1. **State the problem:** Add the fractions and mixed numbers: $1 \frac{2}{6} + \frac{5}{6} + \frac{7}{6}$. 2. **Convert mixed numbers to improper fractions:** $1 \frac{2}{6} = \frac{6}{6} + \frac{2}{6} = \frac{8}{6}$. 3. **Add all fractions:** $$\frac{8}{6} + \frac{5}{6} + \frac{7}{6} = \frac{8+5+7}{6} = \frac{20}{6}$$ 4. **Simplify the fraction:** $$\frac{20}{6} = \frac{\cancel{20}}{\cancel{6}} \text{ where } 20 \div 2 = 10, 6 \div 2 = 3 \Rightarrow \frac{10}{3}$$ 5. **Convert back to mixed number:** $$\frac{10}{3} = 3 \frac{1}{3}$$ **Final answer:** $3 \frac{1}{3}$.