To solve the expression \((-3) \div \left(\frac{3}{4}\right) \times \left(-\frac{5}{16}\right) \div \left(\frac{5}{7}\right)\), we will follow the order of operations and simplify step by step.
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Rewrite the division as multiplication by the reciprocal: \[ (-3) \div \left(\frac{3}{4}\right) = (-3) \times \left(\frac{4}{3}\right) \] This results in: \[ (-3) \times \left(\frac{4}{3}\right) = -\frac{12}{3} = -4. \]
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Now substitute back into the expression: The expression now looks like: \[ -4 \times \left(-\frac{5}{16}\right) \div \left(\frac{5}{7}\right). \]
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Perform the multiplication: \[ -4 \times \left(-\frac{5}{16}\right) = \frac{20}{16} = \frac{5}{4}. \]
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Now rewrite the division: \[ \frac{5}{4} \div \left(\frac{5}{7}\right) = \frac{5}{4} \times \left(\frac{7}{5}\right). \]
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Perform the multiplication: \[ \frac{5}{4} \times \left(\frac{7}{5}\right) = \frac{5 \times 7}{4 \times 5} = \frac{35}{20}. \]
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Simplify the result: \[ \frac{35}{20} = \frac{7}{4}. \]
The final result of the expression \((-3) \div \left(\frac{3}{4}\right) \times \left(-\frac{5}{16}\right) \div \left(\frac{5}{7}\right)\) is: \[ \frac{7}{4}. \]
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