d) \( \frac{\frac{1}{5}-\frac{2}{25}}{\frac{1}{10}-\frac{3}{5}} \)

To solve the expression \( \frac{\frac{1}{5}-\frac{2}{25}}{\frac{1}{10}-\frac{3}{5}} \), let’s break it down step by step! First, simplify the numerator: 1. Convert \( \frac{1}{5} \) to a fraction with a denominator of 25: \[ \frac{1}{5} = \frac{5}{25} \] 2. Now subtract \( \frac{2}{25} \): \[ \frac{5}{25} - \frac{2}{25} = \frac{5-2}{25} = \frac{3}{25} \] Next, simplify the denominator: 1. Convert \( \frac{1}{10} \) to a fraction with a denominator of 10: \[ \frac{3}{5} = \frac{6}{10} \] 2. Now subtract: \[ \frac{1}{10} - \frac{6}{10} = \frac{1-6}{10} = \frac{-5}{10} = -\frac{1}{2} \] Now the expression is simplified to: \[ \frac{\frac{3}{25}}{-\frac{1}{2}} \] To divide by a fraction, multiply by its reciprocal: \[ \frac{3}{25} \times -2 = -\frac{6}{25} \] So, the final answer is: \[ -\frac{6}{25} \]