1. **State the problem:** We want to solve the sum $\frac{1}{2} + \frac{1}{2} + \frac{1}{4}$.\n\n2. **Formula and rules:** To add fractions, they must have a common denominator. If they don't, find the least common denominator (LCD) and convert each fraction.\n\n3. **Find the LCD:** The denominators are 2 and 4. The LCD of 2 and 4 is 4.\n\n4. **Convert fractions:**\n- $\frac{1}{2} = \frac{2}{4}$ (multiply numerator and denominator by 2)\n- $\frac{1}{2} = \frac{2}{4}$\n- $\frac{1}{4}$ stays the same.\n\n5. **Add the fractions:**\n$$\frac{2}{4} + \frac{2}{4} + \frac{1}{4} = \frac{2+2+1}{4} = \frac{5}{4}$$\n\n6. **Simplify if needed:** $\frac{5}{4}$ is an improper fraction and can be written as $1 \frac{1}{4}$.\n\n**Final answer:** $\frac{5}{4}$ or $1 \frac{1}{4}$.