To find the quotient of \(-\frac{5}{9}\) divided by \(\frac{1}{5}\), you can multiply \(-\frac{5}{9}\) by the reciprocal of \(\frac{1}{5}\). The reciprocal of \(\frac{1}{5}\) is \(5\). So the expression becomes:
\[ -\frac{5}{9} \div \frac{1}{5} = -\frac{5}{9} \times 5 \]
Now, multiply \(-\frac{5}{9}\) by \(5\):
\[ -\frac{5 \times 5}{9} = -\frac{25}{9} \]
So, the quotient of \(-\frac{5}{9}\) divided by \(\frac{1}{5}\) is \(-\frac{25}{9}\).
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