The problem requires us to solve for $b$ in the equation $\frac{a}{bc} = \frac{d}{e}$.

1. Problem Description

The problem requires us to solve for $b$ in the equation $\frac{a}{bc} = \frac{d}{e}$.

2. Solution Steps

We are given the equation:

$\frac{a}{bc} = \frac{d}{e}$

First, we can cross-multiply to get rid of the fractions:

$ae = bcd$

Now, to isolate $b$, we divide both sides of the equation by $cd$:

$\frac{ae}{cd} = \frac{bcd}{cd}$

This simplifies to:

$b = \frac{ae}{cd}$

3. Final Answer

$b = \frac{ae}{cd}$