Solve Mixed Number Addition: 6⅑ + 2½ Step by Step

To solve this problem, we will add the mixed numbers $6\frac{1}{9}$ and $2\frac{1}{2}$ through the following steps:

Step 1: Convert each mixed number to an improper fraction.

• $6\frac{1}{9} = \frac{55}{9}$ because $6 \times 9 + 1 = 55$.
• $2\frac{1}{2} = \frac{5}{2}$ because $2 \times 2 + 1 = 5$.

Step 2: Find a common denominator for the fractions $\frac{55}{9}$ and $\frac{5}{2}$. The least common multiple of 9 and 2 is 18.

• Convert $\frac{55}{9}$ to a denominator of 18: $\frac{55}{9} = \frac{110}{18}$.
• Convert $\frac{5}{2}$ to a denominator of 18: $\frac{5}{2} = \frac{45}{18}$.

Step 3: Add the fractions together: $\frac{110}{18} + \frac{45}{18} = \frac{155}{18}$.

Step 4: Convert the improper fraction back to a mixed number.

• Divide 155 by 18 to get $8$ with a remainder, $155 \div 18 = 8$ remainder $11$.
• Thus, the mixed number is $8\frac{11}{18}$.

The solution to the problem is $8\frac{11}{18}$, which corresponds to choice 3.