To solve the expression $\frac{1}{2} + \frac{2}{3}$, we need to find a common denominator.

1. The denominators are 2 and 3. The least common denominator (LCD) is 6.
2. Convert each fraction to have this common denominator:
   • $\frac{1}{2} = \frac{3}{6}$ (since $1 \times 3 = 3$ and $2 \times 3 = 6$)
   • $\frac{2}{3} = \frac{4}{6}$ (since $2 \times 2 = 4$ and $3 \times 2 = 6$)
3. Now, add the fractions:
   $\frac{3}{6} + \frac{4}{6} = \frac{3 + 4}{6} = \frac{7}{6}$

The result is $\frac{7}{6}$, which is an improper fraction and can also be written as $1 \frac{1}{6}$.

Would you like further details or have any questions?

Here are 5 related questions you might find interesting:

1. How do you add fractions with different denominators?
2. How can improper fractions be converted into mixed numbers?
3. What is the least common denominator and how is it used?
4. How do you subtract fractions with unlike denominators?
5. What are the steps to multiply fractions?

Tip: When adding or subtracting fractions, always ensure the denominators are the same before performing the operation.