Printable math worksheet designed to help students distinguish between proper and improper fractions through multiple-choice questions.

Problem: Solving the worksheet on Proper and Improper Fractions

The task involves identifying proper fractions, improper fractions, and understanding their definitions. Let's solve each question step by step.

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#### 1. Which of the following is a proper fraction?
- Definition: A proper fraction is a fraction where the numerator (top number) is less than the denominator (bottom number).

- Options:
- a) \( \frac{17}{17} \)
- b) \( \frac{12}{17} \)
- c) \( \frac{17}{14} \)

- Analysis:
- a) \( \frac{17}{17} \): The numerator (17) is equal to the denominator (17). This is not a proper fraction.
- b) \( \frac{12}{17} \): The numerator (12) is less than the denominator (17). This is a proper fraction.
- c) \( \frac{17}{14} \): The numerator (17) is greater than the denominator (14). This is an improper fraction.

- Answer: b) \( \frac{12}{17} \)

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#### 2. Which of the following is not an improper fraction?
- Definition: An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

- Options:
- a) \( \frac{8}{23} \)
- b) \( \frac{67}{31} \)
- c) \( \frac{13}{9} \)

- Analysis:
- a) \( \frac{8}{23} \): The numerator (8) is less than the denominator (23). This is a proper fraction, not an improper fraction.
- b) \( \frac{67}{31} \): The numerator (67) is greater than the denominator (31). This is an improper fraction.
- c) \( \frac{13}{9} \): The numerator (13) is greater than the denominator (9). This is an improper fraction.

- Answer: a) \( \frac{8}{23} \)

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#### 3. What is the fraction called whose numerator is less than its denominator?
- Definition: A fraction where the numerator is less than the denominator is called a proper fraction.

- Options:
- a) Proper Fraction
- b) Improper Fraction

- Answer: a) Proper Fraction

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#### 4. Which of the following is a proper fraction?
- Definition: A proper fraction has a numerator less than the denominator.

- Options:
- a) \( \frac{16}{3} \)
- b) \( \frac{57}{3} \)
- c) \( \frac{16}{53} \)

- Analysis:
- a) \( \frac{16}{3} \): The numerator (16) is greater than the denominator (3). This is an improper fraction.
- b) \( \frac{57}{3} \): The numerator (57) is greater than the denominator (3). This is an improper fraction.
- c) \( \frac{16}{53} \): The numerator (16) is less than the denominator (53). This is a proper fraction.

- Answer: c) \( \frac{16}{53} \)

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#### 5. Which fraction can also have equal numerator and denominator?
- Definition: A fraction with an equal numerator and denominator is neither strictly proper nor strictly improper but is considered a special case (equal to 1).

- Options:
- a) Proper fraction
- b) Improper fraction

- Analysis:
- A fraction like \( \frac{7}{7} \) is equal to 1 and is classified as an improper fraction because the numerator is not less than the denominator.

- Answer: b) Improper fraction

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#### 6. Which of the following is not a proper fraction?
- Definition: A proper fraction has a numerator less than the denominator.

- Options:
- a) \( \frac{45}{12} \)
- b) \( \frac{1}{67} \)
- c) \( \frac{10}{26} \)

- Analysis:
- a) \( \frac{45}{12} \): The numerator (45) is greater than the denominator (12). This is an improper fraction.
- b) \( \frac{1}{67} \): The numerator (1) is less than the denominator (67). This is a proper fraction.
- c) \( \frac{10}{26} \): The numerator (10) is less than the denominator (26). This is a proper fraction.

- Answer: a) \( \frac{45}{12} \)

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#### 7. Which of the following is an improper fraction?
- Definition: An improper fraction has a numerator greater than or equal to the denominator.

- Options:
- a) \( \frac{19}{21} \)
- b) \( \frac{3}{19} \)
- c) \( \frac{19}{3} \)

- Analysis:
- a) \( \frac{19}{21} \): The numerator (19) is less than the denominator (21). This is a proper fraction.
- b) \( \frac{3}{19} \): The numerator (3) is less than the denominator (19). This is a proper fraction.
- c) \( \frac{19}{3} \): The numerator (19) is greater than the denominator (3). This is an improper fraction.

- Answer: c) \( \frac{19}{3} \)

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#### 8. Which of the following is a proper fraction?
- Definition: A proper fraction has a numerator less than the denominator.

- Options:
- a) \( \frac{5}{37} \)
- b) \( \frac{6}{22} \)
- c) both a & b

- Analysis:
- a) \( \frac{5}{37} \): The numerator (5) is less than the denominator (37). This is a proper fraction.
- b) \( \frac{6}{22} \): The numerator (6) is less than the denominator (22). This is a proper fraction.
- c) Both a and b are proper fractions.

- Answer: c) both a & b

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#### 9. Which of the following is not an improper fraction?
- Definition: An improper fraction has a numerator greater than or equal to the denominator.

- Options:
- a) \( \frac{45}{2} \)
- b) \( \frac{7}{10} \)
- c) \( \frac{10}{3} \)

- Analysis:
- a) \( \frac{45}{2} \): The numerator (45) is greater than the denominator (2). This is an improper fraction.
- b) \( \frac{7}{10} \): The numerator (7) is less than the denominator (10). This is a proper fraction, not an improper fraction.
- c) \( \frac{10}{3} \): The numerator (10) is greater than the denominator (3). This is an improper fraction.

- Answer: b) \( \frac{7}{10} \)

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Final Answers:

1. b) \( \frac{12}{17} \)
2. a) \( \frac{8}{23} \)
3. a) Proper Fraction
4. c) \( \frac{16}{53} \)
5. b) Improper fraction
6. a) \( \frac{45}{12} \)
7. c) \( \frac{19}{3} \)
8. c) both a & b
9. b) \( \frac{7}{10} \)

Boxed Final Answer:
\[
\boxed{
\begin{array}{ll}
1. & \text{b) } \frac{12}{17} \\
2. & \text{a) } \frac{8}{23} \\
3. & \text{a) Proper Fraction} \\
4. & \text{c) } \frac{16}{53} \\
5. & \text{b) Improper fraction} \\
6. & \text{a) } \frac{45}{12} \\
7. & \text{c) } \frac{19}{3} \\
8. & \text{c) both a & b} \\
9. & \text{b) } \frac{7}{10} \\
\end{array}
}
\]