To multiply \(-116 \frac{1}{16}\) by 7, we first convert the mixed number into an improper fraction.
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Convert \(-116 \frac{1}{16}\) to an improper fraction:
\[ -116 \frac{1}{16} = -\left(116 \times 16 + 1\right)/16 = -\left(1856 + 1\right)/16 = -1857/16 \]
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Now multiply by 7:
\[ -\frac{1857}{16} \times 7 = -\frac{1857 \times 7}{16} \]
Calculate \(1857 \times 7\):
\[ 1857 \times 7 = 12999 \]
So, we have:
\[ -\frac{12999}{16} \]
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Now convert \(-\frac{12999}{16}\) into a mixed number.
Divide \(12999\) by \(16\):
\[ 12999 \div 16 = 812 \quad \text{(integer part)} \] Calculate the remainder:
\[ 12999 - (812 \times 16) = 12999 - 12992 = 7 \]
Thus, we can express \(-\frac{12999}{16}\) as:
\[ -812 \frac{7}{16} \]
The final answer, as a mixed number, is:
\[ \boxed{-812 \frac{7}{16}} \]