a) \( \frac{3}{5}: 2-\frac{3}{2} \cdot(-2)+\frac{1}{9} \cdot \frac{3}{5}-\frac{2}{3} \)

To solve the expression \( \frac{3}{5}: 2-\frac{3}{2} \cdot(-2)+\frac{1}{9} \cdot \frac{3}{5}-\frac{2}{3} \), we’ll break it down step by step. 1. First, interpret the division \( \frac{3}{5}: 2 \) as \( \frac{3}{5} \div 2 \) which equals \( \frac{3}{5} \cdot \frac{1}{2} = \frac{3}{10} \). 2. Next, we compute \( -\frac{3}{2} \cdot (-2) \), which equals \( 3 \). 3. Then we calculate \( \frac{1}{9} \cdot \frac{3}{5} \), which equals \( \frac{3}{45} = \frac{1}{15} \). 4. Finally, we need to evaluate all parts: \( \frac{3}{10} - 3 + \frac{1}{15} - \frac{2}{3} \). Now, let's simplify: - Convert \( 3 \) to a fraction over \( 30 \): \( 3 = \frac{90}{30} \). - Convert \( \frac{2}{3} \) to a fraction over \( 30 \): \( \frac{2}{3} = \frac{20}{30} \). - Convert \( \frac{1}{15} \) to a fraction over \( 30 \): \( \frac{1}{15} = \frac{2}{30} \). Now, let’s put it all together: \[ \frac{3}{10} = \frac{9}{30} \] So now we have: \[ \frac{9}{30} - \frac{90}{30} + \frac{2}{30} - \frac{20}{30} = \frac{9 + 2 - 90 - 20}{30} = \frac{-99}{30} \] Finally, simplifying \( \frac{-99}{30} \) gives us: \[ \frac{-33}{10}. \] Thus, the final answer is: \[ \frac{-33}{10} \text{ or } -3.3. \]