-1/4*8/5-5/12*3/25

To simplify the expression \(-\frac{1}{4} \times \frac{8}{5} - \frac{5}{12} \times \frac{3}{25}\), let's break it down step by step. 1. Calculate \(-\frac{1}{4} \times \frac{8}{5}\): \[ -\frac{1 \times 8}{4 \times 5} = -\frac{8}{20} = -\frac{2}{5} \] 2. Calculate \(-\frac{5}{12} \times \frac{3}{25}\): \[ -\frac{5 \times 3}{12 \times 25} = -\frac{15}{300} = -\frac{1}{20} \] 3. Now we need to combine these results: \[ -\frac{2}{5} - \left(-\frac{1}{20}\right) = -\frac{2}{5} + \frac{1}{20} \] 4. To perform the addition, we need a common denominator, which would be 20: \[ -\frac{2}{5} = -\frac{2 \times 4}{5 \times 4} = -\frac{8}{20} \] Now, we can add: \[ -\frac{8}{20} + \frac{1}{20} = -\frac{8 - 1}{20} = -\frac{7}{20} \] Thus, the final answer is: \[ -\frac{7}{20} \]