1. **State the problem:** Calculate the sum $\frac{1}{2} + \frac{1}{2}$.\n\n2. **Formula used:** When adding fractions with the same denominator, add the numerators and keep the denominator the same: $$\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}.$$\n\n3. **Apply the formula:** Here, both fractions have denominator 2, so add the numerators: $$\frac{1}{2} + \frac{1}{2} = \frac{1+1}{2}.$$\n\n4. **Simplify the numerator:** $$\frac{1+1}{2} = \frac{2}{2}.$$\n\n5. **Simplify the fraction:** Since numerator and denominator are equal, $$\frac{2}{2} = 1.$$\n\n**Final answer:** $$1.$$