1. **State the problem:** Add the fractions $\frac{1}{2} + \frac{4}{5} + \frac{1}{2}$.\n\n2. **Formula and rules:** To add fractions, they must have a common denominator. Find the least common denominator (LCD) of the denominators 2 and 5.\n\n3. **Find the LCD:** The denominators are 2 and 5. The LCD is $10$.\n\n4. **Convert each fraction:**\n$\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}$\n$\frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10}$\n$\frac{1}{2} = \frac{5}{10}$ (same as first fraction)\n\n5. **Add the fractions:**\n$$\frac{5}{10} + \frac{8}{10} + \frac{5}{10} = \frac{5 + 8 + 5}{10} = \frac{18}{10}$$\n\n6. **Simplify the fraction:**\n$\frac{18}{10} = \frac{9}{5}$ after dividing numerator and denominator by 2.\n\n7. **Final answer:**\n$$\frac{1}{2} + \frac{4}{5} + \frac{1}{2} = \frac{9}{5}$$