To divide the fractions \(-\frac{5}{9}\) by \(\frac{1}{5}\), you can multiply by the reciprocal of the divisor. So, this can be expressed as:
\[ -\frac{5}{9} \div \frac{1}{5} = -\frac{5}{9} \times \frac{5}{1} \]
Now, multiply the numerators and the denominators:
\[ -\frac{5 \times 5}{9 \times 1} = -\frac{25}{9} \]
Next, to convert \(-\frac{25}{9}\) into a mixed number, divide 25 by 9:
\[ 25 \div 9 = 2 \quad \text{(with a remainder of 7)} \]
So, we can express \(-\frac{25}{9}\) as:
\[ -2 \frac{7}{9} \]
Therefore, \(-\frac{5}{9} \div \frac{1}{5}\) in mixed number form is:
\[ -2 \frac{7}{9} \]
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