To solve the expression \( (9) \div \left(\frac{5}{4}\right) \times \left(\frac{7}{9}\right) \times (-5) \div \left(\frac{7}{2}\right) \), we can follow the order of operations and simplify step by step.
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Convert the Division to Multiplication: Recall that dividing by a fraction is the same as multiplying by its reciprocal. Therefore:
- \( 9 \div \left(\frac{5}{4}\right) = 9 \times \left(\frac{4}{5}\right) \)
- \( -5 \div \left(\frac{7}{2}\right) = -5 \times \left(\frac{2}{7}\right) \)
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Rewrite the Expression: The expression now looks like: \[ 9 \times \left(\frac{4}{5}\right) \times \left(\frac{7}{9}\right) \times (-5) \times \left(\frac{2}{7}\right) \]
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Simplify Step by Step:
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First, \( 9 \times \left(\frac{4}{5}\right) \): \[ = \frac{36}{5} \]
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Now multiply that by \( \left(\frac{7}{9}\right) \): \[ \frac{36}{5} \times \frac{7}{9} = \frac{36 \times 7}{5 \times 9} = \frac{252}{45} \]
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Next, simplify \( \frac{252}{45} \):
- \( 252 \div 9 = 28 \)
- \( 45 \div 9 = 5 \) Thus, \( \frac{252}{45} = \frac{28}{5} \)
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Now, multiply by \( -5 \): \[ \frac{28}{5} \times (-5) = -28 \]
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Finally, divide by \( \left(\frac{7}{2}\right) \): \[ -28 \div \left(\frac{7}{2}\right) = -28 \times \left(\frac{2}{7}\right) = -\frac{56}{7} = -8 \]
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Final Result: The final result of the expression is \( -8 \).
Therefore, the correct response is −8 (negative 8).