To solve the expression \((9)÷(5/4)×(7/9)×(−5)÷(7/2)\), we can follow the order of operations and simplify step by step.
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Convert division into multiplication by multiplying by the reciprocal: \[ 9 \div \left(\frac{5}{4}\right) = 9 \times \left(\frac{4}{5}\right) = \frac{36}{5} \] Thus, the expression becomes: \[ \frac{36}{5} \times \left(\frac{7}{9}\right) \times (-5) \div \left(\frac{7}{2}\right) \] Next, we also rewrite the division by \(\frac{7}{2}\) as multiplication by its reciprocal: \[ \div \left(\frac{7}{2}\right) = \times \left(\frac{2}{7}\right) \] Therefore, the expression now looks like: \[ \frac{36}{5} \times \left(\frac{7}{9}\right) \times (-5) \times \left(\frac{2}{7}\right) \]
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Simplify the expression: Start by multiplying \(\frac{36}{5}\) and \(\frac{7}{9}\): \[ \frac{36}{5} \times \frac{7}{9} = \frac{36 \cdot 7}{5 \cdot 9} = \frac{252}{45} \]
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Multiply by \(-5\): \[ \frac{252}{45} \times (-5) = \frac{252 \times (-5)}{45} = \frac{-1260}{45} \]
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Simplify \(\frac{-1260}{45}\): Divide both the numerator and denominator by 45: \[ -1260 \div 45 = -28 \] (since \(1260\div 45 = 28\))
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Multiply by \(\frac{2}{7}\): \[ -28 \times \frac{2}{7} = \frac{-56}{7} = -8 \]
Thus, the final result is: \[ \boxed{-8} \]