To simplify the expression \( \frac{2}{5} + \frac{7}{15} + \frac{1}{5} \), we first need to find a common denominator for all the fractions. The denominators are 5 and 15. The least common denominator (LCD) is 15.
Now we convert each fraction to have a denominator of 15:
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For \( \frac{2}{5} \): \[ \frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15} \]
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For \( \frac{7}{15} \), it already has the denominator of 15.
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For \( \frac{1}{5} \): \[ \frac{1}{5} = \frac{1 \times 3}{5 \times 3} = \frac{3}{15} \]
Now we can rewrite the original expression with the common denominator: \[ \frac{6}{15} + \frac{7}{15} + \frac{3}{15} \]
Next, we can combine the fractions: \[ \frac{6 + 7 + 3}{15} = \frac{16}{15} \]
Thus, the simplified expression is: \[ \frac{16}{15} \]