To simplify the expression \( 18 - 9 \frac{4}{9} + \frac{7}{9} - 8 \), we can start by rewriting it in terms of fractions.
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First, convert the mixed number \( 9 \frac{4}{9} \) into an improper fraction: \[ 9 \frac{4}{9} = 9 + \frac{4}{9} = \frac{81}{9} + \frac{4}{9} = \frac{85}{9} \]
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Now substitute this back into the expression: \[ 18 - \frac{85}{9} + \frac{7}{9} - 8 \]
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Next, convert \( 18 \) and \( 8 \) to fractions with a common denominator of \( 9 \): \[ 18 = \frac{162}{9}, \quad 8 = \frac{72}{9} \]
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Substitute these back into the expression: \[ \frac{162}{9} - \frac{85}{9} + \frac{7}{9} - \frac{72}{9} \]
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Now combine all the fractions: \[ \frac{162 - 85 + 7 - 72}{9} \]
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Calculate the numerator: \[ 162 - 85 = 77 \] \[ 77 + 7 = 84 \] \[ 84 - 72 = 12 \]
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This gives us: \[ \frac{12}{9} \]
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Finally, simplify the fraction \( \frac{12}{9} \):
- The greatest common divisor of \( 12 \) and \( 9 \) is \( 3 \). \[ \frac{12 \div 3}{9 \div 3} = \frac{4}{3} \]
Thus, the simplified expression is \(\frac{4}{3}\).
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