To divide the fractions \(-\frac{5}{9} \div \frac{1}{5}\), we can multiply by the reciprocal of \(\frac{1}{5}\).
So,
\[ -\frac{5}{9} \div \frac{1}{5} = -\frac{5}{9} \times 5 = -\frac{5 \times 5}{9 \times 1} = -\frac{25}{9} \]
Now, we can convert \(-\frac{25}{9}\) into a mixed number.
To do this, we divide 25 by 9:
- \(25 \div 9 = 2\) with a remainder of \(7\).
So, \(-\frac{25}{9}\) can be expressed as:
\[ -2 \frac{7}{9} \]
Thus, the quotient of \(-\frac{5}{9} \div \frac{1}{5}\) as a mixed number is:
\[ -2 \frac{7}{9} \]
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