a) \( \frac{3}{5}-\frac{2}{3}+\frac{1}{6} \cdot \frac{1}{5}=\frac{13}{30} \)

Let’s break it down step by step! First, we need a common denominator to combine \( \frac{3}{5} \) and \( \frac{2}{3} \). The least common multiple of 5 and 3 is 15. Rewriting, we have: - \( \frac{3}{5} = \frac{9}{15} \) - \( \frac{2}{3} = \frac{10}{15} \) Now we can change the first part of the equation to \( \frac{9}{15} - \frac{10}{15} = -\frac{1}{15} \). Next, we calculate \( \frac{1}{6} \cdot \frac{1}{5} = \frac{1}{30} \). Now, we are combining \( -\frac{1}{15} + \frac{1}{30} \). First, convert \( -\frac{1}{15} \) to a denominator of 30: \( -\frac{2}{30} \). So, we have: \(-\frac{2}{30} + \frac{1}{30} = -\frac{1}{30}\). Hence, the final result is \( -\frac{1}{30} \), indicating that the original statement \( \frac{3}{5} - \frac{2}{3} + \frac{1}{6} \cdot \frac{1}{5} = \frac{13}{30} \) is not correct!