Math worksheet for comparing unit fractions using visual fraction strips and inequality symbols.

Problem Analysis:

The task involves comparing unit fractions using the symbols > (greater than) and < (less than). Unit fractions are fractions with a numerator of 1, such as \( \frac{1}{2} \), \( \frac{1}{3} \), \( \frac{1}{4} \), etc. The goal is to determine which fraction is larger or smaller by analyzing their denominators.

#### Key Concept:
- For unit fractions, the larger the denominator, the smaller the fraction. This is because the whole is divided into more parts, making each part smaller.
- For example:
- \( \frac{1}{2} \) is larger than \( \frac{1}{3} \) because \( \frac{1}{2} \) represents a larger portion of the whole compared to \( \frac{1}{3} \).

Step-by-Step Solution:

#### Part 1: Compare \( \frac{1}{2} \) and \( \frac{1}{3} \)
- Denominators: 2 and 3
- Since 2 is smaller than 3, \( \frac{1}{2} \) represents a larger portion of the whole than \( \frac{1}{3} \).
- Therefore, \( \frac{1}{2} > \frac{1}{3} \).

#### Part 2: Compare \( \frac{1}{4} \) and \( \frac{1}{5} \)
- Denominators: 4 and 5
- Since 4 is smaller than 5, \( \frac{1}{4} \) represents a larger portion of the whole than \( \frac{1}{5} \).
- Therefore, \( \frac{1}{4} > \frac{1}{5} \).

#### Part 3: Compare \( \frac{1}{6} \) and \( \frac{1}{7} \)
- Denominators: 6 and 7
- Since 6 is smaller than 7, \( \frac{1}{6} \) represents a larger portion of the whole than \( \frac{1}{7} \).
- Therefore, \( \frac{1}{6} > \frac{1}{7} \).

#### Part 4: Compare \( \frac{1}{8} \) and \( \frac{1}{9} \)
- Denominators: 8 and 9
- Since 8 is smaller than 9, \( \frac{1}{8} \) represents a larger portion of the whole than \( \frac{1}{9} \).
- Therefore, \( \frac{1}{8} > \frac{1}{9} \).

Final Answers:

1. \( \frac{1}{2} > \frac{1}{3} \)
2. \( \frac{1}{4} > \frac{1}{5} \)
3. \( \frac{1}{6} > \frac{1}{7} \)
4. \( \frac{1}{8} > \frac{1}{9} \)

Boxed Final Answer:

\[
\boxed{
\begin{aligned}
1. & \quad \frac{1}{2} > \frac{1}{3} \\
2. & \quad \frac{1}{4} > \frac{1}{5} \\
3. & \quad \frac{1}{6} > \frac{1}{7} \\
4. & \quad \frac{1}{8} > \frac{1}{9}
\end{aligned}
}
\]