To divide \(-2 \frac{3}{5}\) by \(\frac{4}{5}\), we first convert \(-2 \frac{3}{5}\) to an improper fraction.
\[ -2 \frac{3}{5} = -\left(2 \times 5 + 3\right) / 5 = -\frac{10 + 3}{5} = -\frac{13}{5} \]
Now, we divide \(-\frac{13}{5}\) by \(\frac{4}{5}\):
\[ -\frac{13}{5} \div \frac{4}{5} = -\frac{13}{5} \times \frac{5}{4} \]
Multiply the fractions:
\[ = -\frac{13 \times 5}{5 \times 4} = -\frac{13}{4} \]
Now, let's convert \(-\frac{13}{4}\) back to a mixed number:
\(-\frac{13}{4}\) can be expressed as:
\[ -3 \frac{1}{4} \]
So, the quotient when you divide \(-2 \frac{3}{5}\) by \(\frac{4}{5}\) is:
\(-3 \frac{1}{4}\)
Thus, the correct answer is:
−3 1/4.