To multiply \(-1 \frac{1}{6}\) by \(7\), first convert the mixed number into an improper fraction.
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Convert \(-1 \frac{1}{6}\) to an improper fraction: \[ -1 \frac{1}{6} = -\left(1 \cdot 6 + 1\right)/6 = -\left(6 + 1\right)/6 = -7/6 \]
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Now, multiply \(-\frac{7}{6}\) by \(7\): \[ -\frac{7}{6} \cdot 7 = -\frac{7 \cdot 7}{6} = -\frac{49}{6} \]
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Convert \(-\frac{49}{6}\) back to a mixed number: \(-\frac{49}{6}\) can be expressed as:
- Divide \(49\) by \(6\) which gives \(8\) with a remainder of \(1\): \[ 49 \div 6 = 8 \quad \text{(whole number)} \] \[ 49 - (8 \times 6) = 49 - 48 = 1 \quad \text{(remainder)} \]
Thus, \(-\frac{49}{6} = -8 \frac{1}{6}\).
Therefore, the answer is: \[ \boxed{-8 \frac{1}{6}} \]
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