Solve Mixed Number Addition: 3½ + 8¾ Step-by-Step

To solve the problem of adding $3\frac{1}{2} + 8\frac{3}{4}$, we'll go through these steps:

• Step 1: Separate and add the whole numbers.
• Step 2: Add the fractional parts by finding a common denominator.
• Step 3: Combine the results and simplify if necessary.

Let's apply these steps in detail:

Step 1: Add the whole numbers:
$3 + 8 = 11$.

Step 2: Add the fractions $\frac{1}{2}$ and $\frac{3}{4}$:
The denominators are 2 and 4. The least common denominator is 4.

Convert $\frac{1}{2}$ to an equivalent fraction with a denominator of 4:
$\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}$.

Now, add the fractions:
$\frac{2}{4} + \frac{3}{4} = \frac{2+3}{4} = \frac{5}{4}$.

$\frac{5}{4}$ is an improper fraction, which can be converted to a mixed number:
$\frac{5}{4} = 1\frac{1}{4}$.

Step 3: Combine the whole numbers and the mixed fraction:
$11 + 1\frac{1}{4} = 12\frac{1}{4}$.

Therefore, the solution to the problem is $12\frac{1}{4}$.