Solve Mixed Number Subtraction: 4½ - 2⅔ Step-by-Step

To solve this problem, we'll first convert each mixed number to an improper fraction, find a common denominator, subtract the fractions, and then convert back to a mixed number.

Step 1: Convert the mixed numbers to improper fractions.
- $4\frac{1}{2}$ becomes $\frac{4 \times 2 + 1}{2} = \frac{9}{2}$
- $2\frac{2}{3}$ becomes $\frac{2 \times 3 + 2}{3} = \frac{8}{3}$

Step 2: Find a common denominator for the two fractions.
- The denominators are 2 and 3; the least common denominator is $2 \times 3 = 6$.

Step 3: Convert each fraction to have this common denominator.
- $\frac{9}{2} = \frac{9 \times 3}{2 \times 3} = \frac{27}{6}$
- $\frac{8}{3} = \frac{8 \times 2}{3 \times 2} = \frac{16}{6}$

Step 4: Subtract the fractions.
- $\frac{27}{6} - \frac{16}{6} = \frac{27 - 16}{6} = \frac{11}{6}$

Step 5: Convert the result back to a mixed number.
- $\frac{11}{6}$ as a mixed number is $1\frac{5}{6}$.

Therefore, the solution to the problem is $1\frac{5}{6}$.