To solve the expression \((−2)×(1/5)÷(2/3)×(−5/6)÷(3/4)\), we can follow the order of operations and simplify step by step.
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Start with the first part of the expression: \[ (−2) × (1/5) = -\frac{2}{5} \]
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Next, divide by \((2/3)\): \[ -\frac{2}{5} ÷ \frac{2}{3} = -\frac{2}{5} × \frac{3}{2} \] When you divide by a fraction, you multiply by its reciprocal.
Now perform the multiplication: \[ = -\frac{2 × 3}{5 × 2} = -\frac{6}{10} = -\frac{3}{5} \]
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Now, multiply this result by \( (−5/6) \): \[ -\frac{3}{5} × \left(-\frac{5}{6}\right) = \frac{3 × 5}{5 × 6} = \frac{15}{30} = \frac{1}{2} \]
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Finally, divide by \((3/4)\): \[ \frac{1}{2} ÷ \frac{3}{4} = \frac{1}{2} × \frac{4}{3} = \frac{1 × 4}{2 × 3} = \frac{4}{6} = \frac{2}{3} \]
Thus, the final answer is: \[ \frac{2}{3} \]
The correct response is: Start Fraction 2 over 3 End Fraction