Solve Mixed Number Addition: 10½ + 5⅕ Step-by-Step

To solve this problem, let's follow these steps:

• Step 1: Add the whole numbers $10$ and $5$.
• Step 2: Find a common denominator for the fractions $\frac{1}{2}$ and $\frac{1}{5}$, and add them.

Now, let's work through each step:

Step 1: Adding the whole numbers gives us:
$10 + 5 = 15$

Step 2: To add the fractions $\frac{1}{2}$ and $\frac{1}{5}$, we need a common denominator. The least common multiple of 2 and 5 is 10.

Convert each fraction to have this common denominator:

• Convert $\frac{1}{2}$ to an equivalent fraction with a denominator of 10:
  $\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}$
• Convert $\frac{1}{5}$ to an equivalent fraction with a denominator of 10:
  $\frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10}$

Now, add these fractions:
$\frac{5}{10} + \frac{2}{10} = \frac{5 + 2}{10} = \frac{7}{10}$

Finally, combine the whole number part with the fractional part:
$15 + \frac{7}{10} = 15\frac{7}{10}$

Thus, the solution to the problem is $15\frac{7}{10}$.