5/6+5/2*2/3

Let's simplify the expression step by step: \[ \frac{5}{6} + \frac{5}{2} \times \frac{2}{3} \] First, handle the multiplication: \[ \frac{5}{2} \times \frac{2}{3} = \frac{5 \times 2}{2 \times 3} = \frac{10}{6} = \frac{5}{3} \] Now, add \(\frac{5}{6}\) to \(\frac{5}{3}\): To add these fractions, find a common denominator, which is 6: \[ \frac{5}{6} + \frac{5}{3} = \frac{5}{6} + \frac{5 \times 2}{3 \times 2} = \frac{5}{6} + \frac{10}{6} = \frac{5 + 10}{6} = \frac{15}{6} \] Simplify \(\frac{15}{6}\): \[ \frac{15}{6} = \frac{15 \div 3}{6 \div 3} = \frac{5}{2} \] **Final answer:** \[ \boxed{\frac{5}{2}} \]