1. The problem is to add the fractions $\frac{3}{4}$ and $\frac{1}{3}$.\n\n2. To add fractions, we need a common denominator. The denominators here are 4 and 3.\n\n3. The least common denominator (LCD) of 4 and 3 is 12.\n\n4. Convert each fraction to an equivalent fraction with denominator 12:\n\n$$\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$$\n$$\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$$\n\n5. Now add the fractions with the common denominator:\n\n$$\frac{9}{12} + \frac{4}{12} = \frac{9 + 4}{12} = \frac{13}{12}$$\n\n6. The result $\frac{13}{12}$ is an improper fraction and can be written as a mixed number:\n\n$$1 \frac{1}{12}$$\n\nSo, $\frac{3}{4} + \frac{1}{3} = \frac{13}{12} = 1 \frac{1}{12}$.