To solve the expression \( 11 \frac{2}{9} - 10 - \frac{1}{9} - 8 \), we can follow these steps:
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Convert \( 11 \frac{2}{9} \) to an improper fraction: \[ 11 \frac{2}{9} = \frac{11 \times 9 + 2}{9} = \frac{99 + 2}{9} = \frac{101}{9} \]
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Rewrite the whole numbers \( 10 \) and \( 8 \) as fractions with the common denominator of \( 9 \): \[ 10 = \frac{10 \times 9}{9} = \frac{90}{9} \] \[ 8 = \frac{8 \times 9}{9} = \frac{72}{9} \]
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Substitute these fractions into the expression: \[ \frac{101}{9} - \frac{90}{9} - \frac{1}{9} - \frac{72}{9} \]
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Now combine all the fractions: \[ \frac{101 - 90 - 1 - 72}{9} = \frac{101 - 90 - 1 - 72}{9} = \frac{101 - 163}{9} = \frac{-62}{9} \]
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The final answer in simplest form is: \[ \frac{-62}{9} \]
Thus, the answer is \( -\frac{62}{9} \).