To divide \(-\frac{5}{10}\) by \(\frac{3}{4}\), you can multiply \(-\frac{5}{10}\) by the reciprocal of \(\frac{3}{4}\).
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First, simplify \(-\frac{5}{10}\): \[ -\frac{5}{10} = -\frac{1}{2} \]
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Now multiply by the reciprocal of \(\frac{3}{4}\), which is \(\frac{4}{3}\): \[ -\frac{1}{2} \times \frac{4}{3} = -\frac{1 \cdot 4}{2 \cdot 3} = -\frac{4}{6} \]
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Simplify \(-\frac{4}{6}\): \[ -\frac{4}{6} = -\frac{2}{3} \]
So, the result of dividing \(-\frac{5}{10}\) by \(\frac{3}{4}\) is \(-\frac{2}{3}\).
The correct answer is \(-2/3\) (negative 2 thirds).