To find the quotient of \(-2 \frac{3}{5}\) divided by \(\frac{4}{5}\), we first convert \(-2 \frac{3}{5}\) into an improper fraction.
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Convert \(-2 \frac{3}{5}\) to an improper fraction: \[ -2 \frac{3}{5} = -\left(2 \times 5 + 3\right)/5 = -\left(10 + 3\right)/5 = -13/5 \]
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Next, we divide \(-\frac{13}{5}\) by \(\frac{4}{5}\). Dividing by a fraction is the same as multiplying by its reciprocal. So: \[ -\frac{13}{5} \div \frac{4}{5} = -\frac{13}{5} \times \frac{5}{4} \]
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Now we multiply the fractions: \[ -\frac{13 \times 5}{5 \times 4} = -\frac{13}{4} \]
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The final result, \(-\frac{13}{4}\), can be converted to a mixed number: \[ -\frac{13}{4} = -3 \frac{1}{4} \]
Thus, the quotient when you divide \(-2 \frac{3}{5}\) by \(\frac{4}{5}\) is \(\boxed{-3 \frac{1}{4}}\).