b) \( \frac{2}{3}-\frac{3}{4} \cdot \frac{2}{3}+\frac{5}{6}= \)

To solve the expression \( \frac{2}{3} - \frac{3}{4} \cdot \frac{2}{3} + \frac{5}{6} \), we begin by simplifying the multiplication first. Calculate \( \frac{3}{4} \cdot \frac{2}{3} \): \[ \frac{3}{4} \cdot \frac{2}{3} = \frac{3 \cdot 2}{4 \cdot 3} = \frac{6}{12} = \frac{1}{2} \] Now, substitute this back into the original expression: \[ \frac{2}{3} - \frac{1}{2} + \frac{5}{6} \] Next, we need to find a common denominator. The denominators are 3, 2, and 6, and the least common multiple is 6. We can convert each fraction: \[ \frac{2}{3} = \frac{4}{6}, \quad \frac{1}{2} = \frac{3}{6}, \quad \frac{5}{6} = \frac{5}{6} \] Now substituting back gives us: \[ \frac{4}{6} - \frac{3}{6} + \frac{5}{6} \] Combine the fractions: \[ \left(\frac{4}{6} - \frac{3}{6} + \frac{5}{6}\right) = \frac{4 - 3 + 5}{6} = \frac{6}{6} = 1 \] Thus, the final result is: \[ \boxed{1} \]