To add the fractions $\frac{1}{2} + \frac{8}{11}$, we first need to find a common denominator.

1. The least common denominator (LCD) of 2 and 11 is 22.
2. Rewrite both fractions with the LCD of 22: $\frac{1}{2} = \frac{11}{22}, \quad \frac{8}{11} = \frac{16}{22}$
3. Now, add the two fractions: $\frac{11}{22} + \frac{16}{22} = \frac{27}{22}$

The result is $\frac{27}{22}$, which is an improper fraction and can also be written as a mixed number:

$\frac{27}{22} = 1 \frac{5}{22}$

Would you like more details on this process?

Here are 5 related questions:

1. How do you find the least common denominator between two numbers?
2. What is the difference between an improper fraction and a mixed number?
3. How can you convert a mixed number back into an improper fraction?
4. What are other methods for adding fractions with different denominators?
5. How do you subtract fractions with different denominators?

Tip: Always simplify fractions where possible to get the final result in its simplest form.