To find the quotient when dividing \(-2 \frac{3}{5}\) by \(\frac{4}{5}\), first convert \(-2 \frac{3}{5}\) into an improper fraction.
\[ -2 \frac{3}{5} = -\left(2 \times 5 + 3\right)/5 = -\left(10 + 3\right)/5 = -\frac{13}{5} \]
Now, to divide by \(\frac{4}{5}\), you can multiply by the reciprocal of \(\frac{4}{5}\):
\[ -\frac{13}{5} \div \frac{4}{5} = -\frac{13}{5} \times \frac{5}{4} \]
Now, simplify the multiplication:
\[ -\frac{13 \times 5}{5 \times 4} = -\frac{13}{4} \]
The result can also be written as:
\[ -\frac{13}{4} = -3\frac{1}{4} \]
Thus, the quotient when you divide \(-2 \frac{3}{5}\) by \(\frac{4}{5}\) is:
\(-3 \frac{1}{4}\)
So, the correct response from the options provided is:
\(-3 \frac{1}{4}\) which is represented as \(-314\).