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 $64$: $$3995÷64\approx 62.421875$$ 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: $$10\frac{5}{8}\times 5\frac{7}{8}=62\frac{27}{64}$$