Find the following quotient, leaving your answer as a proper fraction or as a mixed number. \( 2 \frac{5}{6} \div 1 \frac{2}{5}=\square \)

To find the quotient \( 2 \frac{5}{6} \div 1 \frac{2}{5} \), we start by converting the mixed numbers into improper fractions. First, \( 2 \frac{5}{6} = \frac{2 \times 6 + 5}{6} = \frac{12 + 5}{6} = \frac{17}{6} \). Next, \( 1 \frac{2}{5} = \frac{1 \times 5 + 2}{5} = \frac{5 + 2}{5} = \frac{7}{5} \). Now we proceed with the division of fractions, which involves multiplying by the reciprocal of the divisor: \[ \frac{17}{6} \div \frac{7}{5} = \frac{17}{6} \times \frac{5}{7} = \frac{17 \times 5}{6 \times 7} = \frac{85}{42} \] Finally, we simplify \( \frac{85}{42} \) to a mixed number. Dividing 85 by 42 gives us 2 with a remainder of 1. Therefore, \[ \frac{85}{42} = 2 \frac{1}{42} \] So, the final result is: \[ 2 \frac{1}{42} \]