To compute \((1 \frac{1}{6}) \times \left(-\frac{5}{-7}\right)\), we first convert the mixed number into an improper fraction.
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Convert \(1 \frac{1}{6}\) to an improper fraction: \[ 1 \frac{1}{6} = \frac{6 \cdot 1 + 1}{6} = \frac{7}{6} \]
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Simplify \(-\frac{5}{-7}\): \[ -\frac{5}{-7} = \frac{5}{7} \]
Now we multiply the two fractions: \[ \frac{7}{6} \times \frac{5}{7} \]
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Multiply the numerators and the denominators: \[ \frac{7 \times 5}{6 \times 7} = \frac{35}{42} \]
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Simplify \(\frac{35}{42}\):
- Find the greatest common divisor (GCD) of 35 and 42, which is 7. \[ \frac{35 \div 7}{42 \div 7} = \frac{5}{6} \]
Therefore, the final result is: \[ \frac{5}{6} \]