1. **Problem:** Calculate $1 \frac{5}{6} + \frac{2}{15}$. 2. **Convert mixed number to improper fraction:** $$1 \frac{5}{6} = \frac{6 \times 1 + 5}{6} = \frac{11}{6}$$ 3. **Find common denominator:** Denominators are 6 and 15. The least common denominator (LCD) is 30. 4. **Convert fractions to have denominator 30:** $$\frac{11}{6} = \frac{11 \times 5}{6 \times 5} = \frac{55}{30}$$ $$\frac{2}{15} = \frac{2 \times 2}{15 \times 2} = \frac{4}{30}$$ 5. **Add fractions:** $$\frac{55}{30} + \frac{4}{30} = \frac{55 + 4}{30} = \frac{59}{30}$$ 6. **Convert improper fraction to mixed number:** $$\frac{59}{30} = 1 \frac{29}{30}$$ **Final answer:** $1 \frac{29}{30}$