Solve Mixed Number Addition: 3½ + 5⅘ Step by Step

To solve the problem of adding $3\frac{1}{2}$ and $5\frac{4}{5}$, we will proceed as follows:

Step 1: Add the whole numbers.
The whole numbers are $3$ and $5$. Thus, $3 + 5 = 8$.

Step 2: Add the fractional parts.
The fractions are $\frac{1}{2}$ and $\frac{4}{5}$. To add these, we need a common denominator:

• The denominators are $2$ and $5$. The least common denominator (LCD) is $10$.
• 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 $\frac{4}{5}$ to an equivalent fraction with a denominator of $10$:
$\frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10}$
• Add these fractions:
$\frac{5}{10} + \frac{8}{10} = \frac{13}{10}$

Step 3: Convert the improper fraction $\frac{13}{10}$ to a mixed number:
$\frac{13}{10} = 1\frac{3}{10}$.

Step 4: Add the result from step 1 (the sum of whole numbers) to the mixed fraction obtained in step 3:
$8 + 1\frac{3}{10} = 9\frac{3}{10}$.

Therefore, the sum of $3\frac{1}{2} + 5\frac{4}{5}$ is $9\frac{3}{10}$.