1. **State the problem:** Add the fractions $\frac{1}{2}$ and $\frac{2}{12}$. 2. **Recall the formula:** To add fractions, they must have a common denominator. The formula is $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$ where $a,b,c,d$ are integers and $b,d \neq 0$. 3. **Find a common denominator:** The denominators are 2 and 12. The least common denominator (LCD) is 12. 4. **Convert fractions:** $$\frac{1}{2} = \frac{1 \times 6}{2 \times 6} = \frac{6}{12}$$ $$\frac{2}{12}$$ stays the same. 5. **Add the numerators:** $$\frac{6}{12} + \frac{2}{12} = \frac{6 + 2}{12} = \frac{8}{12}$$ 6. **Simplify the fraction:** Divide numerator and denominator by their greatest common divisor (GCD), which is 4: $$\frac{8 \div 4}{12 \div 4} = \frac{2}{3}$$ **Final answer:** $$\frac{1}{2} + \frac{2}{12} = \frac{2}{3}$$