We are asked to solve the expression $\frac{3}{2} \div \frac{5}{4}$.

1. Problem Description

We are asked to solve the expression $\frac{3}{2} \div \frac{5}{4}$.

2. Solution Steps

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.

The reciprocal of $\frac{5}{4}$ is $\frac{4}{5}$.

Therefore, we have

$\frac{3}{2} \div \frac{5}{4} = \frac{3}{2} \times \frac{4}{5}$.

Now, we multiply the numerators and the denominators:

$\frac{3}{2} \times \frac{4}{5} = \frac{3 \times 4}{2 \times 5} = \frac{12}{10}$.

We can simplify the fraction $\frac{12}{10}$ by dividing both the numerator and the denominator by their greatest common divisor, which is

2. $\frac{12}{10} = \frac{12 \div 2}{10 \div 2} = \frac{6}{5}$.

3. Final Answer

$\frac{6}{5}$