Question

Multiply the 2 mixed numbers below.
Be sure to show your improper fractions and the simplified answer.
2 4/5 x 1 3/7 =

Answer 1

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, \(2 \frac{4}{5} \times 1 \frac{3}{7} = 4\).