Proper and Improper Fractions Worksheets - Free Printable

Problem Analysis:

The task involves identifying proper and improper fractions and answering statements about them. Let's break it down step by step.

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#### Part A: Circle the proper fractions.
A proper fraction is a fraction where the numerator (top number) is less than the denominator (bottom number).

Given fractions:
1. \( \frac{7}{10} \)
2. \( \frac{2}{9} \)
3. \( \frac{12}{11} \)
4. \( \frac{5}{2} \)
5. \( \frac{9}{4} \)
6. \( \frac{3}{14} \)
7. \( \frac{1}{2} \)

- \( \frac{7}{10} \): Numerator (7) < Denominator (10) → Proper fraction.
- \( \frac{2}{9} \): Numerator (2) < Denominator (9) → Proper fraction.
- \( \frac{12}{11} \): Numerator (12) > Denominator (11) → Improper fraction.
- \( \frac{5}{2} \): Numerator (5) > Denominator (2) → Improper fraction.
- \( \frac{9}{4} \): Numerator (9) > Denominator (4) → Improper fraction.
- \( \frac{3}{14} \): Numerator (3) < Denominator (14) → Proper fraction.
- \( \frac{1}{2} \): Numerator (1) < Denominator (2) → Proper fraction.

Proper fractions to circle: \( \frac{7}{10}, \frac{2}{9}, \frac{3}{14}, \frac{1}{2} \).

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#### Part B: Circle the improper fractions.
An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

Given fractions:
1. \( \frac{5}{4} \)
2. \( \frac{13}{12} \)
3. \( \frac{2}{3} \)
4. \( \frac{15}{8} \)
5. \( \frac{5}{6} \)
6. \( \frac{8}{7} \)
7. \( \frac{11}{5} \)

- \( \frac{5}{4} \): Numerator (5) > Denominator (4) → Improper fraction.
- \( \frac{13}{12} \): Numerator (13) > Denominator (12) → Improper fraction.
- \( \frac{2}{3} \): Numerator (2) < Denominator (3) → Proper fraction.
- \( \frac{15}{8} \): Numerator (15) > Denominator (8) → Improper fraction.
- \( \frac{5}{6} \): Numerator (5) < Denominator (6) → Proper fraction.
- \( \frac{8}{7} \): Numerator (8) > Denominator (7) → Improper fraction.
- \( \frac{11}{5} \): Numerator (11) > Denominator (5) → Improper fraction.

Improper fractions to circle: \( \frac{5}{4}, \frac{13}{12}, \frac{15}{8}, \frac{8}{7}, \frac{11}{5} \).

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#### Part C: Read each statement and check “Yes” or “No” as appropriate.
1. Statement 1: \( \frac{3}{4} \) is a proper fraction.
- Numerator (3) < Denominator (4) → Proper fraction.
- Answer: Yes

2. Statement 2: \( \frac{9}{8} \) is not an improper fraction.
- Numerator (9) > Denominator (8) → Improper fraction.
- The statement says it is not an improper fraction, which is false.
- Answer: No

3. Statement 3: \( \frac{10}{7} \) is an improper fraction.
- Numerator (10) > Denominator (7) → Improper fraction.
- Answer: Yes

4. Statement 4: \( \frac{14}{13} \) is a proper fraction.
- Numerator (14) > Denominator (13) → Improper fraction.
- The statement says it is a proper fraction, which is false.
- Answer: No

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Final Answers:

- Part A: Circle \( \frac{7}{10}, \frac{2}{9}, \frac{3}{14}, \frac{1}{2} \).
- Part B: Circle \( \frac{5}{4}, \frac{13}{12}, \frac{15}{8}, \frac{8}{7}, \frac{11}{5} \).
- Part C:
1. Yes
2. No
3. Yes
4. No

Boxed Final Answer:
\[
\boxed{
\text{A) } \frac{7}{10}, \frac{2}{9}, \frac{3}{14}, \frac{1}{2}; \quad
\text{B) } \frac{5}{4}, \frac{13}{12}, \frac{15}{8}, \frac{8}{7}, \frac{11}{5}; \quad
\text{C) } \text{Yes, No, Yes, No}
}
\]