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

To solve the expression \( \frac{1}{4} \times \frac{8}{5} - \frac{5}{12} \times \frac{3}{25} \), we will calculate each multiplication first and then perform the subtraction.

1. Calculate \( \frac{1}{4} \times \frac{8}{5} \): \[ \frac{1 \times 8}{4 \times 5} = \frac{8}{20} = \frac{2}{5} \quad \text{(after simplifying)} \]

2. Calculate \( \frac{5}{12} \times \frac{3}{25} \): \[ \frac{5 \times 3}{12 \times 25} = \frac{15}{300} = \frac{1}{20} \quad \text{(after simplifying)} \]

Now we need to subtract \( \frac{1}{20} \) from \( \frac{2}{5} \). To do that, we need a common denominator.

The least common denominator of \( 5 \) and \( 20 \) is \( 20 \):

Convert \( \frac{2}{5} \) to a fraction with a denominator of \( 20 \): \[ \frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20} \]

Now, subtract: \[ \frac{8}{20} - \frac{1}{20} = \frac{8 - 1}{20} = \frac{7}{20} \]

Therefore, the answer is: \[ \frac{7}{20} \]