Solve Mixed Number Addition: 5½ + 2⅗ Step-by-Step

To solve this problem, we will follow these detailed steps:

• Step 1: Convert Mixed Numbers to Improper Fractions
  - For $5\frac{1}{2}$: Multiply 5 by 2 and add 1 to get $\frac{11}{2}$.
  - For $2\frac{3}{5}$: Multiply 2 by 5 and add 3 to get $\frac{13}{5}$.
• Step 2: Find a Common Denominator
  - The denominators are 2 and 5. The LCM is 10.
• Step 3: Convert to Common Denominator
  - Rewrite $\frac{11}{2}$ as $\frac{55}{10}$.
  - Rewrite $\frac{13}{5}$ as $\frac{26}{10}$.
• Step 4: Add the Fractions
  - Combine $\frac{55}{10} + \frac{26}{10} = \frac{81}{10}$.
• Step 5: Convert the Result Back to a Mixed Number
  - Divide 81 by 10: Quotient is 8, Remainder is 1.
  - The answer is $8\frac{1}{10}$.

Thus, the solution to the addition $5\frac{1}{2} + 2\frac{3}{5}$ is $8\frac{1}{10}$, which matches choice 3.