To solve $\frac{2}{9} + \left( -\frac{1}{2} \right)$, we first need a common denominator.

The denominators are 9 and 2. The least common denominator (LCD) of 9 and 2 is 18.

1. Rewrite both fractions with 18 as the denominator:

$\frac{2}{9} = \frac{2 \times 2}{9 \times 2} = \frac{4}{18}$

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

2. Now add the fractions:

$\frac{4}{18} + \frac{-9}{18} = \frac{4 + (-9)}{18} = \frac{-5}{18}$

Thus, the result is $\frac{-5}{18}$.

Would you like further clarification on any part of the process?

Here are 5 questions to expand on this:

1. How do you find the least common denominator of two fractions?
2. What is the process of adding fractions with different denominators?
3. Can a negative sign affect a fraction's numerator or denominator?
4. How do you simplify a fraction if needed?
5. What is the difference between improper fractions and mixed numbers?

Tip: Always look for the least common denominator to make adding or subtracting fractions easier.