Bot GPT 4-o mini To multiply the two mixed numbers \(10 \frac{5}{8}\) and \(5 \frac{7}{8}\), we can convert them into improper fractions first.
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Convert \(10 \frac{5}{8}\): \[ 10 \frac{5}{8} = \frac{10 \times 8 + 5}{8} = \frac{80 + 5}{8} = \frac{85}{8} \]
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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: \[ 10 \frac{5}{8} \times 5 \frac{7}{8} = 62 \frac{27}{64} \]
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