Solve Mixed Number Division: 2⅓ ÷ ½ Step-by-Step

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

• Step 1: Convert the mixed number $2\frac{1}{3}$ to an improper fraction.
• Step 2: Take the reciprocal of $\frac{1}{2}$.
• Step 3: Multiply the improper fraction by the reciprocal.
• Step 4: Simplify the resulting fraction if necessary, and convert back to a mixed number.

Now, let's work through each step:
Step 1: Convert the mixed number $2\frac{1}{3}$ to an improper fraction.
$2\frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3}$.
Step 2: The reciprocal of $\frac{1}{2}$ is $2$.
Step 3: Multiply $\frac{7}{3}$ by $2$:
$\frac{7}{3} \times 2 = \frac{7 \times 2}{3} = \frac{14}{3}$.
Step 4: Convert the improper fraction $\frac{14}{3}$ to a mixed number.
Divide 14 by 3, which is 4 with a remainder of 2, so we have $4\frac{2}{3}$.

Therefore, the solution to the problem is $4\frac{2}{3}$.