Solve Mixed Number Division: 5¼ ÷ 2⅜ Step-by-Step

To solve this problem, we will divide the mixed numbers by following these steps:

• Step 1: Convert Mixed Numbers to Improper Fractions
  First, let's convert the mixed numbers to improper fractions.
  For $5\frac{1}{4}$:
  Convert using $\text{Whole part} \times \text{Denominator} + \text{Numerator}$:
  $5\frac{1}{4} = \frac{(5 \times 4) + 1}{4} = \frac{20 + 1}{4} = \frac{21}{4}$.

• For $2\frac{3}{8}$:
  Convert using the same method:
  $2\frac{3}{8} = \frac{(2 \times 8) + 3}{8} = \frac{16 + 3}{8} = \frac{19}{8}$.

• Step 2: Calculate the Division Using Reciprocal
  Now, we divide $\frac{21}{4}$ by $\frac{19}{8}$ by multiplying by the reciprocal:
  $\frac{21}{4} \div \frac{19}{8} = \frac{21}{4} \times \frac{8}{19} = \frac{21 \times 8}{4 \times 19}$.

• Simplify:
  Before multiplication, simplify where possible. Factor the numerator and denominator:
  $\frac{168}{76}$.

• Step 3: Simplify and Convert to Mixed Number
  Simplify $\frac{168}{76}$ by finding the greatest common divisor (GCD), which is 4:
  $\frac{168}{76} = \frac{168 \div 4}{76 \div 4} = \frac{42}{19}.$
  Convert $\frac{42}{19}$ to a mixed number:
  Divide 42 by 19 gives 2 with a remainder of 4:
  Thus, $\frac{42}{19} = 2\frac{4}{19}$.

Therefore, the solution to the problem is $2\frac{4}{19}$, which corresponds to choice 4.