Question

10 1/2 x 7 6/7

Answer 1

To multiply \(10 \frac{1}{2}\) by \(7 \frac{6}{7}\), we first convert the mixed numbers into improper fractions.

1. Convert \(10 \frac{1}{2}\):
\[
10 \frac{1}{2} = 10 \times 2 + 1 = 20 + 1 = 21 \quad \text{(so, } 10 \frac{1}{2} = \frac{21}{2} \text{)}
\]

2. Convert \(7 \frac{6}{7}\):
\[
7 \frac{6}{7} = 7 \times 7 + 6 = 49 + 6 = 55 \quad \text{(so, } 7 \frac{6}{7} = \frac{55}{7} \text{)}
\]

Now, multiply the two improper fractions:
\[
\frac{21}{2} \times \frac{55}{7} = \frac{21 \times 55}{2 \times 7} = \frac{1155}{14}
\]

Next, we can convert \(\frac{1155}{14}\) back into a mixed number:

1. Divide \(1155\) by \(14\):
\[
1155 \div 14 \approx 82.5
\]
The integer part is \(82\) and to find the remainder:
\[
82 \times 14 = 1148
\]
\[
1155 - 1148 = 7
\]

Thus, the final result as a mixed number is:
\[
82 \frac{7}{14}
\]

We can simplify \(\frac{7}{14}\) to \(\frac{1}{2}\):
\[
82 \frac{7}{14} = 82 \frac{1}{2}
\]

So, the final answer is:
\[
\boxed{82 \frac{1}{2}}
\]