1/5 +2/6

To add the fractions \( \frac{1}{5} \) and \( \frac{2}{6} \), you need a common denominator.

1. First, find the least common denominator (LCD). The denominators are 5 and 6. The LCD of 5 and 6 is 30.

2. Convert each fraction to have a denominator of 30:

   • For \( \frac{1}{5} \): \[ \frac{1}{5} = \frac{1 \times 6}{5 \times 6} = \frac{6}{30} \]

   • For \( \frac{2}{6} \): \[ \frac{2}{6} = \frac{2 \times 5}{6 \times 5} = \frac{10}{30} \]

3. Now add the two fractions: \[ \frac{6}{30} + \frac{10}{30} = \frac{6 + 10}{30} = \frac{16}{30} \]

4. Finally, simplify \( \frac{16}{30} \): \[ \frac{16}{30} = \frac{8}{15} \quad \text{(dividing numerator and denominator by 2)} \]

Thus, \( \frac{1}{5} + \frac{2}{6} = \frac{8}{15} \).