To divide \(-\frac{5}{10}\) by \(\frac{3}{4}\), you can multiply by the reciprocal of \(\frac{3}{4}\):
\[ -\frac{5}{10} \div \frac{3}{4} = -\frac{5}{10} \times \frac{4}{3} \]
Now, multiply the numerators and the denominators:
\[ = -\frac{5 \times 4}{10 \times 3} = -\frac{20}{30} \]
Now simplify \(-\frac{20}{30}\):
\[ -\frac{20 \div 10}{30 \div 10} = -\frac{2}{3} \]
Thus, the answer is negative 2 thirds.