To evaluate the expression \( 1.4 \cdot \frac{(5 + 3)}{0.2} - \frac{2}{(-8.4 + 12.4)} \), we will follow the order of operations step by step.
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Calculate the expression inside the parentheses: \[ 5 + 3 = 8 \]
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Substitute this back into the expression: \[ 1.4 \cdot \frac{8}{0.2} - \frac{2}{(-8.4 + 12.4)} \]
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Calculate \(-8.4 + 12.4\): \[ -8.4 + 12.4 = 4 \]
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Substitute this value back into the expression: \[ 1.4 \cdot \frac{8}{0.2} - \frac{2}{4} \]
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Now calculate \(\frac{2}{4}\): \[ \frac{2}{4} = \frac{1}{2} \]
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Now we need to calculate \(\frac{8}{0.2}\): \[ \frac{8}{0.2} = 8 \div 0.2 = 8 \div \frac{2}{10} = 8 \cdot \frac{10}{2} = 8 \cdot 5 = 40 \]
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Substituting this into the expression: \[ 1.4 \cdot 40 - \frac{1}{2} \]
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Now multiply \(1.4 \cdot 40\): \[ 1.4 \cdot 40 = 56 \]
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Now we substitute this back into the expression: \[ 56 - \frac{1}{2} \]
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Rewrite \(56\) as a fraction in terms of halves: \[ 56 = \frac{112}{2} \]
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Now subtract \(\frac{1}{2}\): \[ \frac{112}{2} - \frac{1}{2} = \frac{112 - 1}{2} = \frac{111}{2} \]
Finally, the expression evaluates to \[ \boxed{\frac{111}{2}} \] or as a mixed number, it is \( 55 \frac{1}{2} \).
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