Addition or subtraction of mixed numbers with different denominators... Subtract. Write your answer as a mixed number in simplest form. \[ 2 \frac{5}{6}-1 \frac{1}{2} \]

Step 1 ：Convert the mixed numbers to improper fractions. The first mixed number, \(2 \frac{5}{6}\), becomes \(\frac{17}{6}\) and the second mixed number, \(1 \frac{1}{2}\), becomes \(\frac{3}{2}\).

Step 2 ：Find a common denominator for the two fractions. In this case, the common denominator is 6.

Step 3 ：Subtract the fractions. \(\frac{17}{6} - \frac{9}{6} = \frac{8}{6}\).

Step 4 ：Convert the result back to a mixed number. \(\frac{8}{6}\) becomes \(1 \frac{2}{6}\).

Step 5 ：Simplify the mixed number. \(1 \frac{2}{6}\) simplifies to \(1 \frac{1}{3}\).

Step 6 ：Final Answer: The result of the subtraction is \(\boxed{1 \frac{1}{3}}\).