Solve 2/5x = 3/8: Unraveling the Fraction Equation

To solve the equation $\frac{2}{5}x = \frac{3}{8}$, we need to isolate $x$. We can achieve this by multiplying both sides by the reciprocal of $\frac{2}{5}$.

Step 1: Multiply both sides by $\frac{5}{2}$, which is the reciprocal of $\frac{2}{5}$:

$\frac{5}{2} \times \frac{2}{5}x = \frac{5}{2} \times \frac{3}{8}$

Step 2: Simplify the left side. The $\frac{5}{2}$ and $\frac{2}{5}$ cancel each other out:

$x = \frac{5 \times 3}{2 \times 8}$

Step 3: Simplify the right side by multiplying the numerators and denominators:

$x = \frac{15}{16}$

Therefore, the solution to the equation is $\boxed{\frac{15}{16}}$, which matches choice 3.