1. **State the problem:** Add the fractions $\frac{1}{2} + \frac{1}{2}$ and simplify the result. 2. **Formula and rules:** When adding fractions with the same denominator, add the numerators and keep the denominator the same: $$\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$$ 3. **Apply the formula:** $$\frac{1}{2} + \frac{1}{2} = \frac{1+1}{2}$$ 4. **Simplify the numerator:** $$\frac{2}{2}$$ 5. **Simplify the fraction:** Since numerator and denominator are the same, the fraction equals 1: $$\frac{\cancel{2}}{\cancel{2}} = 1$$ 6. **Final answer:** $$1$$