Solve the Fraction Division Problem: (1 7/8 ÷ 4/5) ÷ (3 x 8) = ?

To solve this problem, we'll follow these steps:

• Step 1: Convert mixed number to improper fraction.
• Step 2: Perform division of fractions and evaluate further operations.
• Step 3: Simplify the final expression.

Let's work through each step:
Step 1: Convert $1\frac{7}{8}$ to an improper fraction:
$1\frac{7}{8} = \frac{15}{8}$, since $1 \times 8 + 7 = 15$.

Step 2: Divide $\frac{15}{8}$ by $\frac{4}{5}$:
Instead of dividing, multiply by the reciprocal of $\frac{4}{5}$. Thus, $\frac{15}{8} : \frac{4}{5} = \frac{15}{8} \times \frac{5}{4} = \frac{75}{32}$.

Step 3: Divide the result by $3 \cdot 8$, which equals $24$:
We have $\frac{75}{32} : 24 = \frac{75}{32} \times \frac{1}{24} = \frac{75}{768}$.

Simplifying $\frac{75}{768}$, we find the greatest common divisor of the numerator and the denominator is 3:
$\frac{75 \div 3}{768 \div 3} = \frac{25}{256}$.

Therefore, the answer to the problem is $\frac{25}{256}$.