To evaluate the expression \( \frac{5mn}{-2p} \) given \( m = \frac{2}{3} \), \( n = -7 \), and \( p = 5 \), we will first substitute the values of \( m \), \( n \), and \( p \) into the expression.
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Substitute \( m \), \( n \), and \( p \): \[ \frac{5 \left(\frac{2}{3}\right)(-7)}{-2(5)} \]
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Calculate \( 5 \left(\frac{2}{3}\right)(-7) \): \[ 5 \times \frac{2}{3} = \frac{10}{3} \] Then, \[ \frac{10}{3} \times -7 = \frac{10 \times -7}{3} = \frac{-70}{3} \]
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Now, calculate the denominator \( -2(5) \): \[ -2 \times 5 = -10 \]
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Now substitute back into the expression: \[ \frac{\frac{-70}{3}}{-10} \]
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Simplify this expression: \[ = \frac{-70}{3} \div -10 = \frac{-70}{3} \times \frac{1}{-10} = \frac{-70 \times 1}{3 \times -10} = \frac{70}{30} \]
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Simplify \( \frac{70}{30} \): \[ = \frac{7}{3} \]
Thus, the evaluated expression is: \[ \boxed{\frac{7}{3}} \]
3 answers