To solve the expression \( 11 \frac{2}{9} - 10 - \frac{1}{9} - 8 \), we can start by converting the mixed number into an improper fraction.
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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 expression with all terms: \[ \frac{101}{9} - 10 - \frac{1}{9} - 8 \]
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Convert the whole numbers to fractions with a denominator of 9: \[ 10 = \frac{10 \times 9}{9} = \frac{90}{9}, \quad \text{and} \quad 8 = \frac{8 \times 9}{9} = \frac{72}{9} \]
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Now rewrite the expression: \[ \frac{101}{9} - \frac{90}{9} - \frac{1}{9} - \frac{72}{9} \]
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Combine the fractions: \[ \frac{101 - 90 - 1 - 72}{9} = \frac{101 - 163}{9} = \frac{-62}{9} \]
Thus, the final answer is: \[ -\frac{62}{9} \]
If you want to express it as a mixed number, it equals \( -6 \frac{8}{9} \).