Fraction multiplication and simplification practice worksheet.

To solve the problem, we need to multiply the fractions and then simplify the results where possible. Let's go through each step systematically.

1. First Row:

\[
\frac{2}{4} \times \frac{1}{2} = \frac{2 \times 1}{4 \times 2} = \frac{2}{8}
\]
Simplify \(\frac{2}{8}\):
\[
\frac{2}{8} = \frac{1}{4}
\]
So, the answer is:
\[
\frac{2}{8} = \frac{1}{4}
\]

2. Second Row:

\[
\frac{1}{2} \times \frac{2}{3} = \frac{1 \times 2}{2 \times 3} = \frac{2}{6}
\]
Simplify \(\frac{2}{6}\):
\[
\frac{2}{6} = \frac{1}{3}
\]
So, the answer is:
\[
\frac{2}{6} = \frac{1}{3}
\]

3. Third Row:

\[
\frac{2}{6} \times \frac{1}{2} = \frac{2 \times 1}{6 \times 2} = \frac{2}{12}
\]
Simplify \(\frac{2}{12}\):
\[
\frac{2}{12} = \frac{1}{6}
\]
So, the answer is:
\[
\frac{2}{12} = \frac{1}{6}
\]

4. Fourth Row:

\[
\frac{2}{4} \times \frac{2}{4} = \frac{2 \times 2}{4 \times 4} = \frac{4}{16}
\]
Simplify \(\frac{4}{16}\):
\[
\frac{4}{16} = \frac{1}{4}
\]
So, the answer is:
\[
\frac{4}{16} = \frac{1}{4}
\]

5. Fifth Row:

\[
\frac{2}{5} \times \frac{1}{4} = \frac{2 \times 1}{5 \times 4} = \frac{2}{20}
\]
Simplify \(\frac{2}{20}\):
\[
\frac{2}{20} = \frac{1}{10}
\]
So, the answer is:
\[
\frac{2}{20} = \frac{1}{10}
\]

6. Sixth Row:

\[
\frac{1}{3} \times \frac{3}{4} = \frac{1 \times 3}{3 \times 4} = \frac{3}{12}
\]
Simplify \(\frac{3}{12}\):
\[
\frac{3}{12} = \frac{1}{4}
\]
So, the answer is:
\[
\frac{3}{12} = \frac{1}{4}
\]

7. Seventh Row:

\[
\frac{3}{7} \times \frac{1}{3} = \frac{3 \times 1}{7 \times 3} = \frac{3}{21}
\]
Simplify \(\frac{3}{21}\):
\[
\frac{3}{21} = \frac{1}{7}
\]
So, the answer is:
\[
\frac{3}{21} = \frac{1}{7}
\]

Final Answer:

\[
\boxed{
\begin{array}{ccc}
\frac{2}{4} \times \frac{1}{2} & = & \frac{2}{8} = \frac{1}{4} \\
\frac{1}{2} \times \frac{2}{3} & = & \frac{2}{6} = \frac{1}{3} \\
\frac{2}{6} \times \frac{1}{2} & = & \frac{2}{12} = \frac{1}{6} \\
\frac{2}{4} \times \frac{2}{4} & = & \frac{4}{16} = \frac{1}{4} \\
\frac{2}{5} \times \frac{1}{4} & = & \frac{2}{20} = \frac{1}{10} \\
\frac{1}{3} \times \frac{3}{4} & = & \frac{3}{12} = \frac{1}{4} \\
\frac{3}{7} \times \frac{1}{3} & = & \frac{3}{21} = \frac{1}{7} \\
\end{array}
}
\]