To solve the division of fractions, we can multiply by the reciprocal. Here’s how you can simplify \(-\frac{5}{9} \div \frac{1}{5}\):
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Rewrite the division as multiplication by the reciprocal of \(\frac{1}{5}\): \[ -\frac{5}{9} \div \frac{1}{5} = -\frac{5}{9} \times 5 \]
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Multiply: \[ -\frac{5 \times 5}{9} = -\frac{25}{9} \]
Now, to convert \(-\frac{25}{9}\) into a mixed number:
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Divide \(25\) by \(9\): \(25 \div 9 = 2\) with a remainder of \(7\).
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The mixed number is: \[ -2 \frac{7}{9} \]
Thus, the quotient of \(-\frac{5}{9} \div \frac{1}{5}\) as a mixed number is \(-2 \frac{7}{9}\).