To solve the expression \((9) ÷ (5/4) × (7/9) × (−5) ÷ (7/2)\), let's follow the order of operations while utilizing multiplication and division rules.
Step 1: Rewrite the division as multiplication by the reciprocal.
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Rewrite \(9 ÷ (5/4)\) as \(9 × (4/5)\): \[ 9 × (4/5) = \frac{9 × 4}{5} = \frac{36}{5} \]
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Rewrite \(÷ (7/2)\) as \(× (2/7)\): \[ \frac{36}{5} × \frac{2}{7} \]
Combining the above, we have: \[ \frac{36}{5} × \frac{2}{7} = \frac{36 × 2}{5 × 7} = \frac{72}{35} \]
Step 2: Now, incorporate the other factors \((7/9)\) and \((-5)\):
Continuing from the last expression: \[ (−5) × (\frac{72}{35}) = \frac{−5 × 72}{35} = \frac{−360}{35} \]
Step 3: Now, multiply by \(7/9\):
\[ \frac{−360}{35} × \frac{7}{9} = \frac{−360 × 7}{35 × 9} \]
Step 4: Simplify that:
Calculating the numerator: \[ −360 × 7 = -2520 \]
Calculating the denominator: \[ 35 × 9 = 315 \]
Step 5: Combine the results:
Final expression: \[ \frac{-2520}{315} \]
Step 6: Simplify the fraction:
To simplify \(-2520/315\), we find the GCD: \[ 2520 ÷ 315 = 8 \] This can also be confirmed by reducing it: \[ \frac{-2520 ÷ 315}{315 ÷ 315} = \frac{-8}{1} \]
Thus, we obtain: \[ -8 \]
The final answer is: \[ \text{Negative } 8 \] So the correct response is: \[ −8 \]