Primary 5 Mathematics Fractions Quiz

Primary 5 Mathematics Quiz - Fractions - Answer Key

Total Marks: 60 | Marking: award method marks for correct working even if the final answer is wrong; deduct only for final-answer errors unless stated.

Answer 1.

Final answer: $\frac{3}{4}$ is greater. (2 marks)

• Concept: to compare fractions, rewrite them with the same denominator (a common multiple).
• LCM of 4 and 7 is 28: $\frac{3}{4} = \frac{21}{28}$ and $\frac{5}{7} = \frac{20}{28}$.
• Since $\frac{21}{28} > \frac{20}{28}$, $\frac{3}{4} > \frac{5}{7}$.
• Marks: [1] correct common denominator; [1] correct comparison and choice.
• Common mistake: comparing numerators (3 vs 5) or denominators directly without a common denominator.

Answer 2.

(a) $3\frac{2}{5}$ (b) $3.4$ (2 marks)

• Concept: a fraction like $\frac{17}{5}$ means "17 divided by 5".
• Step 1: $17 \div 5 = 3$ remainder $2$, so $\frac{17}{5} = 3\frac{2}{5}$ [1 mark].
• Step 2: $\frac{2}{5} = \frac{4}{10} = 0.4$, so the decimal is $3.4$ [1 mark].
• Teaching point: dividing a whole number by a whole number can give a fraction or decimal quotient.

Answer 3.

Final answer: $5\frac{1}{5}$ (2 marks)

• Step 1: add the whole numbers: $3 + 1 = 4$.
• Step 2: add the fractions: $\frac{2}{5} + \frac{4}{5} = \frac{6}{5} = 1\frac{1}{5}$.
• Step 3: combine: $4 + 1\frac{1}{5} = 5\frac{1}{5}$.
• Marks: [1] correct method; [1] correct simplified answer.
• Common mistake: leaving the answer as $4\frac{6}{5}$ instead of regrouping $\frac{6}{5}$ into $1\frac{1}{5}$.

Answer 4.

Final answer: $1\frac{5}{12}$ (2 marks)

• Step 1: rename with denominator 12: $4\frac{1}{6} = 4\frac{2}{12}$ and $2\frac{3}{4} = 2\frac{9}{12}$.
• Step 2: cannot subtract $\frac{9}{12}$ from $\frac{2}{12}$, so regroup: $4\frac{2}{12} = 3\frac{14}{12}$.
• Step 3: $3\frac{14}{12} - 2\frac{9}{12} = 1\frac{5}{12}$.
• Marks: [1] correct renaming/regrouping; [1] correct answer.
• Common mistake: subtracting both whole numbers and fractions without regrouping.

Answer 5.

Final answer: $\frac{3}{5}, \frac{2}{3}, \frac{7}{10}$ (2 marks)

• Concept: convert all fractions to equivalent fractions with the same denominator (LCM of 3, 10, 5 is 30).
• $\frac{2}{3} = \frac{20}{30}$, $\frac{7}{10} = \frac{21}{30}$, $\frac{3}{5} = \frac{18}{30}$.
• Order: $\frac{18}{30} < \frac{20}{30} < \frac{21}{30}$, so $\frac{3}{5} < \frac{2}{3} < \frac{7}{10}$.
• Marks: [1] correct equivalents; [1] fully correct order.

Answer 6.

Final answer: $\frac{8}{21}$ (3 marks)

• Concept: multiplying fractions means "a fraction of a fraction"; multiply numerator by numerator and denominator by denominator.
• Step 1: $\frac{2}{3} \times \frac{4}{7} = \frac{2 \times 4}{3 \times 7} = \frac{8}{21}$ [2 marks].
• Step 2: check simplifying: 8 and 21 share no common factor, so it is already in simplest form [1 mark].
• Common mistake: cross-cancelling wrongly, e.g. cancelling the 2 with nothing in sight; only cancel factors shared between a numerator and a denominator.

Answer 7.

Final answer: $7\frac{1}{2}$ (3 marks)

• Method: multiply the whole number by the numerator, keeping the denominator.
• Step 1: $\frac{5}{6} \times 9 = \frac{5 \times 9}{6} = \frac{45}{6}$ [1 mark].
• Step 2: simplify before or after multiplying: $\frac{45}{6} = \frac{15}{2}$ (divide top and bottom by 3) [1 mark].
• Step 3: $\frac{15}{2} = 7\frac{1}{2}$ [1 mark].
• Common mistake: multiplying both the numerator and denominator by 9.

Answer 8.

Final answer: $2\frac{1}{10}$ (3 marks)

• Step 1: multiply straight across: $\frac{7}{4} \times \frac{6}{5} = \frac{42}{20}$ [1 mark].
• Step 2: simplify: divide top and bottom by 2 to get $\frac{21}{10}$ [1 mark].
• Step 3: convert to a mixed

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Primary 5 Mathematics Quiz - Fractions - Answer Key

Total Marks: 60 | Award method marks for correct working even if the final answer is wrong.

Answer 1.

Final answer: $\frac{3}{4}$ is greater. (2 marks)

• Concept: compare fractions using a common denominator.
• LCM of 4 and 7 is 28: $\frac{3}{4} = \frac{21}{28}$ and $\frac{5}{7} = \frac{20}{28}$.
• Since $\frac{21}{28} > \frac{20}{28}$, $\frac{3}{4} > \frac{5}{7}$.
• Marks: [1] correct common denominator; [1] correct comparison and choice.
• Common mistake: comparing numerators or denominators directly without a common denominator.

Answer 2.

(a) $3\frac{2}{5}$ (b) $3.4$ (2 marks)

• Step 1: $17 \div 5 = 3$ remainder $2$, so $\frac{17}{5} = 3\frac{2}{5}$ [1 mark].
• Step 2: $\frac{2}{5} = \frac{4}{10} = 0.4$, so the decimal is $3.4$ [1 mark].
• Common mistake: writing the decimal as 3.2 by reading the remainder as tenths.

Answer 3.

Final answer: $5\frac{1}{5}$ (2 marks)

• Step 1: add whole numbers: $3 + 1 = 4$.
• Step 2: add fractions: $\frac{2}{5} + \frac{4}{5} = \frac{6}{5} = 1\frac{1}{5}$.
• Step 3: combine: $4 + 1\frac{1}{5} = 5\frac{1}{5}$.
• Marks: [1] correct method; [1] correct simplified answer.
• Common mistake: leaving the answer as $4\frac{6}{5}$ instead of regrouping.

Answer 4.

Final answer: $1\frac{5}{12}$ (2 marks)

• Step 1: rename with denominator 12: $4\frac{1}{6} = 4\frac{2}{12}$ and $2\frac{3}{4} = 2\frac{9}{12}$.
• Step 2: regroup since $\frac{2}{12} < \frac{9}{12}$: $4\frac{2}{12} = 3\frac{14}{12}$.
• Step 3: $3\frac{14}{12} - 2\frac{9}{12} = 1\frac{5}{12}$.
• Marks: [1] correct renaming/regrouping; [1] correct answer.
• Common mistake: subtracting without regrouping.

Answer 5.

Final answer: $\frac{3}{5}, \frac{2}{3}, \frac{7}{10}$ (2 marks)

• Convert to denominator 30 (LCM of 3, 10, 5): $\frac{2}{3} = \frac{20}{30}$, $\frac{7}{10} = \frac{21}{30}$, $\frac{3}{5} = \frac{18}{30}$.
• Order: $\frac{18}{30} < \frac{20}{30} < \frac{21}{30}$, so $\frac{3}{5} < \frac{2}{3} < \frac{7}{10}$.
• Marks: [1] correct equivalents; [1] fully correct order.

Answer 6.

Final answer: $\frac{8}{21}$ (3 marks)

• Concept: multiply numerator by numerator and denominator by denominator.
• Step 1: $\frac{2}{3} \times \frac{4}{7} = \frac{2 \times 4}{3 \times 7} = \frac{8}{21}$ [2 marks].
• Step 2: 8 and 21 share no common factor, so it is in simplest form [1 mark].
• Common mistake: cross-cancelling factors that are not numerator-with-denominator pairs.

Answer 7.

Final answer: $7\frac{1}{2}$ (3 marks)

• Step 1: $\frac{5}{6} \times 9 = \frac{5 \times 9}{6} = \frac{45}{6}$ [1 mark].
• Step 2: simplify: $\frac{45}{6} = \frac{15}{2}$ (divide top and bottom by 3) [1 mark].
• Step 3: $\frac{15}{2} = 7\frac{1}{2}$ [1 mark].
• Common mistake: multiplying both the numerator and denominator by 9.

Answer 8.

Final answer: $2\frac{1}{10}$ (3 marks)

• Step 1: multiply straight across: $\frac{7}{4} \times \frac{6}{5} = \frac{42}{20}$ [1 mark].
• Step 2: simplify: divide top and bottom by 2 to get $\frac{21}{10}$ [1 mark].
• Step 3: convert to a mixed number: $\frac{21}{10} = 2\frac{1}{10}$ [1 mark].
• Common mistake: forgetting to simplify before converting, or leaving the answer as an improper fraction when a mixed number is required.

Answer 9.

Final answer: $12\ \ell$ (3 marks)

• Step 1: write $1\frac{1}{2}\ \ell = \frac{3}{2}\ \ell$ [1 mark].
• Step 2: total volume $= \frac{3}{2} \times 8 = \frac{24}{2} = 12$ [1 mark].
• Step 3: include the unit: $12\ \ell$ [1 mark].
• Common mistake: multiplying only the whole number part ($1 \times 8$) and ignoring the fraction.

Answer 10.

(a) 24 stickers (b) 36 stickers (3 marks)

• Step 1: stickers given away $= \frac{2}{5} \times 60 = \frac{120}{5} = 24$ [1 mark].
• Step 2: stickers left $= 60 - 24 = 36$ [1 mark].
• Alternative: left $= \frac{3}{5} \times 60 = 36$ [1 mark for method].
• Common mistake: finding $\frac{2}{5}$ of the remaining stickers in part (b) instead of subtracting from 60.

Answer 11.

Final answer: $\frac{3}{4}\ m$ (3 marks)

• Concept: dividing a whole number by a whole number gives a fraction: $3 \div 4 = \frac{3}{4}$.
• Step 1: length of each piece $= 3 \div 4 = \frac{3}{4}\ m$ [2 marks].
• Step 2: check: $4 \times \frac{3}{4} = 3\ m$ [1 mark].
• Common mistake: answering $\frac{1}{3}\ m$ by dividing the number of pieces by the length.

Answer 12.

(a) $0.35$ (b) $\frac{2}{25}$ (3 marks)

• (a) $\frac{7}{20} = \frac{35}{100} = 0.35$ (multiply numerator and denominator by 5) [1 mark].
• (b) $0.08 = \frac{8}{100}$; simplify by dividing top and bottom by 4: $\frac{8}{100} = \frac{2}{25}$ [2 marks: conversion + simplification].
• Common mistake: writing $0.08$ as $\frac{8}{10}$ instead of $\frac{8}{100}$.

Answer 13.

Final answer: $\frac{7}{8}\ \ell$ (3 marks)

• Step 1: rename with denominator 8: $1\frac{1}{4}\ \ell = 1\frac{2}{8}\ \ell = \frac{10}{8}\ \ell$ [1 mark].
• Step 2: water used $= \frac{3}{8}\ \ell$, so water left $= \frac{10}{8} - \frac{3}{8} = \frac{7}{8}$ [1 mark].
• Step 3: include the unit: $\frac{7}{8}\ \ell$ [1 mark].
• Common mistake: subtracting $\frac{3}{8}$ from $\frac{1}{4}$ without renaming first.

Answer 14.

Final answer: 30 girls (3 marks)

• Using the bar model: 48 children split into 8 equal parts, so each part $= 48 \div 8 = 6$ children [1 mark].
• Boys: 3 parts $= 3 \times 6 = 18$ children.
• Girls: 5 parts $= 5 \times 6 = 30$ children [1 mark].
• Check: $18 + 30 = 48$ [1 mark for correct method/check].
• Alternative: girls $= \frac{5}{8} \times 48 = 30$.
• Common mistake: giving the number of boys (18) as the final answer.

Answer 15.

Final answer: $3\frac{3}{4}$ cups (3 marks)

• Step 1: flour needed $= \frac{3}{4} \times 5 = \frac{15}{4}$ cups [1 mark].
• Step 2: convert to a mixed number: $\frac{15}{4} = 3\frac{3}{4}$ [1 mark].
• Step 3: state with units: $3\frac{3}{4}$ cups [1 mark].
• Common mistake: multiplying only the numerator by 5 and leaving $\frac{15}{4}$ unconverted when a mixed number is required.

Answer 16.

Final answer: $135 (4 marks)

• Step 1: after buying the bag, remainder $= 1 - \frac{1}{3} = \frac{2}{3}$ of her money [1 mark].
• Step 2: money left $= \frac{3}{5}$ of the remainder, so fraction left $= \frac{3}{5} \times \frac{2}{3} = \frac{2}{5}$ of her money at first [1 mark].
• Step 3: $\frac{2}{5}$ of her money = \54$, so$\frac{1}{5} = $54 \div 2 = $27$ [1 mark].
• Step 4: money at first = 5 \times \27 = $135$ [1 mark].
• Check: \135 - $45 \text{ (bag)} = $90$; shoes$= \frac{2}{5} \times $90 = $36$; left$= $90 - $36 = $54$. ✓
• Common mistake: taking $\frac{2}{5}$ of the original amount instead of the remainder.

Answer 17.

Final answer: 168 marbles (4 marks)

• Step 1: Monday: $\frac{1}{4} \times 240 = 60$ marbles taken; remaining $= 240 - 60 = 180$ [1 mark].
• Step 2: Tuesday: $\frac{3}{5} \times 180 = 108$ marbles taken [1 mark].
• Step 3: altogether $= 60 + 108 = 168$ marbles [1 mark].
• Step 4: check: remaining after Tuesday $= 180 - 108 = 72$; $60 + 108 + 72 = 240$. ✓ [1 mark]
• Common mistake: taking $\frac{3}{5}$ of 240 instead of $\frac{3}{5}$ of the remaining 180.

Answer 18.

Final answer: $1\frac{1}{8}\ \ell$ (4 marks)

• Step 1: rename with denominator 8: $5\frac{1}{2} = \frac{44}{8}$, $2\frac{3}{4} = \frac{22}{8}$, $1\frac{5}{8} = \frac{13}{8}$ [1 mark].
• Step 2: total used $= \frac{22}{8} + \frac{13}{8} = \frac{35}{8} = 4\frac{3}{8}\ \ell$ [1 mark].
• Step 3: water left $= \frac{44}{8} - \frac{35}{8} = \frac{9}{8} = 1\frac{1}{8}$ [1 mark].
• Step 4: include the unit: $1\frac{1}{8}\ \ell$ [1 mark].
• Common mistake: adding the whole numbers and fractions separately without renaming to eighths first.

Answer 19.

Final answer: $1\frac{1}{4}\ kg$ (4 marks)

• Step 1: flour for bread $= \frac{2}{3} \times 6 = 4\ kg$ [1 mark].
• Step 2: flour for cookies $= \frac{3}{4}\ kg$ (an amount, not a fraction of the flour) [1 mark].
• Step 3: total used $= 4 + \frac{3}{4} = 4\frac{3}{4}\ kg$ [1 mark].
• Step 4: flour left $= 6 - 4\frac{3}{4} = 1\frac{1}{4}\ kg$ [1 mark].
• Common mistake: treating $\frac{3}{4}\ kg$ as $\frac{3}{4}$ of the remaining flour.

Answer 20.

Final answer: 8 kg (4 marks)

• Step 1: draw a model of 8 units. Monday: $\frac{1}{2}$ of the bag $= 4$ units [1 mark].
• Step 2: remainder $= 4$ units; Tuesday: $\frac{1}{4}$ of the remainder $= 1$ unit [1 mark].
• Step 3: difference $= 4 - 1 = 3$ units $= 3\ kg$, so 1 unit $= 1\ kg$ [1 mark].
• Step 4: bag at first $= 8$ units $= 8\ kg$ [1 mark].
• Check: 8 kg at first; Monday 4 kg; remainder 4 kg; Tuesday 1 kg; difference $4 - 1 = 3\ kg$. ✓
• Common mistake: taking $\frac{1}{4}$ of the whole bag instead of $\frac{1}{4}$ of the remainder.

END OF ANSWER KEY