To simplify the expression \( 11 \frac{3}{9} - 10 - \frac{1}{9} - 8 \), we can follow these steps:
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Convert the mixed number to an improper fraction: \[ 11 \frac{3}{9} = 11 + \frac{3}{9} = \frac{11 \times 9 + 3}{9} = \frac{99 + 3}{9} = \frac{102}{9} \]
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Rewrite the expression: \[ \frac{102}{9} - 10 - \frac{1}{9} - 8 \]
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Convert 10 and 8 to fractions with a common denominator of 9: \[ 10 = \frac{90}{9}, \quad 8 = \frac{72}{9} \]
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Substitute these back into the expression: \[ \frac{102}{9} - \frac{90}{9} - \frac{1}{9} - \frac{72}{9} \]
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Combine all the fractions: \[ \frac{102 - 90 - 1 - 72}{9} = \frac{102 - 163}{9} = \frac{-61}{9} \]
The final result is: \[ -\frac{61}{9} \]
If you want to also express this as a mixed number: \[ -\frac{61}{9} = -6 \frac{7}{9} \]
So, the final answer is: \[ -\frac{61}{9} \text{ or } -6 \frac{7}{9} \]