Solve Mixed Number Addition: 9½ + 2⅓

To solve $9\frac{1}{2} + 2\frac{1}{3}$, we will perform the following steps:

• Convert each mixed number to an improper fraction.
• Find a common denominator for these fractions.
• Add the fractions together.
• Convert the result back to a mixed number, if necessary.

Let's start by converting the mixed numbers:

$9\frac{1}{2}$ becomes $\frac{19}{2}$ because $9 \times 2 + 1 = 19$.

$2\frac{1}{3}$ becomes $\frac{7}{3}$ because $2 \times 3 + 1 = 7$.

Next, we find a common denominator for $\frac{19}{2}$ and $\frac{7}{3}$. The common denominator of 2 and 3 is 6.

Convert $\frac{19}{2}$ to an equivalent fraction with a denominator of 6:

$\frac{19}{2} = \frac{19 \times 3}{6} = \frac{57}{6}$.

Convert $\frac{7}{3}$ to an equivalent fraction with a denominator of 6:

$\frac{7}{3} = \frac{7 \times 2}{6} = \frac{14}{6}$.

Add the fractions:

$\frac{57}{6} + \frac{14}{6} = \frac{57 + 14}{6} = \frac{71}{6}$.

Convert $\frac{71}{6}$ back to a mixed number:

$71 \div 6 = 11$ with a remainder $5$.

Therefore, $\frac{71}{6} = 11\frac{5}{6}$.

Thus, the result of adding $9\frac{1}{2} + 2\frac{1}{3}$ is $\mathbf{11\frac{5}{6}}$.