Solve the Fraction Addition: 1/2 + 1/6 Step-by-Step

To solve the problem of adding $\frac{1}{2}$ and $\frac{1}{6}$, we need to follow these steps:

• Step 1: Determine the least common denominator (LCD).
• Step 2: Convert the fractions to have this common denominator.
• Step 3: Add the fractions.
• Step 4: Simplify the result if necessary.

Step 1: The denominators are 2 and 6. The least common multiple of 2 and 6 is 6.

Step 2: We convert each fraction:
- Convert $\frac{1}{2}$ to a denominator of 6: $\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}$.
- The fraction $\frac{1}{6}$ already has the denominator 6.

Step 3: Add the fractions with common denominators:
$\frac{3}{6} + \frac{1}{6} = \frac{3 + 1}{6} = \frac{4}{6}.$

Step 4: Simplify the fraction $\frac{4}{6}$.
The greatest common divisor of 4 and 6 is 2, so divide both the numerator and the denominator by 2:
$\frac{4}{6} = \frac{4 \div 2}{6 \div 2} = \frac{2}{3}.$

Therefore, the solution to the problem is $\frac{2}{3}$.