Educational worksheet teaching students to identify proper, improper, and mixed fractions with examples and practice problems.

Problem Overview:

The task is to classify the given fractions as proper, improper, or mixed numbers based on their definitions:

1. Proper Fraction: The numerator is smaller than the denominator.
2. Improper Fraction: The numerator is larger than or equal to the denominator.
3. Mixed Number: A number that includes both a whole number and a fraction.

Given Fractions:

We need to classify the following fractions:
- \( \frac{9}{10} \)
- \( 1 \frac{2}{3} \)
- \( 2 \frac{1}{3} \)
- \( \frac{100}{2} \)
- \( \frac{9}{7} \)
- \( \frac{8}{15} \)
- \( \frac{6}{3} \)
- \( 9 \frac{1}{2} \)

Solution:

#### 1. \( \frac{9}{10} \)
- Numerator: 9
- Denominator: 10
- Since the numerator (9) is smaller than the denominator (10), this is a proper fraction.

#### 2. \( 1 \frac{2}{3} \)
- This is a mixed number because it includes a whole number (1) and a fraction (\( \frac{2}{3} \)).
- Classification: Mixed Number

#### 3. \( 2 \frac{1}{3} \)
- This is also a mixed number because it includes a whole number (2) and a fraction (\( \frac{1}{3} \)).
- Classification: Mixed Number

#### 4. \( \frac{100}{2} \)
- Numerator: 100
- Denominator: 2
- Since the numerator (100) is larger than the denominator (2), this is an improper fraction.

#### 5. \( \frac{9}{7} \)
- Numerator: 9
- Denominator: 7
- Since the numerator (9) is larger than the denominator (7), this is an improper fraction.

#### 6. \( \frac{8}{15} \)
- Numerator: 8
- Denominator: 15
- Since the numerator (8) is smaller than the denominator (15), this is a proper fraction.

#### 7. \( \frac{6}{3} \)
- Numerator: 6
- Denominator: 3
- Since the numerator (6) is larger than the denominator (3), this is an improper fraction.

#### 8. \( 9 \frac{1}{2} \)
- This is a mixed number because it includes a whole number (9) and a fraction (\( \frac{1}{2} \)).
- Classification: Mixed Number

Final Classification:

| Fraction | Classification |
|----------------|----------------|
| \( \frac{9}{10} \) | Proper |
| \( 1 \frac{2}{3} \) | Mixed Number |
| \( 2 \frac{1}{3} \) | Mixed Number |
| \( \frac{100}{2} \) | Improper |
| \( \frac{9}{7} \) | Improper |
| \( \frac{8}{15} \) | Proper |
| \( \frac{6}{3} \) | Improper |
| \( 9 \frac{1}{2} \) | Mixed Number |

Final Answer:

\[
\boxed{
\begin{array}{|c|c|}
\hline
\text{Fraction} & \text{Classification} \\
\hline
\frac{9}{10} & \text{Proper} \\
1 \frac{2}{3} & \text{Mixed Number} \\
2 \frac{1}{3} & \text{Mixed Number} \\
\frac{100}{2} & \text{Improper} \\
\frac{9}{7} & \text{Improper} \\
\frac{8}{15} & \text{Proper} \\
\frac{6}{3} & \text{Improper} \\
9 \frac{1}{2} & \text{Mixed Number} \\
\hline
\end{array}
}
\]