To solve the expression \((−2)×(1/5)÷(2/3)×(−5/6)÷(3/4)\), let's break it down step by step.
First, we can rewrite the divisions as multiplications by the reciprocal:
\[ (−2)×(1/5)×(3/2)×(−5/6)×(4/3) \]
We also need to keep track of the negative signs as we proceed. Now, let's multiply the numbers in the expression step by step:
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Start with \(−2\): \[ -2 × \frac{1}{5} = \frac{-2}{5} \]
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Now take this result and multiply by \(\frac{3}{2}\): \[ \frac{-2}{5} × \frac{3}{2} = \frac{-2 × 3}{5 × 2} = \frac{-6}{10} = \frac{-3}{5} \]
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Next, multiply by \(-\frac{5}{6}\): \[ \frac{-3}{5} × \frac{-5}{6} = \frac{3 × 5}{5 × 6} = \frac{15}{30} = \frac{1}{2} \]
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Finally, multiply this by \(\frac{4}{3}\): \[ \frac{1}{2} × \frac{4}{3} = \frac{1 × 4}{2 × 3} = \frac{4}{6} = \frac{2}{3} \]
Thus, the final answer to the expression \((−2)×(1/5)÷(2/3)×(−5/6)÷(3/4)\) is:
\[ \frac{2}{3} \]
So the correct response is:
\(\frac{2}{3}\) (Start Fraction 2 over 3 End Fraction)