To solve the expression \((9) ÷ (5/4) × (7/9) × (−5) ÷ (7/2)\), we'll break it down step by step.
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Start with the first division: \[ 9 ÷ (5/4) = 9 × \left(\frac{4}{5}\right) = \frac{9 × 4}{5} = \frac{36}{5} \]
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Now multiply by \((7/9)\): \[ \frac{36}{5} × \frac{7}{9} = \frac{36 × 7}{5 × 9} = \frac{252}{45} \]
We can simplify \(\frac{252}{45}\) by dividing both the numerator and the denominator by their greatest common divisor, which is \(9\):
\[ \frac{252 ÷ 9}{45 ÷ 9} = \frac{28}{5} \]
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Now multiply by \((−5)\): \[ \frac{28}{5} × (−5) = -\frac{28 × 5}{5} = -28 \]
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Finally, divide by \((7/2)\): \[ -28 ÷ (7/2) = -28 × \left(\frac{2}{7}\right) = -\frac{28 × 2}{7} = -\frac{56}{7} = -8 \]
Thus, the final result is: \[ \boxed{-8} \]