To solve \( 11 \frac{2}{9} - 10 - \frac{1}{9} - 8 \), we first convert the mixed number into an improper fraction.
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Convert \( 11 \frac{2}{9} \) into an improper fraction: \[ 11 \frac{2}{9} = 11 \times 9 + 2 = 99 + 2 = 101 \quad \text{so} \quad 11 \frac{2}{9} = \frac{101}{9} \]
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Rewrite the equation: \[ \frac{101}{9} - 10 - \frac{1}{9} - 8 \] We can convert \( 10 \) and \( 8 \) into fractions with the same denominator (9): \[ 10 = \frac{90}{9} \quad \text{and} \quad 8 = \frac{72}{9} \]
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Substitute these back into the equation: \[ \frac{101}{9} - \frac{90}{9} - \frac{1}{9} - \frac{72}{9} \]
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Combine the terms: \[ \frac{101 - 90 - 1 - 72}{9} = \frac{101 - 163}{9} = \frac{-62}{9} \]
The answer in simplest form is: \[ \boxed{-\frac{62}{9}} \]
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