1. **Stating the problem:** We want to add two fractions representing parts of a pizza, for example, $\frac{1}{4}$ and $\frac{1}{3}$.\n\n2. **Formula and rules:** To add fractions, we need a common denominator. The formula is:\n$$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$\nwhere $a$, $b$, $c$, and $d$ are integers, and $b$, $d \neq 0$.\n\n3. **Find the common denominator:** The denominators are 4 and 3. The least common denominator (LCD) is 12.\n\n4. **Convert fractions:**\n$$\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$$\n$$\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$$\n\n5. **Add the fractions:**\n$$\frac{3}{12} + \frac{4}{12} = \frac{3 + 4}{12} = \frac{7}{12}$$\n\n6. **Simplify if possible:** $\frac{7}{12}$ cannot be simplified further.\n\n**Final answer:** The sum of $\frac{1}{4}$ and $\frac{1}{3}$ is $\frac{7}{12}$.