To add \(\frac{2}{6} + \frac{1}{2}\), we first need to make the denominators the same.
### Step-by-Step Solution
1. **Simplify Fractions**:
- \(\frac{2}{6}\) can be simplified to \(\frac{1}{3}\), since 2 and 6 have a common factor of 2.
- Now the problem is \(\frac{1}{3} + \frac{1}{2}\).
2. **Find a Common Denominator**:
- The denominators are 3 and 2. The least common multiple (LCM) of 3 and 2 is 6, so we’ll use 6 as the common denominator.
3. **Convert Fractions**:
- To convert \(\frac{1}{3}\) to a fraction with a denominator of 6, multiply both the numerator and denominator by 2:
\[
\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}
\]
- To convert \(\frac{1}{2}\) to a fraction with a denominator of 6, multiply both the numerator and denominator by 3:
\[
\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}
\]
4. **Add the Fractions**:
- Now that we have \(\frac{2}{6} + \frac{3}{6}\), we can add the numerators while keeping the denominator the same:
\[
\frac{2}{6} + \frac{3}{6} = \frac{2 + 3}{6} = \frac{5}{6}
\]
### Final Answer
\[
\frac{2}{6} + \frac{1}{2} = \frac{5}{6}
\]
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