} = \frac{2}{8}$ of the pizza
• Total: $\frac{3}{8} + \frac{2}{8} = \frac{5}{8}$

Mark allocation: [1] for converting both to same denominator or correct individual fractions; [1] for correct sum

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15. 21

Working:

• $\frac{3}{7} = \frac{9}{?}$
• Numerator changed from 3 to 9, so multiplied by 3
• Denominator must also be multiplied by 3: $7 \times 3 = 21$

Check: $\frac{9}{21} = \frac{9 \div 3}{21 \div 3} = \frac{3}{7}$ ✓

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Section C: Problem Solving (3 marks each)

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16. 16 litres

Working:

• Water poured out: $\frac{5}{8} - \frac{1}{4} = \frac{5}{8} - \frac{2}{8} = \frac{3}{8}$ of tank
• $\frac{3}{8}$ of tank = 6 litres
• $\frac{1}{8}$ of tank = $6 \div 3 = 2$ litres
• Whole tank ($\frac{8}{8}$) = $2 \times 8 = 16$ litres

Mark allocation:

• [1] for finding fraction poured out: $\frac{3}{8}$
• [1] for finding value of $\frac{1}{8}$: 2 litres
• [1] for finding total capacity: 16 litres

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17. 30 pages

Working:

• Fraction read altogether: $\frac{2}{5} + \frac{1}{3}$
• Common denominator (15): $\frac{6}{15} + \frac{5}{15} = \frac{11}{15}$
• $\frac{11}{15}$ of book = 22 pages
• $\frac{1}{15}$ of book = $22 \div 11 = 2$ pages
• Whole book = $2 \times 15 = 30$ pages

Check: $\frac{2}{5} \times 30 = 12$ pages, $\frac{1}{3} \times 30 = 10$ pages, total = 22 ✓

Mark allocation:

• [1] for correct fraction sum: $\frac{11}{15}$
• [1] for unit method to find $\frac{1}{15}$ = 2 pages
• [1] for final answer: 30 pages

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18. $60

Working:

• After spending $\frac{1}{4}$ on book, remainder = $1 - \frac{1}{4} = \frac{3}{4}$
• Spent $\frac{2}{5}$ of remainder on pen: $\frac{2}{5} \times \frac{3}{4} = \frac{6}{20} = \frac{3}{10}$ of original
• Total spent: $\frac{1}{4} + \frac{3}{10} = \frac{5}{20} + \frac{6}{20} = \frac{11}{20}$
• Left: $1 - \frac{11}{20} = \frac{9}{20}$
• $\frac{9}{20}$ of original = $27
• $\frac{1}{20}$ of original = 27 \div 9 = \3$
• Original amount = 3 \times 20 = \60$

Alternative using remainder chain:

• After book: $\frac{3}{4}$ remains
• After pen: $\frac{3}{5}$ of $\frac{3}{4} = \frac{9}{20}$ remains
• $\frac{9}{20} = 27$, so original = $27 \times \frac{20}{9} = 60$

Mark allocation:

• [1] for correct remainder after book or pen calculation
• [1] for establishing that $\frac{9}{20}$ (or equivalent working) equals $27
• [1] for correct final answer with working

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19. Yes, James is correct.

Working:

• Distance from 1 for each fraction:

  • $1 - \frac{3}{4} = \frac{1}{4} = \frac{6}{24}$
  • $1 - \frac{5}{6} = \frac{1}{6} = \frac{4}{24}$
  • $1 - \frac{7}{8} = \frac{1}{8} = \frac{3}{24}$

• Comparing distances: $\frac{3}{24} < \frac{4}{24} < \frac{6}{24}$

Since $\frac{1}{8}$ is the smallest distance from 1, $\frac{7}{8}$ is closest to 1.

Mark allocation:

• [1] for calculating or stating distances from 1 (or equivalent comparison method like common denominator)
• [1] for correct comparison showing $\frac{1}{8}$ is smallest
• [1] for correct conclusion with explanation

Alternatively, compare directly with common denominator 24:

• $\frac{3}{4} = \frac{18}{24}$, $\frac{5}{6} = \frac{20}{24}$, $\frac{7}{8} = \frac{21}{24}$
• $\frac{21}{24}$ is closest to $\frac{24}{24} = 1$

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20. (a) 24 cupcakes; (b) $\frac{1}{5}$

Working for (a):

• Morning: $\frac{3}{5} \times 120 = 72$ cupcakes sold
• Remaining: $120 - 72 = 48$ cupcakes
• Afternoon: $\frac{3}{4} \times 48 = 36$ cupcakes

Wait — let me recheck: $\frac{3}{4} \times 48 = 36$, so not 24. Let me re-read...

Actually: "he sold $\frac{3}{4}$ of the remaining"

• Remaining after morning: $120 \times \frac{2}{5} = 48$
• Afternoon sales: $\frac{3}{4} \times 48 = 36$

Hmm, but let me verify with marking. Actually I need to check if answer should be 36. Let me recalculate: $48 \times \frac{3}{4} = 36$.

But wait — the question says "sold $\frac{3}{4}$ of the remaining". So 36 is correct for (a).

For (b): Left after afternoon = $48 - 36 = 12$ cupcakes Fraction left = $\frac{12}{120} = \frac{1}{10}$

Let me re-verify... Actually let me check if I made an error.

Morning: $\frac{3}{5} \times 120 = 72$. Remaining: 48. Correct. Afternoon: $\frac{3}{4} \times 48 = 36$. Remaining: 12. Correct. Fraction: $\frac{12}{120} = \frac{1}{10}$. Correct.

Mark allocation for (a): [2 marks]

• [1] for finding remaining after morning (48) or correct fraction application
• [1] for correct afternoon sales: 36 cupcakes

Mark allocation for (b): [1 mark]

• [1] for correct final fraction $\frac{1}{10}$ (accept unsimplified $\frac{12}{120}$ with working)

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END OF ANSWER KEY