Question

10 5/8 x 5 7/8

Answer 1

To multiply the two mixed numbers \(10 \frac{5}{8}\) and \(5 \frac{7}{8}\), we can convert them into improper fractions first.

1. Convert \(10 \frac{5}{8}\):
\[
10 \frac{5}{8} = \frac{10 \times 8 + 5}{8} = \frac{80 + 5}{8} = \frac{85}{8}
\]

2. Convert \(5 \frac{7}{8}\):
\[
5 \frac{7}{8} = \frac{5 \times 8 + 7}{8} = \frac{40 + 7}{8} = \frac{47}{8}
\]

Now, we multiply the two improper fractions:
\[
\frac{85}{8} \times \frac{47}{8} = \frac{85 \times 47}{8 \times 8} = \frac{3995}{64}
\]

Next, we can convert \(\frac{3995}{64}\) back into a mixed number.

First, divide \(3995\) by \(64\):
\[
3995 \div 64 \approx 62.421875
\]
The whole number part is \(62\).

Now, we calculate the remainder:
\[
64 \times 62 = 3968
\]
\[
3995 - 3968 = 27
\]

Thus, we can express \(\frac{3995}{64}\) as a mixed number:
\[
\frac{3995}{64} = 62 \frac{27}{64}
\]

So, the final answer is:
\[
10 \frac{5}{8} \times 5 \frac{7}{8} = 62 \frac{27}{64}
\]