1 3/5:1/4

To divide the fraction \( \frac{1 \frac{3}{5}}{\frac{1}{4}} \), you can first convert the mixed number to an improper fraction.

1. Convert \( 1 \frac{3}{5} \) to an improper fraction: \[ 1 \frac{3}{5} = \frac{5 \cdot 1 + 3}{5} = \frac{5 + 3}{5} = \frac{8}{5} \]

2. Now, rewrite the division of fractions: \[ \frac{8}{5} \div \frac{1}{4} \]

3. To divide by a fraction, multiply by its reciprocal: \[ \frac{8}{5} \times \frac{4}{1} \]

4. Multiply the numerators and the denominators: \[ = \frac{8 \cdot 4}{5 \cdot 1} = \frac{32}{5} \]

So, \( 1 \frac{3}{5} : \frac{1}{4} = \frac{32}{5} \), or as a mixed number: \[ \frac{32}{5} = 6 \frac{2}{5} \]

Thus, the solution is \( 6 \frac{2}{5} \) or \( \frac{32}{5} \).