To multiply the mixed numbers \(2 \frac{4}{5}\) and \(1 \frac{3}{7}\), we first convert them to improper fractions.
Step 1: Convert mixed numbers to improper fractions.
For \(2 \frac{4}{5}\):
\[ 2 \frac{4}{5} = \frac{(2 \times 5) + 4}{5} = \frac{10 + 4}{5} = \frac{14}{5} \]
For \(1 \frac{3}{7}\):
\[ 1 \frac{3}{7} = \frac{(1 \times 7) + 3}{7} = \frac{7 + 3}{7} = \frac{10}{7} \]
Step 2: Multiply the improper fractions.
Now we multiply \(\frac{14}{5}\) by \(\frac{10}{7}\):
\[ \frac{14}{5} \times \frac{10}{7} = \frac{14 \times 10}{5 \times 7} = \frac{140}{35} \]
Step 3: Simplify the resulting fraction.
To simplify \(\frac{140}{35}\), we find the greatest common divisor (GCD) of 140 and 35, which is 35.
\[ \frac{140 \div 35}{35 \div 35} = \frac{4}{1} = 4 \]
Final Answer:
Therefore, \(2 \frac{4}{5} \times 1 \frac{3}{7} = 4\).