1. **State the problem:** Simplify the expression $$\frac{2}{3} + \frac{5}{3} \times \left( \frac{3}{2} - \frac{1}{2} \right)$$. 2. **Recall the order of operations:** Perform operations inside parentheses first, then multiplication, and finally addition. 3. **Simplify inside the parentheses:** $$\frac{3}{2} - \frac{1}{2} = \frac{3-1}{2} = \frac{2}{2} = 1$$ 4. **Substitute back:** $$\frac{2}{3} + \frac{5}{3} \times 1$$ 5. **Multiply:** $$\frac{5}{3} \times 1 = \frac{5}{3}$$ 6. **Add the fractions:** $$\frac{2}{3} + \frac{5}{3} = \frac{2+5}{3} = \frac{7}{3}$$ **Final answer:** $$\frac{7}{3}$$