To solve the expression \((-3) \div \left(\frac{3}{4}\right) \times \left(\frac{2}{7}\right) \times \left(-\frac{15}{6}\right) \div \left(\frac{5}{7}\right)\), we will follow the order of operations (PEMDAS), specifically handling division and multiplication from left to right.
Let's break it down step by step:
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Calculate \(-3 \div \left(\frac{3}{4}\right)\): \[ -3 \div \left(\frac{3}{4}\right) = -3 \times \left(\frac{4}{3}\right) = -\frac{12}{3} = -4 \]
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Now take that result and multiply by \(\left(\frac{2}{7}\right)\): \[ -4 \times \left(\frac{2}{7}\right) = -\frac{8}{7} \]
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Now multiply that result by \(\left(-\frac{15}{6}\right)\): \[ -\frac{8}{7} \times \left(-\frac{15}{6}\right) = \frac{8 \times 15}{7 \times 6} = \frac{120}{42} \]
We can simplify \(\frac{120}{42}\): \[ \frac{120 \div 6}{42 \div 6} = \frac{20}{7} \]
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Finally, divide that result by \(\left(\frac{5}{7}\right)\): \[ \frac{20}{7} \div \left(\frac{5}{7}\right) = \frac{20}{7} \times \left(\frac{7}{5}\right) = \frac{20 \times 7}{7 \times 5} = \frac{20}{5} = 4 \]
Thus, the final result of the expression is \(\boxed{4}\).
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