The problem asks us to add two fractions, $\frac{7}{9}$ and $\frac{1}{2}$. We need to find a common denominator, express each fraction using the common denominator, add the fractions, and then simplify the result.

1. Problem Description

The problem asks us to add two fractions, $\frac{7}{9}$ and $\frac{1}{2}$. We need to find a common denominator, express each fraction using the common denominator, add the fractions, and then simplify the result.

2. Solution Steps

First, we need to find the least common multiple (LCM) of the denominators 9 and

2. The LCM of 9 and 2 is

1

8.

Next, we convert each fraction to an equivalent fraction with a denominator of

1

8. To convert $\frac{7}{9}$ to an equivalent fraction with a denominator of 18, we multiply both the numerator and the denominator by 2:

$\frac{7}{9} = \frac{7 \times 2}{9 \times 2} = \frac{14}{18}$.

To convert $\frac{1}{2}$ to an equivalent fraction with a denominator of 18, we multiply both the numerator and the denominator by 9:

$\frac{1}{2} = \frac{1 \times 9}{2 \times 9} = \frac{9}{18}$.

Now we can add the two fractions:

$\frac{14}{18} + \frac{9}{18} = \frac{14 + 9}{18} = \frac{23}{18}$.

Since 23 > 18, the fraction $\frac{23}{18}$ is an improper fraction. We can convert it to a mixed number.

$\frac{23}{18} = \frac{18}{18} + \frac{5}{18} = 1 + \frac{5}{18} = 1\frac{5}{18}$.

3. Final Answer

$\frac{7}{9} + \frac{1}{2} = \frac{14}{18} + \frac{9}{18} = \frac{23}{18} = 1\frac{5}{18}$.