To add the fractions \( \frac{2}{10} \) and \( \frac{1}{3} \), we first need to find a common denominator. The least common multiple (LCM) of 10 and 3 is 30.
Now, we will convert each fraction to have a denominator of 30:
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Convert \( \frac{2}{10} \): \[ \frac{2}{10} = \frac{2 \times 3}{10 \times 3} = \frac{6}{30} \]
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Convert \( \frac{1}{3} \): \[ \frac{1}{3} = \frac{1 \times 10}{3 \times 10} = \frac{10}{30} \]
Now we can add the two fractions: \[ \frac{6}{30} + \frac{10}{30} = \frac{6 + 10}{30} = \frac{16}{30} \]
Next, we can simplify \( \frac{16}{30} \): \[ \frac{16}{30} = \frac{8}{15} \quad \text{(dividing both the numerator and denominator by 2)} \]
Thus, the final result is: \[ \frac{8}{15} \]