b) \( \left(\frac{1}{3}+\frac{2}{5}\right)+\frac{1}{2} \)

To solve the expression \( \left(\frac{1}{3}+\frac{2}{5}\right)+\frac{1}{2} \), we first need to find a common denominator to add the fractions inside the parentheses. The least common multiple of 3 and 5 is 15. So we convert the fractions: \[ \frac{1}{3} = \frac{5}{15} \] \[ \frac{2}{5} = \frac{6}{15} \] Now we can add: \[ \frac{5}{15} + \frac{6}{15} = \frac{11}{15} \] Next, we add \(\frac{1}{2}\). The least common multiple of 15 and 2 is 30. We convert the fractions again: \[ \frac{11}{15} = \frac{22}{30} \] \[ \frac{1}{2} = \frac{15}{30} \] Now we can add these: \[ \frac{22}{30} + \frac{15}{30} = \frac{37}{30} \] Thus, the final answer is \(\frac{37}{30}\) or \(1 \frac{7}{30}\) when converted to a mixed number.