1. The problem is to add the fractions $\frac{1}{2}$ and $\frac{2}{4}$.\n\n2. To add fractions, they must have a common denominator. The denominators here are 2 and 4.\n\n3. The least common denominator (LCD) of 2 and 4 is 4.\n\n4. Convert $\frac{1}{2}$ to an equivalent fraction with denominator 4: $$\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}.$$\n\n5. Now add the fractions: $$\frac{2}{4} + \frac{2}{4} = \frac{2+2}{4} = \frac{4}{4}.$$\n\n6. Simplify the fraction: $$\frac{4}{4} = 1.$$\n\nSo, $\frac{1}{2} + \frac{2}{4} = 1$.