To solve the expression \(-13 \frac{5}{7} + 6 - \frac{2}{7} - 4\), we can first convert the mixed number into an improper fraction and then combine all the terms.
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Convert \(-13 \frac{5}{7}\) to an improper fraction: \[ -13 \frac{5}{7} = -\left(13 \times 7 + 5\right) / 7 = -\frac{91+5}{7} = -\frac{96}{7} \]
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Convert the whole numbers into fractions with a common denominator of 7: \[ 6 = \frac{6 \times 7}{7} = \frac{42}{7} \] \[ 4 = \frac{4 \times 7}{7} = \frac{28}{7} \]
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Rewrite the entire expression with a common denominator: \[ -\frac{96}{7} + \frac{42}{7} - \frac{2}{7} - \frac{28}{7} \]
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Combine the fractions: \[ -\frac{96 + 42 + 2 + 28}{7} = -\frac{96 + 42 + 2 + 28}{7} = -\frac{124}{7} \]
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Convert \(-\frac{124}{7}\) back to a mixed number: \[ \frac{124}{7} = 17 \frac{5}{7} \] Therefore, \(-\frac{124}{7}\) is \(-17 \frac{5}{7}\).
So, the result of the expression \(-13 \frac{5}{7} + 6 - \frac{2}{7} - 4\) is: \[ -\frac{124}{7} \text{ or } -17 \frac{5}{7}. \]