To multiply the mixed number \(9 \frac{7}{8}\) by \(7\), we first convert the mixed number into an improper fraction.
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Convert \(9 \frac{7}{8}\) to an improper fraction: \[ 9 \frac{7}{8} = \frac{9 \times 8 + 7}{8} = \frac{72 + 7}{8} = \frac{79}{8} \]
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Now, multiply \(\frac{79}{8}\) by \(7\): \[ \frac{79}{8} \times 7 = \frac{79 \times 7}{8} \]
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Calculate \(79 \times 7\): \[ 79 \times 7 = 553 \]
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So, we have: \[ \frac{79 \times 7}{8} = \frac{553}{8} \]
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Now, convert \(\frac{553}{8}\) to a mixed number:
- Divide \(553\) by \(8\): \[ 553 \div 8 = 69 \quad \text{(quotient)} \quad \text{with a remainder of } 1 \]
Thus, \(553 = 8 \times 69 + 1\).
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Therefore, the mixed number is: \[ 69 \frac{1}{8} \]
The answer to \(9 \frac{7}{8} \times 7\) is: \[ \frac{553}{8} \quad \text{or} \quad 69 \frac{1}{8} \]