1. The problem is to add the mixed numbers $2 \frac{1}{2}$ and $3 \frac{1}{6}$. 2. Convert each mixed number to an improper fraction: - $2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}$ - $3 \frac{1}{6} = \frac{3 \times 6 + 1}{6} = \frac{19}{6}$ 3. Find a common denominator to add the fractions. The denominators are 2 and 6. The least common denominator is 6. 4. Convert $\frac{5}{2}$ to sixths: $\frac{5}{2} = \frac{5 \times 3}{2 \times 3} = \frac{15}{6}$. 5. Now add $\frac{15}{6} + \frac{19}{6} = \frac{34}{6}$. 6. Simplify the fraction by dividing numerator and denominator by 2: $\frac{34}{6} = \frac{17}{3}$. 7. Convert $\frac{17}{3}$ back to a mixed number: - Divide 17 by 3: $17 \div 3 = 5$ remainder $2$. - So $\frac{17}{3} = 5 \frac{2}{3}$. Final answer: $5 \frac{2}{3}$