Solve Mixed Number Division: 4¼ ÷ 2⅛ Step-by-Step

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

• Step 1: Convert each mixed number to an improper fraction.
• Step 2: Perform the division by multiplying by the reciprocal of the divisor.
• Step 3: Simplify the resulting fraction if necessary.

Now, let's work through each step:
Step 1: Convert the mixed number $4\frac{1}{4}$ to an improper fraction. This is done by multiplying the whole number by the denominator and adding the numerator: $4 \times 4 + 1 = 17$. So, $4\frac{1}{4} = \frac{17}{4}$.
Convert $2\frac{1}{8}$ to an improper fraction: $2 \times 8 + 1 = 17$. Therefore, $2\frac{1}{8} = \frac{17}{8}$.

Step 2: Divide the fractions by multiplying by the reciprocal of the divisor. In this case, divide $\frac{17}{4}$ by $\frac{17}{8}$, which is equivalent to multiplying $\frac{17}{4}$ by $\frac{8}{17}$:
$\frac{17}{4} \times \frac{8}{17} = \frac{17 \times 8}{4 \times 17} = \frac{136}{68}$.

Step 3: Simplify the resulting fraction $\frac{136}{68}$. Since the numerator and the denominator are both divisible by 68, simplification gives: $\frac{136 \div 68}{68 \div 68} = \frac{2}{1} = 2$.

Therefore, the solution to the problem is $2$.