Comparing Fractions Worksheet with Visual Aids and Inequality Symbols

To solve the problem, we need to compare the fractions given in the worksheet. We will use the symbols \( > \), \( < \), or \( = \) to indicate the relationship between each pair of fractions. Let's go through each comparison step by step.

First Row:

1. \(\frac{1}{2} \quad ? \quad \frac{1}{3}\)
- \(\frac{1}{2}\) means 1 part out of 2.
- \(\frac{1}{3}\) means 1 part out of 3.
- Since \(\frac{1}{2}\) is larger than \(\frac{1}{3}\), we have:
\[
\frac{1}{2} > \frac{1}{3}
\]

2. \(\frac{4}{12} \quad ? \quad \frac{2}{4}\)
- Simplify \(\frac{4}{12}\):
\[
\frac{4}{12} = \frac{1}{3}
\]
- Simplify \(\frac{2}{4}\):
\[
\frac{2}{4} = \frac{1}{2}
\]
- Since \(\frac{1}{3}\) is smaller than \(\frac{1}{2}\), we have:
\[
\frac{4}{12} < \frac{2}{4}
\]

Second Row:

3. \(\frac{3}{4} \quad ? \quad \frac{2}{3}\)
- Convert both fractions to a common denominator (12):
\[
\frac{3}{4} = \frac{9}{12}, \quad \frac{2}{3} = \frac{8}{12}
\]
- Since \(\frac{9}{12}\) is larger than \(\frac{8}{12}\), we have:
\[
\frac{3}{4} > \frac{2}{3}
\]

4. \(\frac{6}{12} \quad ? \quad \frac{3}{8}\)
- Simplify \(\frac{6}{12}\):
\[
\frac{6}{12} = \frac{1}{2}
\]
- Convert \(\frac{1}{2}\) and \(\frac{3}{8}\) to a common denominator (8):
\[
\frac{1}{2} = \frac{4}{8}, \quad \frac{3}{8} = \frac{3}{8}
\]
- Since \(\frac{4}{8}\) is larger than \(\frac{3}{8}\), we have:
\[
\frac{6}{12} > \frac{3}{8}
\]

Third Row:

5. \(\frac{1}{2} \quad ? \quad \frac{3}{4}\)
- Convert both fractions to a common denominator (4):
\[
\frac{1}{2} = \frac{2}{4}, \quad \frac{3}{4} = \frac{3}{4}
\]
- Since \(\frac{2}{4}\) is smaller than \(\frac{3}{4}\), we have:
\[
\frac{1}{2} < \frac{3}{4}
\]

6. \(\frac{2}{4} \quad ? \quad \frac{2}{5}\)
- Simplify \(\frac{2}{4}\):
\[
\frac{2}{4} = \frac{1}{2}
\]
- Convert \(\frac{1}{2}\) and \(\frac{2}{5}\) to a common denominator (10):
\[
\frac{1}{2} = \frac{5}{10}, \quad \frac{2}{5} = \frac{4}{10}
\]
- Since \(\frac{5}{10}\) is larger than \(\frac{4}{10}\), we have:
\[
\frac{2}{4} > \frac{2}{5}
\]

Final Answers:

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