To multiply \(-1 \frac{1}{6}\) by \(7\), we first convert the mixed number to an improper fraction.
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Convert \(-1 \frac{1}{6}\) to an improper fraction: \[ -1 \frac{1}{6} = -\left(1 \times 6 + 1\right) / 6 = -\frac{7}{6} \]
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Now multiply \(-\frac{7}{6}\) by \(7\): \[ -\frac{7}{6} \times 7 = -\frac{7 \times 7}{6} = -\frac{49}{6} \]
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Convert \(-\frac{49}{6}\) to a mixed number:
- Divide \(49\) by \(6\):
- \(49 \div 6 = 8\) remainder \(1\).
- So, \(-\frac{49}{6} = -8 \frac{1}{6}\).
- Divide \(49\) by \(6\):
Therefore, the final answer is: \[ \boxed{-8 \frac{1}{6}} \]