To multiply \(-1 \frac{1}{6}\) by \(7\), follow these steps:
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Convert the mixed number \(-1 \frac{1}{6}\) into an improper fraction. \[ -1 \frac{1}{6} = -\left(1 \times 6 + 1\right)/6 = -\frac{7}{6} \]
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Now multiply this by \(7\): \[ -\frac{7}{6} \times 7 = -\frac{7 \times 7}{6} = -\frac{49}{6} \]
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Convert \(-\frac{49}{6}\) back into a mixed number:
- Divide \(49\) by \(6\): \[ 49 \div 6 = 8 \quad \text{(remainder } 1\text{)} \]
- So, \(-\frac{49}{6} = -8 \frac{1}{6}\).
Therefore, the answer is: \[ \boxed{-8 \frac{1}{6}} \]