To multiply \(-1 \frac{1}{6}\) by \(7\), we first convert the mixed number into an improper fraction.
\[ -1 \frac{1}{6} = -\left(1 \times 6 + 1\right)/6 = -\left(6 + 1\right)/6 = -\frac{7}{6} \]
Now we can multiply this fraction by \(7\):
\[ -\frac{7}{6} \times 7 = -\frac{7 \times 7}{6} = -\frac{49}{6} \]
Thus, \(-1 \frac{1}{6} \times 7 = -\frac{49}{6}\).
If you want to convert \(-\frac{49}{6}\) back to a mixed number:
\[ -\frac{49}{6} = -8 \frac{1}{6} \]
So, \(-1 \frac{1}{6} \times 7 = -\frac{49}{6}\) or \(-8 \frac{1}{6}\).