1. **State the problem:** Calculate the sum $3 + \frac{1}{12} + \frac{2}{15}$. 2. **Find a common denominator:** The denominators are 1 (for 3), 12, and 15. The least common multiple (LCM) of 12 and 15 is 60. 3. **Convert each term to have denominator 60:** $$3 = \frac{3 \times 60}{60} = \frac{180}{60}$$ $$\frac{1}{12} = \frac{1 \times 5}{12 \times 5} = \frac{5}{60}$$ $$\frac{2}{15} = \frac{2 \times 4}{15 \times 4} = \frac{8}{60}$$ 4. **Add the fractions:** $$\frac{180}{60} + \frac{5}{60} + \frac{8}{60} = \frac{180 + 5 + 8}{60} = \frac{193}{60}$$ 5. **Simplify the fraction if possible:** 193 and 60 have no common factors other than 1, so the fraction is in simplest form. 6. **Convert to mixed number:** $$\frac{193}{60} = 3 + \frac{13}{60}$$ **Final answer:** $$3 + \frac{1}{12} + \frac{2}{15} = \frac{193}{60} = 3 \frac{13}{60}$$