To divide \(-2 \frac{3}{5}\) by \(\frac{4}{5}\), you first need to convert the mixed number into an improper fraction.
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Convert \(-2 \frac{3}{5}\) to an improper fraction:
\[ -2 \frac{3}{5} = -\left(2 \times 5 + 3\right)/5 = -\left(10 + 3\right)/5 = -\frac{13}{5} \]
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Now divide \(-\frac{13}{5}\) by \(\frac{4}{5}\):
\[ -\frac{13}{5} \div \frac{4}{5} \] To divide by a fraction, we multiply by its reciprocal:
\[ -\frac{13}{5} \times \frac{5}{4} = -\frac{13 \times 5}{5 \times 4} = -\frac{13}{4} \]
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Therefore, the final result is \(-\frac{13}{4}\), which can also be expressed as \(-3 \frac{1}{4}\) as a mixed number.
Looking at the provided options, the correct response is:
−314 (which represents \(-3 \frac{1}{4}\)).