Question

Multiply.

3 3/5×8 3/4

Enter your answer in the box as a mixed number in simplest form.

Answer 1

To multiply the mixed numbers \( 3 \frac{3}{5} \) and \( 8 \frac{3}{4} \), we start by converting them into improper fractions.

1. Convert \( 3 \frac{3}{5} \):
\[
3 \frac{3}{5} = 3 \times 5 + 3 = 15 + 3 = 18 \quad \text{(so, } 3\frac{3}{5} = \frac{18}{5}\text{)}
\]

2. Convert \( 8 \frac{3}{4} \):
\[
8 \frac{3}{4} = 8 \times 4 + 3 = 32 + 3 = 35 \quad \text{(so, } 8\frac{3}{4} = \frac{35}{4}\text{)}
\]

Now we can multiply the improper fractions:
\[
\frac{18}{5} \times \frac{35}{4} = \frac{18 \times 35}{5 \times 4}
\]

Calculating the numerator:
\[
18 \times 35 = 630
\]

Calculating the denominator:
\[
5 \times 4 = 20
\]

So, we have:
\[
\frac{630}{20}
\]

Next, we simplify this fraction. We can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 10:
\[
\frac{630 \div 10}{20 \div 10} = \frac{63}{2}
\]

Now, converting \( \frac{63}{2} \) back to a mixed number:
- Divide 63 by 2:
\[
63 \div 2 = 31 \quad \text{(remainder } 1\text{)}
\]

Thus, \( \frac{63}{2} = 31 \frac{1}{2} \).

Putting it all together, the answer is:
\[
\boxed{31 \frac{1}{2}}
\]