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'll simplify it step by step using the properties of operations.
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Rewrite the expression: \[ 9 \div \left(\frac{5}{4}\right) \times \left(\frac{7}{9}\right) \times (-5) \div \left(\frac{7}{2}\right) \]
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When dividing by a fraction, multiply by its reciprocal: \[ 9 \times \left(\frac{4}{5}\right) \times \left(\frac{7}{9}\right) \times (-5) \times \left(\frac{2}{7}\right) \]
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Rewrite the expression with multiplication: \[ \left(9 \times \frac{4}{5} \times \frac{7}{9} \times (-5) \times \frac{2}{7}\right) \]
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Cancel out the \(9\) and \(7\):
- The \(9\) and \(7\) in the numerator and denominator will cancel: \[ \left(\frac{4}{5} \times (-5) \times 2\right) \]
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Now simplify step by step:
- First, simplify \( (-5) \times \frac{4}{5} \): \[ -\frac{5 \times 4}{5} = -4 \]
- Now multiply by \(2\): \[ -4 \times 2 = -8 \]
Thus, the value of the expression \( (9) \div \left(\frac{5}{4}\right) \times \left(\frac{7}{9}\right) \times (-5) \div \left(\frac{7}{2}\right) \) is \(-8\).