1. The problem is to add the fractions $\frac{11}{12}$ and $\frac{1}{3}$.\n\n2. To add fractions, they must have a common denominator. The denominators here are 12 and 3.\n\n3. Find the least common denominator (LCD) of 12 and 3, which is 12.\n\n4. Convert $\frac{1}{3}$ to an equivalent fraction with denominator 12: $$\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}.$$\n\n5. Now add the fractions: $$\frac{11}{12} + \frac{4}{12} = \frac{11 + 4}{12} = \frac{15}{12}.$$\n\n6. Simplify $\frac{15}{12}$ by dividing numerator and denominator by their greatest common divisor (GCD), which is 3: $$\frac{\cancel{15}^{5}}{\cancel{12}^{4}} = \frac{5}{4}.$$\n\n7. The final answer is $\frac{5}{4}$ or 1.25 in decimal form.