To solve the expression \( 17 \frac{4}{9} + \frac{5}{6} - 8 - 10 \), we can first convert the mixed number \( 17 \frac{4}{9} \) to an improper fraction.
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Convert \( 17 \frac{4}{9} \) to an improper fraction: \[ 17 \frac{4}{9} = 17 + \frac{4}{9} = \frac{17 \times 9}{9} + \frac{4}{9} = \frac{153}{9} + \frac{4}{9} = \frac{157}{9} \]
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Now we can rewrite the expression: \[ \frac{157}{9} + \frac{5}{6} - 8 - 10 \]
We can express \( 8 \) and \( 10 \) as fractions: \[ 8 = \frac{72}{9}, \quad 10 = \frac{90}{9} \]
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Substitute these values into the expression: \[ \frac{157}{9} + \frac{5}{6} - \frac{72}{9} - \frac{90}{9} \]
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Combine the fractions: \[ = \frac{157}{9} - \frac{72}{9} - \frac{90}{9} + \frac{5}{6} \] \[ = \frac{157 - 72 - 90}{9} + \frac{5}{6} \] \[ = \frac{157 - 162}{9} + \frac{5}{6} \] \[ = \frac{-5}{9} + \frac{5}{6} \]
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Now we need a common denominator to add \( \frac{-5}{9} \) and \( \frac{5}{6} \):
- The least common multiple of 9 and 6 is 18.
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Convert both fractions to have the same denominator: \[ \frac{-5}{9} = \frac{-5 \times 2}{9 \times 2} = \frac{-10}{18} \] \[ \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18} \]
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Now combine the two fractions: \[ \frac{-10}{18} + \frac{15}{18} = \frac{-10 + 15}{18} = \frac{5}{18} \]
Thus, the result of the expression \( 17 \frac{4}{9} + \frac{5}{6} - 8 - 10 \) is \( \frac{5}{18} \).