Primary 3 Mathematics Fractions Quiz

Primary 3 Mathematics Quiz - Fractions: Answer Key

Total Marks: 40 | Duration: 40 minutes

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Section A: Understanding Fractions

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1. Answer: $\frac{3}{8}$ [2 marks]

Explanation: A fraction shows parts of a whole. The denominator (bottom number) tells us how many equal parts the whole is divided into. The numerator (top number) tells us how many parts we are counting.

In this diagram:

• The rectangle is divided into 8 equal parts (denominator = 8)
• 3 parts are shaded (numerator = 3)
• Therefore, the fraction shaded is $\frac{3}{8}$

Common mistake: Counting unequal parts or forgetting that fractions require equal division.

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2. Answer: 3 [2 marks]

Explanation: To find equivalent fractions, we use the property that multiplying or dividing both numerator and denominator by the same number keeps the fraction equivalent.

$\frac{?}{6} = \frac{1}{2}$

Notice that the denominator changed from 2 to 6. Since $2 \times 3 = 6$, we must multiply the numerator by 3 as well:

$1 \times 3 = 3$

So $\frac{3}{6} = \frac{1}{2}$

Check: Both fractions represent the same amount — half of a whole.

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3. Answer: $\frac{3}{8}, \frac{1}{2}, \frac{5}{8}, \frac{3}{4}$ [2 marks]

Explanation: To compare fractions with different denominators, we convert them to equivalent fractions with the same denominator (a common denominator). The easiest common denominator here is 8.

• $\frac{3}{8}$ stays as $\frac{3}{8}$
• $\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}$
• $\frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8}$ (or $\frac{1 \times 2}{2 \times 2} = \frac{2}{4}$, then find equivalent)
• $\frac{5}{8}$ stays as $\frac{5}{8}$

Actually, let's use 8 throughout:

• $\frac{1}{2} = \frac{4}{8}$ ✓

Now ordering from smallest: $\frac{3}{8}, \frac{4}{8}, \frac{5}{8}, \frac{6}{8}$

So: $\frac{3}{8} < \frac{1}{2} < \frac{5}{8} < \frac{3}{4}$

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4. Answer: $\frac{2}{3}$ is larger [2 marks]

Working: Find a common denominator. The LCM of 3 and 5 is 15.

$\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}$

$\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}$

Since $\frac{10}{15} > \frac{9}{15}$, we conclude $\frac{2}{3} > \frac{3}{5}$

Concept: When denominators are the same, the fraction with the larger numerator is larger.

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5. Answer: $\frac{3}{4}$ [2 marks]

Working: $\frac{1}{4} + \frac{2}{4} = \frac{1+2}{4} = \frac{3}{4}$

Explanation: When adding fractions with the same denominator, we simply add the numerators and keep the denominator the same. The denominator tells us the size of the pieces — since both fractions use quarters, we can add them directly.

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6. Answer: $\frac{2}{3}$ [2 marks]

Working: To simplify a fraction, divide both numerator and denominator by their highest common factor (HCF).

Factors of 6: 1, 2, 3, 6 Factors of 9: 1, 3, 9 HCF of 6 and 9 = 3

$\frac{6 \div 3}{9 \div 3} = \frac{2}{3}$

Concept: A fraction is in simplest form when the numerator and denominator have no common factors other than 1.

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7. Answer: $\frac{4}{5}$ [2 marks]

Explanation: The number line from 0 to 1 is divided into 5 equal parts. Each part represents $\frac{1}{5}$.

Counting from 0:

• Point A (2nd tick): $\frac{2}{5}$
• Point B (4th tick): $\frac{4}{5}$
• Point C (1st tick): $\frac{1}{5}$

Point B is at position $\frac{4}{5}$.

Check: $\frac{4}{5}$ is close to 1, and point B is indeed near the right end of the number line.

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8. Answer: $\frac{2}{5}$ [2 marks]

Working: John ate 4 out of 10 slices: $\frac{4}{10}$

Simplify by dividing numerator and denominator by HCF = 2:

$\frac{4 \div 2}{10 \div 2} = \frac{2}{5}$

Teaching note: Always check if your answer can be simplified. A fraction should normally be given in simplest form unless otherwise stated.

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Section B: Equivalent Fractions

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9. Answer: 6 [2 marks]

Working: $\frac{2}{5} = \frac{?}{15}$

The denominator changed: $5 \times 3 = 15$

So multiply numerator by 3: $2 \times 3 = 6$

$\frac{2}{5} = \frac{6}{15}$

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10. Answer: $\frac{6}{8}$, $\frac{9}{12}$, $\frac{12}{16}$ [2 marks]

Working: Check each fraction by simplifying or cross-multiplying:

• $\frac{6}{8} = \frac{6\div2}{8\div2} = \frac{3}{4}$ ✓
• $\frac{9}{12} = \frac{9\div3}{12\div3} = \frac{3}{4}$ ✓
• $\frac{4}{3} = \frac{4}{3}$ (this is greater than 1, not equivalent) ✗
• $\frac{12}{16} = \frac{12\div4}{16\div4} = \frac{3}{4}$ ✓
• $\frac{5}{6}$ (already in simplest form, not equal to $\frac{3}{4}$) ✗

Check for $\frac{5}{6}$ vs $\frac{3}{4}$: Cross multiply: $5 \times 4 = 20$ and $3 \times 6 = 18$. Since $20 \neq 18$, they are not equal.

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11. Answer: Yes, they coloured the same fraction. [2 marks]

Explanation: Both fractions are equivalent.

$\frac{4}{10} = \frac{4 \div 2}{10 \div 2} = \frac{2}{5}$

OR

$\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}$

So Mei Ling's $\frac{4}{10}$ equals her brother's $\frac{2}{5}$.

Marking: [1 mark] for correct answer (Yes), [1 mark] for correct explanation with working.

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12. Answer: $\frac{4}{3} = \frac{8}{6} = \frac{16}{12}$ [2 marks]

Working: Start with $\frac{16}{12}$ and simplify:

$\frac{16}{12} = \frac{16 \div 4}{12 \div 4} = \frac{4}{3}$

So the first fraction is $\frac{4}{3}$.

For the middle fraction: $\frac{4}{3} = \frac{8}{?}$

Since $4 \times 2 = 8$, we need $3 \times 2 = 6$

So $\frac{8}{6}$

Check: $\frac{8}{6} = \frac{8 \div 2}{6 \div 2} = \frac{4}{3}$ ✓

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13. Answer: Bar 2 = $\frac{4}{6}$, Bar 3 = $\frac{6}{9}$ [2 marks]

Explanation: The three bars are the same total length. The shaded portions are also the same total amount.

• Bar 1: 2 out of 3 parts shaded = $\frac{2}{3}$
• Bar 2: To shade the same amount with 6 parts, we need 4 shaded parts = $\frac{4}{6}$
• Bar 3: To shade the same amount with 9 parts, we need 6 shaded parts = $\frac{6}{9}$

Pattern: $\frac{2}{3} = \frac{4}{6} = \frac{6}{9}$ — each time both numerator and denominator are multiplied by 2, then by 3.

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14. Answer: 4 stickers [2 marks]

Working:

Image pending generation: diagram for Q14.

Method: Divide 12 into 3 equal groups. $12 \div 3 = 4$

Each group represents $\frac{1}{3}$, so $\frac{1}{3}$ of 12 = 4.

Alternative: $\frac{1}{3} \times 12 = \frac{12}{3} = 4$

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Section C: Comparing and Ordering Fractions

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15. Answer: $\frac{5}{6} < \frac{7}{8}$ [2 marks]

Working: Common denominator = LCM of 6 and 8 = 24.

$\frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24}$

$\frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24}$

Since $\frac{20}{24} < \frac{21}{24}$, we have $\frac{5}{6} < \frac{7}{8}$

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16. Answer: Jug C [2 marks]

Working: Find common denominator. The LCM of 4, 3, and 6 is 12.

• Jug A: $\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$
• Jug B: $\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}$
• Jug C: $\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}$

Since $\frac{10}{12} > \frac{9}{12} > \frac{8}{12}$, Jug C has the most water.

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17. Answer: Points plotted at correct positions [2 marks]

Working: The number line has 8 equal divisions (eighths).

• $\frac{1}{2} = \frac{4}{8}$ — plot at the 4th tick mark from 0
• $\frac{3}{4} = \frac{6}{8}$ — plot at the 6th tick mark from 0
• $\frac{1}{8}$ — plot at the 1st tick mark from 0

Expected visual in answer: Three points marked and labelled on the number line:

• $\frac{1}{8}$ near the left (position 1)
• $\frac{1}{2} = \frac{4}{8}$ in the middle (position 4)
• $\frac{3}{4} = \frac{6}{8}$ further right (position 6)

Marking: [1 mark] for all three fractions converted correctly, [1 mark] for correct placement on number line.

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Section D: Word Problems

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18. (a) Answer: $\frac{1}{2}$ m or $\frac{4}{8}$ m [1 mark]

Explanation: The question states she cut off $\frac{1}{2}$ m. This is given information.

(b) Answer: $\frac{3}{8}$ [2 marks]

Working: $\frac{7}{8} - \frac{1}{2} = \frac{7}{8} - \frac{4}{8} = \frac{3}{8}$

Step by step:

1. Convert to common denominator: $\frac{1}{2} = \frac{4}{8}$
2. Subtract: $\frac{7}{8} - \frac{4}{8} = \frac{3}{8}$

Check: $\frac{3}{8} + \frac{4}{8} = \frac{7}{8}$ ✓

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19. (a) Answer: $\frac{7}{10}$ [1 mark]

Working: $\frac{2}{5} + \frac{3}{10} = \frac{4}{10} + \frac{3}{10} = \frac{7}{10}$

(b) Answer: $\frac{3}{10}$ [2 marks]

Working: The whole = 1 = $\frac{10}{10}$

$\frac{10}{10} - \frac{7}{10} = \frac{3}{10}$

Alternative: $1 - \frac{7}{10} = \frac{3}{10}$

Marking: [1 mark] for method of finding remainder from whole, [1 mark] for correct answer.

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20. (a) Answer: Tom was in the lead [2 marks]

Working: Compare $\frac{5}{6}$ and $\frac{3}{4}$

Common denominator = 12:

$\frac{5}{6} = \frac{10}{12}$

$\frac{3}{4} = \frac{9}{12}$

Since $\frac{10}{12} > \frac{9}{12}$, Tom ran further. Tom was in the lead.

Explanation: In a race, whoever has completed the larger fraction of the total distance is in the lead.

(b) Answer: $\frac{1}{4}$ [1 mark]

Working: Jerry had run $\frac{3}{4}$ of the race.

Remaining: $1 - \frac{3}{4} = \frac{1}{4}$

Or: $\frac{4}{4} - \frac{3}{4} = \frac{1}{4}$

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End of Answer Key