To multiply \(-116 \frac{1}{6}\) by \(7\), we first need to convert the mixed number into an improper fraction.
-
Convert \(-116 \frac{1}{6}\) into an improper fraction: \[ -116 \frac{1}{6} = -\left(116 \times 6 + 1\right)/6 = -\left(696 + 1\right)/6 = -\frac{697}{6} \]
-
Now, multiply by \(7\): \[ -\frac{697}{6} \times 7 = -\frac{697 \times 7}{6} = -\frac{4879}{6} \]
-
Next, convert \(-\frac{4879}{6}\) back into a mixed number:
- Divide \(4879\) by \(6\): \[ 4879 \div 6 = 813 \quad \text{(the quotient)} \] \[ 4879 - (813 \times 6) = 4879 - 4878 = 1 \quad \text{(the remainder)} \]
Therefore, we can express \(-\frac{4879}{6}\) as: \[ -813 \frac{1}{6} \]
So, the final answer is: \[ \boxed{-813 \frac{1}{6}} \]