To find the quotient of \(-\frac{5}{9}\) divided by \(\frac{1}{5}\), we can multiply \(-\frac{5}{9}\) by the reciprocal of \(\frac{1}{5}\).
The reciprocal of \(\frac{1}{5}\) is \(5\). Therefore, we have:
\[ -\frac{5}{9} \div \frac{1}{5} = -\frac{5}{9} \times 5 \]
Now, we can multiply:
\[ -\frac{5 \cdot 5}{9} = -\frac{25}{9} \]
Next, we can convert \(-\frac{25}{9}\) into a mixed number. We divide \(25\) by \(9\):
\[ 25 \div 9 = 2 \quad \text{(since \(9 \times 2 = 18\))} \] with a remainder of \(25 - 18 = 7\).
Thus, we can write:
\[ -\frac{25}{9} = -2 \frac{7}{9} \]
Therefore, the quotient of \(-\frac{5}{9}\) divided by \(\frac{1}{5}\) as a mixed number is:
\[ \boxed{-2 \frac{7}{9}} \]
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