Solve Mixed Number Division: 100¼ ÷ (¼ × 5)

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

• Step 1: Convert $100\frac{1}{4}$ to an improper fraction.
• Step 2: Calculate the product $\frac{1}{4} \times 5$.
• Step 3: Perform the division of the improper fraction by the product from step 2.
• Step 4: Convert the result to a mixed number if needed.

Now, let's work through each step:
Step 1: The mixed number $100\frac{1}{4}$ converts to an improper fraction as follows:
$100\frac{1}{4} = \frac{100 \times 4 + 1}{4} = \frac{401}{4}$.
Step 2: The product of the fraction and integer is $\frac{1}{4} \times 5 = \frac{5}{4}$.
Step 3: We perform the division $\frac{401}{4} : \frac{5}{4}$. In fraction terms, this is:
$\frac{401}{4} \times \frac{4}{5} = \frac{401 \times 4}{4 \times 5} = \frac{401}{5}$.
Step 4: Convert $\frac{401}{5}$ to a mixed number:
Perform the division $401 \div 5$; quotient is 80 and remainder is 1.
Thus, $\frac{401}{5} = 80\frac{1}{5}$.

Therefore, the solution to the problem is $80\frac{1}{5}$.