Primary 3 Mathematics Fractions Quiz

Primary 3 Mathematics Quiz - Fractions: Answer Key

Total Marks: 45 marks

Section A: Multiple Choice (1 mark each)

1. A) $\frac{4}{6}$

Working: To find an equivalent fraction, multiply both numerator and denominator by the same number. $\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}$. Equivalent fractions represent the same amount even though they look different. Common mistake: Choosing B ($\frac{3}{6}$) which equals $\frac{1}{2}$, not $\frac{2}{3}$.

2. B) $\frac{7}{8}$

Working: When adding fractions with the same denominator, add only the numerators. Keep the denominator the same: $\frac{5}{8} + \frac{2}{8} = \frac{5+2}{8} = \frac{7}{8}$. The denominator does not change because the "size" of each part stays the same—we're just counting how many eighths we have in total. Common mistake: Adding denominators to get $\frac{7}{16}$.

3. B) $\frac{5}{6}$

Working: Convert to common denominator or compare using benchmarks. Using 12 as common denominator: $\frac{3}{4} = \frac{9}{12}$, $\frac{5}{6} = \frac{10}{12}$, $\frac{2}{3} = \frac{8}{12}$, $\frac{7}{12} = \frac{7}{12}$. Alternatively, compare to $\frac{1}{2}$: $\frac{5}{6}$ is closest to 1 (only $\frac{1}{6}$ away). Teaching note: When denominators differ, find equivalent fractions with a common denominator, or compare how far each is from 1.

4. B) $\frac{5}{8}$

Working: Total slices eaten = $3 + 2 = 5$ slices. Total slices = 8. Fraction eaten = $\frac{5}{8}$. The denominator stays 8 because the whole is still 8 equal slices. Commonmistake: Adding denominators to get $\frac{5}{16}$ (the "total" number of slices doesn't create new slices).

5. C) $\frac{2}{3}$

Working: Simplify by dividing numerator and denominator by their highest common factor (HCF). HCF of 12 and 18 is 6. $\frac{12 \div 6}{18 \div 6} = \frac{2}{3}$. Step-by-step: factors of 12 are (1, 2, 3, 4, 6, 12); factors of 18 are (1, 2, 3, 6, 9, 18). Common factors are 1, 2, 3, 6. The largest is 6. Teaching note: A fraction is in simplest form when numerator and denominator share no common factor other than 1.

Section B: Short Answer (2 marks each)

6. $\frac{4}{5}$

Working: HCF of 8 and 10 is 2. $\frac{8 \div 2}{10 \div 2} = \frac{4}{5}$. [1 mark for correct method, 1 mark for correct answer]

Teaching note: To simplify, divide top and bottom by the same number. Keep dividing until no common factors remain. $\frac{4}{5}$ cannot be simplified further because HCF of 4 and 5 is 1.

7. 9

Working: $\frac{3}{5} = \frac{?}{15}$. Denominator changes from 5 to 15, which is $5 \times 3$. So multiply numerator by 3 as well: $3 \times 3 = 9$. Check: $\frac{3}{5} = \frac{9}{15}$. [1 mark for identifying multiplication by 3, 1 mark for answer]

Teaching note: Equivalent fractions use the same multiplication or division on both parts. Think of it as: "What times 5 equals 15?" Then do the same to the top.

8. $\frac{3}{9} = \frac{1}{3}$

Working: $\frac{7}{9} - \frac{4}{9} = \frac{7-4}{9} = \frac{3}{9} = \frac{1}{3}$. [1 mark for $\frac{3}{9}$, 1 mark for simplifying to $\frac{1}{3}$]

Teaching note: Subtract numerators, keep denominator. Always check if answer can be simplified. $\frac{3}{9}$ simplifies by dividing by 3.

9. $\frac{3}{8}$, $\frac{1}{2}$, $\frac{5}{8}$

Working: Convert to common denominator of 8: $\frac{1}{2} = \frac{4}{8}$. Now compare: $\frac{3}{8}$, $\frac{4}{8}$, $\frac{5}{8}$. Order is $\frac{3}{8} < \frac{4}{8} < \frac{5}{8}$. [1 mark for correct conversion or comparison method, 1 mark for correct order]

Teaching note: "Ascending" means smallest to largest. Common denominator makes comparison easy—just look at numerators.

10. $\frac{3}{6} = \frac{1}{2}$

Working: $\frac{5}{6} - \frac{2}{6} = \frac{3}{6} = \frac{1}{2}$. [1 mark for $\frac{3}{6}$, 1 mark for $\frac{1}{2}$ or acceptable unsimplified form if working shown]

Teaching note: "Left" means subtraction. Mary started with $\frac{5}{6}$ and gave away $\frac{2}{6}$, so we subtract.

11. $\frac{3}{4}$

Working: HCF of 18 and 24. Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. HCF is 6. $\frac{18 \div 6}{24 \div 6} = \frac{3}{4}$. [1 mark for identifying HCF or equivalent method, 1 mark for answer]

Teaching note: If stuck finding HCF, divide by any common factor (like 2, getting $\frac{9}{12}$), then divide again ($\frac{3}{4}$). Both steps are valid.

12. $\frac{3}{8}$

Working: Convert to same units. 2 hours = 120 minutes. Fraction = $\frac{45}{120}$. Simplify: HCF of 45 and 120 is 15. $\frac{45 \div 15}{120 \div 15} = \frac{3}{8}$. [1 mark for correct unsimplified fraction or conversion, 1 mark for simplified answer]

Alternative: 1 hour = 60 min, so 45 min = $\frac{3}{4}$ hour. Then $\frac{3}{4} \div 2 = \frac{3}{4} \times \frac{1}{2} = \frac{3}{8}$. (This method is harder for P3; unit conversion is preferred.)

Teaching note: The "whole" is 2 hours (120 minutes), not 1 hour. Common mistake: Using $\frac{45}{60} = \frac{3}{4}$ without considering the 2 hours.

13. $\frac{7}{10}$

Working: $\frac{3}{10} + \frac{4}{10} = \frac{7}{10}$. [1 mark for correct addition, 1 mark for answer]

Teaching note: Both fractions have denominator 10, representing tenths of the same bottle. Simply add the numerators. The answer is already in simplest form.

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

Working: $\frac{7}{8} - \frac{1}{4}$. First convert to common denominator: $\frac{1}{4} = \frac{2}{8}$. Then $\frac{7}{8} - \frac{2}{8} = \frac{5}{8}$ m. [1 mark for common denominator conversion, 1 mark for correct subtraction and answer]

Teaching note: Cannot subtract directly because denominators differ. Find equivalent fraction: "What times 4 equals 8?" Then subtract. Keep the unit (metres) in the answer.

15. $\frac{4}{7} > \frac{5}{9}$

Working: Common denominator of 7 and 9 is 63. $\frac{4}{7} = \frac{36}{63}$ and $\frac{5}{9} = \frac{35}{63}$. Since $36 > 35$, we have $\frac{4}{7} > \frac{5}{9}$. [1 mark for correct method, 1 mark for correct symbol]

Alternative: Cross-multiply: $4 \times 9 = 36$ and $5 \times 7 = 35$. Since $36 > 35$, $\frac{4}{7} > \frac{5}{9}$.

Teaching note: The ">" symbol opens toward the larger number, like a crocodile's mouth opening toward more food.

Section C: Problem Solving (4 marks each)

16. (a) $\frac{3}{5}$

Working: $\frac{2}{5} + \frac{1}{5} = \frac{3}{5}$. [2 marks]

(b) $\frac{2}{5}$

Working: Whole cake = 1 = $\frac{5}{5}$. Left: $\frac{5}{5} - \frac{3}{5} = \frac{2}{5}$. [2 marks; 1 mark for converting 1 to $\frac{5}{5}$, 1 mark for subtraction]

Teaching note: The whole is 1, which can be written as any fraction with equal numerator and denominator. Here we need fifths. Common mistake: Writing "1 – 3" instead of dealing with fractions properly.

17. (a) $\frac{3}{4}$

Working: $\frac{1}{4} + \frac{1}{2} = \frac{1}{4} + \frac{2}{4} = \frac{3}{4}$. [2 marks; 1 mark for common denominator, 1 mark for answer]

(b) $\frac{1}{4}$

Working: $1 - \frac{3}{4} = \frac{4}{4} - \frac{3}{4} = \frac{1}{4}$. [2 marks; 1 mark for converting 1, 1 mark for answer]

Teaching note: The whole watermelon is 1. To add $\frac{1}{4}$ and $\frac{1}{2}$, convert half to quarters. Note that $\frac{2}{4}$ simplifies to $\frac{1}{2}$—both are correct at different stages.

18. (a) $\frac{2}{3}$

Working: From diagram: 8 shaded out of 12 equal parts = $\frac{8}{12} = \frac{2}{3}$. [2 marks; 1 mark for correct fraction from diagram, 1 mark for simplification]

(b) $\frac{1}{3}$

Working: 4 unshaded out of 12 = $\frac{4}{12} = \frac{1}{3}$. Or: $1 - \frac{2}{3} = \frac{1}{3}$. [2 marks]

Expected visual features: Rectangle divided into 12 equal smaller rectangles (3 rows × 4 columns). 8 parts shaded (e.g., first 2 rows completely shaded, or a clear pattern). 4 parts unshaded visible. The answer requires counting shaded parts against total.

19. (a) $\frac{7}{9}$

Working: $\frac{2}{9} + \frac{5}{9} = \frac{7}{9}$. [2 marks]

(b) $\frac{1}{9}$

Working: Used: $\frac{7}{9}$. Spilled: $\frac{1}{9}$. Total gone: $\frac{7}{9} + \frac{1}{9} = \frac{8}{9}$. Left: $1 - \frac{8}{9} = \frac{9}{9} - \frac{8}{9} = \frac{1}{9}$. [2 marks; 1 mark for finding total used/spilled, 1 mark for final subtraction]

Teaching note: Two separate "losses"—used AND spilled. Must add both before finding remainder. Common mistake: Forgetting to include the spilled amount.

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

Working: Total eaten by Ben and Cindy: $\frac{1}{6} + \frac{1}{3} = \frac{1}{6} + \frac{2}{6} = \frac{3}{6} = \frac{1}{2}$. David: $1 - \frac{1}{2} = \frac{1}{2}$. Or directly: David = $1 - \frac{1}{6} - \frac{1}{3} = \frac{6}{6} - \frac{1}{6} - \frac{2}{6} = \frac{3}{6} = \frac{1}{2}$. [2 marks]

(b) David (or Cindy, depending on interpretation); $\frac{1}{6}$ more

Working: Compare amounts: Ben = $\frac{1}{6}$, Cindy = $\frac{1}{3} = \frac{2}{6}$, David = $\frac{3}{6} = \frac{1}{2}$. David ate the most. Difference from Ben: $\frac{3}{6} - \frac{1}{6} = \frac{2}{6} = \frac{1}{3}$. Or if Cindy: $\frac{2}{6} - \frac{1}{6} = \frac{1}{6}$.

Wait—rechecking: Cindy ate $\frac{1}{3} = \frac{2}{6}$, David ate $\frac{3}{6}$. David ate the most. David ate $\frac{3}{6} - \frac{1}{6} = \frac{2}{6} = \frac{1}{3}$ more than Ben. [2 marks; 1 mark for identifying correct person, 1 mark for correct difference]

Teaching note: Must convert all to same denominator to compare. "How much more" requires subtraction. Common mistake: Comparing without converting—$\frac{1}{3}$ looks smaller than $\frac{1}{2}$ but need to verify.

Marking Summary

For any alternative correct methods, award full marks. Deduct $\frac{1}{2}$ mark for correct answer with no working in Section C only (working is required for problem solving).