Primary 3 Mathematics Fractions Quiz

Primary 3 Mathematics Quiz - Fractions

Answer Key

Section A: Understanding Fractions (1 mark each)

1. $\frac{1}{2}$
The shape has 12 squares in total. 6 are shaded. $\frac{6}{12} = \frac{1}{2}$.
Marking note: Accept $\frac{6}{12}$ but simplified form $\frac{1}{2}$ is preferred.

2. (a) 3
(b) 5
Marking note: 1 mark for each correct part. The numerator is the top number; the denominator is the bottom number.

3. $\frac{3}{8}$
"Three-eighths" means 3 parts out of 8 equal parts.

4. $\frac{1}{3}$
Amy ate 2 out of 6 slices: $\frac{2}{6} = \frac{1}{3}$ (simplify by dividing numerator and denominator by 2).
Marking note: Award 1 mark for $\frac{2}{6}$ if simplification is not required, but simplified form is expected at P3 level.

5. $\frac{3}{6}$
$\frac{3}{6} = \frac{1}{2}$ (divide numerator and denominator by 3).
Marking note: Award 1 mark for correctly circling $\frac{3}{6}$.

Section B: Equivalent Fractions (2 marks each)

6. 3
To get from 3 to 9 in the denominator, multiply by 3. Multiply the numerator by 3 as well: $1 \times 3 = 3$.
Marking note: Award 2 marks for correct answer with working. Award 1 mark for correct answer only.

7. 15
To get from 2 to 6 in the numerator, multiply by 3. Multiply the denominator by 3 as well: $5 \times 3 = 15$.
Marking note: Award 2 marks for correct answer with working. Award 1 mark for correct answer only.

8. $\frac{6}{8}$ and $\frac{9}{12}$ (other valid answers accepted, e.g., $\frac{12}{16}$, $\frac{15}{20}$)
Multiply both numerator and denominator by the same number: $\frac{3 \times 2}{4 \times 2} = \frac{6}{8}$, $\frac{3 \times 3}{4 \times 3} = \frac{9}{12}$.
Marking note: Award 1 mark for each correct equivalent fraction. Answers must be mathematically correct.

9. 24
To get from 5 to 15 in the numerator, multiply by 3. Multiply the denominator by 3: $8 \times 3 = 24$.
Marking note: Award 2 marks for correct answer with working. Award 1 mark for correct answer only.

10. Yes, Tom is correct.
$\frac{4}{6} = \frac{4 \div 2}{6 \div 2} = \frac{2}{3}$. When you divide both the numerator and denominator by the same number (2), you get an equivalent fraction.
Marking note: Award 1 mark for "Yes" and 1 mark for a valid explanation. Accept any correct reasoning showing simplification.

Section C: Comparing and Ordering Fractions (2 marks each)

11. $\frac{5}{7}$
When two fractions have the same denominator, the one with the larger numerator is larger. Since $5 > 2$, $\frac{5}{7} > \frac{2}{7}$.
Marking note: Award 1 mark for circling the correct fraction. Award 1 mark for explanation (if required by teacher).

12. $\frac{1}{4},\quad \frac{2}{4},\quad \frac{3}{4}$
All fractions have the same denominator (4), so compare numerators: $1 < 2 < 3$.
Marking note: Award 2 marks for fully correct order. Award 1 mark if only one fraction is in the correct position.

13. $\frac{1}{5}$ is smaller.
When two fractions have the same numerator (both are 1), the one with the larger denominator is smaller. Since $5 > 3$, $\frac{1}{5} < \frac{1}{3}$. Think of it this way: cutting something into 5 pieces gives smaller pieces than cutting it into 3 pieces.
Marking note: Award 1 mark for identifying $\frac{1}{5}$ and 1 mark for a valid explanation.

14. $<$
Both fractions have the same denominator (8). Since $3 < 5$, $\frac{3}{8} < \frac{5}{8}$.
Marking note: Award 2 marks for correct symbol. Common mistake: students may write $>$ — check carefully.

15. Raj ate more. He ate $\frac{1}{6}$ more than Mei Ling.
Compare: $\frac{3}{6} > \frac{2}{6}$, so Raj ate more.
Difference: $\frac{3}{6} - \frac{2}{6} = \frac{1}{6}$.
Marking note: Award 1 mark for identifying Raj and 1 mark for the correct difference of $\frac{1}{6}$.

Section D: Adding and Subtracting Fractions (3 marks each)

16. $\frac{5}{7}$
When adding fractions with the same denominator, add the numerators and keep the denominator: $\frac{2+3}{7} = \frac{5}{7}$.
Marking note: Award 3 marks for correct answer with working. Award 2 marks for correct answer only. Award 1 mark for showing the correct method with an arithmetic error.

17. $\frac{3}{9} = \frac{1}{3}$
$\frac{5-2}{9} = \frac{3}{9} = \frac{1}{3}$ (simplify by dividing numerator and denominator by 3).
Marking note: Award 3 marks for correct simplified answer with working. Accept $\frac{3}{9}$ for 2 marks. Award 1 mark for correct method.

18. $\frac{3}{4}$
$\frac{1}{4} + \frac{2}{4} = \frac{1+2}{4} = \frac{3}{4}$.
Marking note: Award 3 marks for correct answer with working. Award 2 marks for correct answer only. Common mistake: adding denominators — watch for $\frac{3}{8}$.

19. $\frac{3}{10}$
$\frac{7}{10} - \frac{4}{10} = \frac{7-4}{10} = \frac{3}{10}$.
Marking note: Award 3 marks for correct answer with working. Award 2 marks for correct answer only.

20. (a) $\frac{3}{5}$
$\frac{2}{5} + \frac{1}{5} = \frac{2+1}{5} = \frac{3}{5}$.

(b) $\frac{2}{5}$
The whole ribbon is $\frac{5}{5}$. Fraction left: $\frac{5}{5} - \frac{3}{5} = \frac{2}{5}$.
Marking note: Award 1 mark for part (a) correct answer, 2 marks for part (b) correct answer with working. For part (b), award 1 mark if the student writes $\frac{5}{5} - \frac{3}{5}$ but makes an arithmetic error.

Summary of Marks

Common Mistakes to Watch For

1. Adding denominators — Students may write $\frac{2}{7} + \frac{3}{7} = \frac{5}{14}$. Remind them to keep the denominator the same.
2. Confusing numerator and denominator — The numerator (top) counts the parts; the denominator (bottom) tells how many equal parts in total.
3. Not simplifying fractions — Encourage students to simplify where possible (e.g., $\frac{2}{6} = \frac{1}{3}$).
4. Comparing fractions with different denominators — At P3, most comparison questions use same denominators or same numerators. Students should not need to find common denominators at this level.
5. "Larger denominator means larger fraction" — This is only true when numerators are the same. Emphasise the counter-intuitive idea that $\frac{1}{5} < \frac{1}{3}$.