Bot GPT 4-o mini To multiply \(10 \frac{1}{2}\) by \(7 \frac{6}{7}\), we first convert the mixed numbers into improper fractions.
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Convert \(10 \frac{1}{2}\): \[ 10 \frac{1}{2} = 10 \times 2 + 1 = 20 + 1 = 21 \quad \text{(so, } 10 \frac{1}{2} = \frac{21}{2} \text{)} \]
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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:
- 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: \[ \boxed{82 \frac{1}{2}} \]
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