1. **State the problem:** Simplify the expression $$\frac{1}{2} - \frac{3}{2} + \frac{2}{3}$$. 2. **Find a common denominator:** The denominators are 2, 2, and 3. The least common denominator (LCD) is 6. 3. **Rewrite each fraction with denominator 6:** $$\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}$$ $$\frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6}$$ $$\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}$$ 4. **Substitute back into the expression:** $$\frac{3}{6} - \frac{9}{6} + \frac{4}{6}$$ 5. **Combine the numerators over the common denominator:** $$\frac{3 - 9 + 4}{6}$$ 6. **Simplify the numerator:** $$3 - 9 + 4 = (3 - 9) + 4 = -6 + 4 = -2$$ 7. **Final simplified expression:** $$\frac{-2}{6}$$ 8. **Simplify the fraction by dividing numerator and denominator by 2:** $$\frac{\cancel{-2}}{\cancel{6}} = \frac{-1}{3}$$ **Answer:** $$-\frac{1}{3}$$