To find the quotient when dividing \(-\frac{3}{4}\) by \(\frac{3}{8}\), you can multiply by the reciprocal of the divisor.
The reciprocal of \(\frac{3}{8}\) is \(\frac{8}{3}\).
Now, perform the multiplication:
\[ -\frac{3}{4} \div \frac{3}{8} = -\frac{3}{4} \times \frac{8}{3} \]
Next, multiply the fractions:
\[ -\frac{3 \times 8}{4 \times 3} = -\frac{24}{12} \]
Now simplify \(-\frac{24}{12}\):
\[ -\frac{24}{12} = -2 \]
Thus, the quotient when \(-\frac{3}{4}\) is divided by \(\frac{3}{8}\) is \(-2\).