To divide \(-\frac{5}{10}\) by \(\frac{3}{4}\), we 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:
\[ -\frac{5}{10} \times \frac{4}{3} = -\frac{5 \times 4}{10 \times 3} \]
Calculating the numerator and denominator:
\[ -\frac{20}{30} \]
Now, simplify \(-\frac{20}{30}\):
\[ -\frac{20 \div 10}{30 \div 10} = -\frac{2}{3} \]
Thus, the answer is:
\(-\frac{2}{3}\) or "negative two thirds".
So, the correct response is:
−2 thirds.
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