Let's solve each of the first 5 questions from your quiz step by step and explain the reasoning.
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Question 1: Reduce the following fraction:
16/20 = ?
To reduce a fraction, we divide both the numerator and denominator by their
greatest common divisor (GCD).
- GCD of 16 and 20 is
4.
- Divide both by 4:
$$
\frac{16 ÷ 4}{20 ÷ 4} = \frac{4}{5}
$$
✔ Answer: A) 4/5
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Question 2: Write the improper fraction as a mixed number
12/4 = ?
An improper fraction has a numerator greater than or equal to the denominator. To convert it to a mixed number:
- Divide 12 ÷ 4 = 3 with no remainder.
- So, $ \frac{12}{4} = 3 $
✔ Answer: D) 3
> Note: Option C is just "4", which is incorrect. Option B is 3¹⁄₄ — that would be 3 + 1/4 = 13/4, not 12/4.
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Question 3: Write the improper fraction as a mixed number
22/3 = ?
Divide 22 by 3:
- 3 × 7 = 21 → quotient = 7
- Remainder = 22 - 21 = 1
- So, $ \frac{22}{3} = 7 \frac{1}{3} $
✔ Answer: A) 7¹⁄₃
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Question 4: Write the improper fraction as a mixed number
36/4 = ?
Divide 36 ÷ 4 = 9 exactly.
So, $ \frac{36}{4} = 9 $
✔ Answer: A) 9
> Note: Option B is 8⁴⁄₄, but ⁴⁄₄ = 1, so 8⁴⁄₄ = 9 — technically correct, but
simplified form is just 9, and since ⁴⁄₄ reduces to 1, this is redundant.
But among choices:
- A) 9
✔ (correct and simplified)
- B) 8⁴⁄₄ = 9, but it's not simplified
- C) 9¹⁄₄ = 9.25
✘
- D) 9³⁄₄ = 9.75
✘
So best answer is
A) 9
✔ Answer: A) 9
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Question 5: Which symbol is correct for these two fractions?
$$
\frac{1}{2} \quad \boxed{\phantom{=}} \quad \frac{1}{3}
$$
We need to compare $ \frac{1}{2} $ and $ \frac{1}{3} $
- Convert to common denominator: LCM of 2 and 3 is 6
- $ \frac{1}{2} = \frac{3}{6} $
- $ \frac{1}{3} = \frac{2}{6} $
- Since $ \frac{3}{6} > \frac{2}{6} $, then $ \frac{1}{2} > \frac{1}{3} $
✔ Answer: B) >
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✔ Final Answers Summary:
| Question | Answer |
|--------|--------|
| 1 | A) 4/5 |
| 2 | D) 3 |
| 3 | A) 7¹⁄₃ |
| 4 | A) 9 |
| 5 | B) > |
Let me know if you'd like help with the rest of the quiz!
Parent Tip: Review the logic above to help your child master the concept of test 5th grade math worksheet.