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To solve \( 1 \frac{1}{6} \times \frac{2}{4} \frac{2}{5} \), first convert the mixed number to an improper fraction. \( 1 \frac{1}{6} = \frac{7}{6} \). Now, simplify \( \frac{2}{4} = \frac{1}{2} \). Thus, the problem becomes \( \frac{7}{6} \times \frac{1}{2} \times \frac{2}{5} \). Now, multiply the fractions together: \[ \frac{7}{6} \times \frac{1}{2} = \frac{7}{12} \] Then multiply that result by \( \frac{2}{5} \): \[ \frac{7}{12} \times \frac{2}{5} = \frac{14}{60} \] Now simplify \( \frac{14}{60} \) to \( \frac{7}{30} \). Therefore, the answer is \( \frac{7}{30} \).