To solve $\frac{1}{2} + \frac{1}{3} + \frac{1}{6}$, we need a common denominator.

Step 1: Determine the Least Common Denominator (LCD)

The denominators are $2$, $3$, and $6$. The least common multiple of these numbers is $6$.

Step 2: Rewrite Each Fraction with the LCD

• $\frac{1}{2} = \frac{3}{6}$
• $\frac{1}{3} = \frac{2}{6}$
• $\frac{1}{6} = \frac{1}{6}$

Step 3: Add the Fractions

Combine the fractions over the common denominator: $\frac{3}{6} + \frac{2}{6} + \frac{1}{6} = \frac{3+2+1}{6} = \frac{6}{6}.$

Step 4: Simplify

$\frac{6}{6} = 1.$

Final Answer:

$\boxed{1}$

Would you like a deeper breakdown of the steps or have any related questions? Here are some follow-up ideas:

1. How do you find the least common denominator (LCD)?
2. Can you add fractions with different denominators directly?
3. Why does $\frac{6}{6} = 1$?
4. How do you subtract or multiply fractions?
5. What is the process for dividing fractions?

Tip: Always simplify fractions after performing any operation to ensure clarity and correctness!