Solve Mixed Number Division: 1½ ÷ ⅔ Step-by-Step

To solve the given problem, we need to divide the mixed number by the fraction $\frac{2}{3}$. Here's a detailed step-by-step solution:

Step 1: Convert Mixed Number to Improper Fraction.
The mixed number $1\frac{1}{2}$ can be converted into an improper fraction. Multiply the whole number 1 by the denominator 2, and add the numerator 1. This gives us:

$1 \times 2 + 1 = 2 + 1 = 3$ Thus, the improper fraction is $\frac{3}{2}$.

Step 2: Divide by the Fraction $\frac{2}{3}$.
Dividing by a fraction is equivalent to multiplying by its reciprocal. So, $\frac{3}{2} \div \frac{2}{3}$ becomes $\frac{3}{2} \times \frac{3}{2}$.

Step 3: Perform the Multiplication.
Multiply the numerators together and the denominators together:

$\frac{3}{2} \times \frac{3}{2} = \frac{3 \times 3}{2 \times 2} = \frac{9}{4}$

Step 4: Convert to a Mixed Number if Needed.
Convert $\frac{9}{4}$ back to a mixed number. Divide 9 by 4, which gives 2 with a remainder of 1:

$9 \div 4 = 2 \quad \text{(whole number)}, \quad \text{remainder } 1$ Thus, $\frac{9}{4} = 2\frac{1}{4}$.

Therefore, the solution to the problem is $\boxed{2\frac{1}{4}}$.