To divide \(-7 \frac{1}{5}\) by \(\frac{4}{5}\), we first convert the mixed number into an improper fraction.
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Convert \(-7 \frac{1}{5}\): \[ -7 \frac{1}{5} = -\left(7 \times 5 + 1\right)/5 = -\left(35 + 1\right)/5 = -\frac{36}{5} \]
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Now, we divide by \(\frac{4}{5}\). Dividing by a fraction is the same as multiplying by its reciprocal: \[ -\frac{36}{5} \div \frac{4}{5} = -\frac{36}{5} \times \frac{5}{4} \]
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Multiply the fractions: \[ -\frac{36 \cdot 5}{5 \cdot 4} = -\frac{36}{4} \]
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Simplify \(-\frac{36}{4}\): \[ -\frac{36}{4} = -9 \]
Thus, \(-7 \frac{1}{5}\) divided by \(\frac{4}{5}\) is \(-9\).
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