1. The problem is to divide the fractions $\frac{2}{5}$ by $\frac{3}{4}$.\n\n2. The formula for dividing fractions is: \n$$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$\nThis means we multiply the first fraction by the reciprocal of the second fraction.\n\n3. Applying the formula: \n$$\frac{2}{5} \div \frac{3}{4} = \frac{2}{5} \times \frac{4}{3}$$\n\n4. Multiply the numerators and denominators: \n$$\frac{2 \times 4}{5 \times 3} = \frac{8}{15}$$\n\n5. The fraction $\frac{8}{15}$ cannot be simplified further because 8 and 15 have no common factors other than 1.\n\n6. Therefore, the final answer is: \n$$\frac{2}{5} \div \frac{3}{4} = \frac{8}{15}$$