1. The problem is to calculate the value of $\frac{1}{25} \times 4$. 2. The formula for multiplication of fractions is $\frac{a}{b} \times c = \frac{a \times c}{b}$. 3. Applying the formula: $$\frac{1}{25} \times 4 = \frac{1 \times 4}{25} = \frac{4}{25}$$ 4. The fraction $\frac{4}{25}$ cannot be simplified further because 4 and 25 have no common factors other than 1. 5. Therefore, the final answer is $\frac{4}{25}$.