Comparing Fractions Worksheet with Visuals and Symbols

To solve the problem, we need to compare the fractions given in each pair and determine whether one fraction is greater than, less than, or equal to the other. We will use the visual representations provided in the image to help us understand the comparisons.

Step-by-Step Solution:

#### First Row:
1. $\frac{1}{2} \quad \boxed{>} \quad \frac{1}{3}$
- The first circle is divided into 2 parts, with 1 part shaded.
- The second circle is divided into 3 parts, with 1 part shaded.
- Clearly, $\frac{1}{2}$ is larger than $\frac{1}{3}$ because the shaded portion of the first circle is larger.

2. $\frac{4}{12} \quad \boxed{<} \quad \frac{2}{4}$
- The first circle is divided into 12 parts, with 4 parts shaded.
- The second circle is divided into 4 parts, with 2 parts shaded.
- Simplify $\frac{4}{12}$ to $\frac{1}{3}$ and $\frac{2}{4}$ to $\frac{1}{2}$.
- Clearly, $\frac{1}{3}$ is smaller than $\frac{1}{2}$.

#### Second Row:
3. $\frac{3}{4} \quad \boxed{>} \quad \frac{2}{3}$
- The first circle is divided into 4 parts, with 3 parts shaded.
- The second circle is divided into 3 parts, with 2 parts shaded.
- To compare, find a common denominator (12):
- $\frac{3}{4} = \frac{9}{12}$
- $\frac{2}{3} = \frac{8}{12}$
- Clearly, $\frac{9}{12}$ is larger than $\frac{8}{12}$.

4. $\frac{6}{12} \quad \boxed{=} \quad \frac{3}{8}$
- The first circle is divided into 12 parts, with 6 parts shaded.
- The second circle is divided into 8 parts, with 3 parts shaded.
- Simplify $\frac{6}{12}$ to $\frac{1}{2}$.
- Compare $\frac{1}{2}$ and $\frac{3}{8}$:
- Convert $\frac{1}{2}$ to $\frac{4}{8}$.
- Clearly, $\frac{4}{8}$ is not equal to $\frac{3}{8}$.
- Correct comparison: $\frac{6}{12} = \frac{1}{2}$ and $\frac{3}{8}$ is less than $\frac{1}{2}$, so the correct answer should be $\frac{6}{12} > \frac{3}{8}$.

#### Third Row:
5. $\frac{1}{2} \quad \boxed{<} \quad \frac{3}{4}$
- The first circle is divided into 2 parts, with 1 part shaded.
- The second circle is divided into 4 parts, with 3 parts shaded.
- Clearly, $\frac{1}{2}$ is smaller than $\frac{3}{4}$ because the shaded portion of the second circle is larger.

6. $\frac{2}{4} \quad \boxed{>} \quad \frac{2}{5}$
- The first circle is divided into 4 parts, with 2 parts shaded.
- The second circle is divided into 5 parts, with 2 parts shaded.
- Simplify $\frac{2}{4}$ to $\frac{1}{2}$.
- Compare $\frac{1}{2}$ and $\frac{2}{5}$:
- Convert $\frac{1}{2}$ to $\frac{5}{10}$ and $\frac{2}{5}$ to $\frac{4}{10}$.
- Clearly, $\frac{5}{10}$ is larger than $\frac{4}{10}$.

Final Answer:

\[
\boxed{
\begin{array}{cc}
\frac{1}{2} > \frac{1}{3} & \frac{4}{12} < \frac{2}{4} \\
\frac{3}{4} > \frac{2}{3} & \frac{6}{12} > \frac{3}{8} \\
\frac{1}{2} < \frac{3}{4} & \frac{2}{4} > \frac{2}{5}
\end{array}
}
\]