Educational worksheet for identifying types of fractions.

Problem Analysis:

The task involves identifying and classifying fractions into three categories:
1. Proper Fractions: Fractions where the numerator is less than the denominator.
2. Improper Fractions: Fractions where the numerator is greater than or equal to the denominator.
3. Mixed Numbers: Numbers that consist of a whole number and a proper fraction.

Solution:

#### Part A: Classify the given fractions
We will analyze each fraction and determine whether it is a proper fraction, improper fraction, or mixed number.

1. $\frac{2}{5}$
- Numerator = 2, Denominator = 5
- Since the numerator (2) is less than the denominator (5), this is a proper fraction.

2. $\frac{12}{11}$
- Numerator = 12, Denominator = 11
- Since the numerator (12) is greater than the denominator (11), this is an improper fraction.

3. $\frac{6}{4}$
- Numerator = 6, Denominator = 4
- Since the numerator (6) is greater than the denominator (4), this is an improper fraction.

4. $3 \frac{5}{8}$
- This is a mixed number because it consists of a whole number (3) and a proper fraction ($\frac{5}{8}$).
- Therefore, this is a mixed number.

5. $5 \frac{8}{9}$
- This is a mixed number because it consists of a whole number (5) and a proper fraction ($\frac{8}{9}$).
- Therefore, this is a mixed number.

6. $\frac{1}{7}$
- Numerator = 1, Denominator = 7
- Since the numerator (1) is less than the denominator (7), this is a proper fraction.

#### Final Answers for Part A:
1. $\frac{2}{5}$ → Proper Fraction
2. $\frac{12}{11}$ → Improper Fraction
3. $\frac{6}{4}$ → Improper Fraction
4. $3 \frac{5}{8}$ → Mixed Number
5. $5 \frac{8}{9}$ → Mixed Number
6. $\frac{1}{7}$ → Proper Fraction

---

#### Part B: Identify and classify each fraction
We will classify each fraction as "proper," "improper," or "mixed number."

1. $\frac{3}{10}$
- Numerator = 3, Denominator = 10
- Since the numerator (3) is less than the denominator (10), this is a proper fraction.
- Classification: Proper

2. $\frac{9}{2}$
- Numerator = 9, Denominator = 2
- Since the numerator (9) is greater than the denominator (2), this is an improper fraction.
- Classification: Improper

3. $4 \frac{1}{6}$
- This is a mixed number because it consists of a whole number (4) and a proper fraction ($\frac{1}{6}$).
- Classification: Mixed Number

4. $\frac{7}{3}$
- Numerator = 7, Denominator = 3
- Since the numerator (7) is greater than the denominator (3), this is an improper fraction.
- Classification: Improper

#### Final Answers for Part B:
| S.No | Types of Fractions | Proper | Improper | Mixed Number |
|------|--------------------|--------|----------|--------------|
| 1 | $\frac{3}{10}$ | ✓ | | |
| 2 | $\frac{9}{2}$ | | ✓ | |
| 3 | $4 \frac{1}{6}$ | | | ✓ |
| 4 | $\frac{7}{3}$ | | ✓ | |

---

Final Answer:

Part A:
1. Proper Fraction
2. Improper Fraction
3. Improper Fraction
4. Mixed Number
5. Mixed Number
6. Proper Fraction

Part B:
| S.No | Types of Fractions | Proper | Improper | Mixed Number |
|------|--------------------|--------|----------|--------------|
| 1 | $\frac{3}{10}$ | ✓ | | |
| 2 | $\frac{9}{2}$ | | ✓ | |
| 3 | $4 \frac{1}{6}$ | | | ✓ |
| 4 | $\frac{7}{3}$ | | ✓ | |

$$
\boxed{
\text{See classifications above.}
}
$$