1. **State the problem:** Add the mixed numbers $2 \frac{7}{12}$, $1 \frac{5}{6}$, and $3 \frac{3}{4}$. 2. **Formula and rules:** To add mixed numbers, first convert them to improper fractions or add the whole numbers and fractions separately by finding a common denominator. 3. **Convert each mixed number to improper fractions:** $2 \frac{7}{12} = \frac{2 \times 12 + 7}{12} = \frac{24 + 7}{12} = \frac{31}{12}$ $1 \frac{5}{6} = \frac{1 \times 6 + 5}{6} = \frac{6 + 5}{6} = \frac{11}{6}$ $3 \frac{3}{4} = \frac{3 \times 4 + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4}$ 4. **Find a common denominator:** The denominators are 12, 6, and 4. The least common denominator (LCD) is 12. 5. **Convert fractions to have denominator 12:** $\frac{31}{12}$ stays the same. $\frac{11}{6} = \frac{11 \times 2}{6 \times 2} = \frac{22}{12}$ $\frac{15}{4} = \frac{15 \times 3}{4 \times 3} = \frac{45}{12}$ 6. **Add the fractions:** $$\frac{31}{12} + \frac{22}{12} + \frac{45}{12} = \frac{31 + 22 + 45}{12} = \frac{98}{12}$$ 7. **Simplify the fraction:** Divide numerator and denominator by 2: $$\frac{98}{12} = \frac{49}{6}$$ 8. **Convert back to mixed number:** $49 \div 6 = 8$ remainder $1$, so $$\frac{49}{6} = 8 \frac{1}{6}$$ **Final answer:** $$8 \frac{1}{6}$$