To solve the expression \((9) / (5/4) \times (7/9) \times (-5) /(7/2)\), we will follow the order of operations and apply the rules for multiplication and division of fractions.
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Rewrite the expression: \[ \frac{9}{\frac{5}{4}} \times \frac{7}{9} \times \frac{-5}{\frac{7}{2}} \]
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Change the divisions into multiplications: When dividing by a fraction, you can multiply by its reciprocal: \[ \frac{9}{\frac{5}{4}} = 9 \times \frac{4}{5} = \frac{9 \times 4}{5} = \frac{36}{5} \] \[ \frac{-5}{\frac{7}{2}} = -5 \times \frac{2}{7} = \frac{-5 \times 2}{7} = \frac{-10}{7} \]
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Substitute back into the expression: Now our expression becomes: \[ \frac{36}{5} \times \frac{7}{9} \times \frac{-10}{7} \]
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Multiply the fractions together: \[ \frac{36 \times 7 \times -10}{5 \times 9 \times 7} \]
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Notice that the \(7\) in the numerator and denominator can cancel: \[ = \frac{36 \times -10}{5 \times 9} \]
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Calculate the numerator and denominator: \[ = \frac{-360}{45} \]
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Simplify: Dividing the numerator and denominator by 45: \[ -360 \div 45 = -8 \]
Thus, the final answer is: \[ \boxed{-8} \]