Simplify the Nested Fraction: Calculating 32m Divided by (8t Divided by 3m)

To solve this problem, follow these steps:

• Step 1: Simplify the inner division $8t : 3m$. This can be rewritten as $\frac{8t}{3m}$.
• Step 2: Find the reciprocal of $\frac{8t}{3m}$. The reciprocal is $\frac{3m}{8t}$.
• Step 3: Multiply $32m$ by the reciprocal of the inner division result, which is $\frac{3m}{8t}$.

Carrying out the multiplication:

$32m \times \frac{3m}{8t} = \frac{32m \times 3m}{8t} = \frac{96m^2}{8t}$

Simplify the expression $\frac{96m^2}{8t}$ by dividing the numerator and the denominator by 8:

$= \frac{12m^2}{t}$

Thus, the final simplified solution is $12\frac{m^2}{t}$.

The correct choice from the given options is $12\frac{m^2}{t}$.