To divide \(-\frac{5}{10}\) by \(\frac{3}{4}\), you can multiply \(-\frac{5}{10}\) by the reciprocal of \(\frac{3}{4}\). The reciprocal of \(\frac{3}{4}\) is \(\frac{4}{3}\).
Now, perform the multiplication:
\[ -\frac{5}{10} \times \frac{4}{3} \]
First, simplify \(-\frac{5}{10}\):
\[ -\frac{5}{10} = -\frac{1}{2} \]
So, the expression becomes:
\[ -\frac{1}{2} \times \frac{4}{3} \]
Now, multiply the fractions:
\[ -\frac{1 \times 4}{2 \times 3} = -\frac{4}{6} \]
Next, simplify \(-\frac{4}{6}\):
\[ -\frac{4}{6} = -\frac{2}{3} \]
Therefore, the result of \(-\frac{5}{10}\) divided by \(\frac{3}{4}\) is:
\[ -\frac{2}{3} \]