The problem is to evaluate the expression $\frac{1}{2} - \frac{1}{3} + \frac{1}{9}$.

1. Problem Description

The problem is to evaluate the expression $\frac{1}{2} - \frac{1}{3} + \frac{1}{9}$.

2. Solution Steps

To solve the problem, we need to find a common denominator for the fractions. The least common multiple (LCM) of 2, 3, and 9 is

1

8. We rewrite each fraction with the common denominator of

1

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

$\frac{1}{3} = \frac{1 \times 6}{3 \times 6} = \frac{6}{18}$

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

Now we can rewrite the expression with the common denominator:

$\frac{1}{2} - \frac{1}{3} + \frac{1}{9} = \frac{9}{18} - \frac{6}{18} + \frac{2}{18}$

Next, we perform the subtraction and addition:

$\frac{9}{18} - \frac{6}{18} + \frac{2}{18} = \frac{9 - 6 + 2}{18} = \frac{3 + 2}{18} = \frac{5}{18}$

3. Final Answer

$\frac{5}{18}$