To add $\frac{1}{2}$ and $\frac{2}{3}$, we need to find a common denominator.

Step 1: Find the least common denominator (LCD)

The denominators are 2 and 3. The least common denominator of 2 and 3 is 6.

Step 2: Convert the fractions

Convert $\frac{1}{2}$ and $\frac{2}{3}$ to fractions with a denominator of 6.

• $\frac{1}{2}$ becomes $\frac{1 \times 3}{2 \times 3} = \frac{3}{6}$
• $\frac{2}{3}$ becomes $\frac{2 \times 2}{3 \times 2} = \frac{4}{6}$

Step 3: Add the fractions

Now that the fractions have the same denominator, you can add them: $\frac{3}{6} + \frac{4}{6} = \frac{3 + 4}{6} = \frac{7}{6}$

Step 4: Simplify the fraction (if needed)

$\frac{7}{6}$ is already in its simplest form, but it can also be expressed as a mixed number: $\frac{7}{6} = 1 \frac{1}{6}$

So, $\frac{1}{2} + \frac{2}{3} = \frac{7}{6}$ or $1 \frac{1}{6}$.

Do you want more details or have any questions?

Here are 5 related questions:

1. How do you subtract fractions with different denominators?
2. What is the decimal equivalent of $\frac{7}{6}$?
3. How do you add mixed numbers?
4. Can you simplify $\frac{7}{6}$ further?
5. What is the result of $\frac{7}{6}$ multiplied by $\frac{1}{2}$?

Tip: Always make sure to find the least common denominator when adding or subtracting fractions!