Solve Mixed Number Expression: 5½ - 2¾ + 4⅓

$5\frac{1}{2}-2\frac{3}{4}+4\frac{2}{6}=$

To solve this problem, we will perform the following steps:

• Convert each mixed fraction into an improper fraction.
• Find a common denominator for these fractions.
• Perform the subtraction and addition operations.
• Convert the result back into a mixed number.
• Simplify the final answer if necessary.

Let’s proceed with these steps.

Step 1: Convert to improper fractions
For $5\frac{1}{2}$:
$5\frac{1}{2} = \frac{5 \times 2 + 1}{2} = \frac{11}{2}$

For $2\frac{3}{4}$:
$2\frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{11}{4}$

For $4\frac{2}{6}$ (simplified as $4\frac{1}{3}$):
$4\frac{2}{6} = 4\frac{1}{3} = \frac{4 \times 3 + 1}{3} = \frac{13}{3}$

Step 2: Find a common denominator
The denominators are $2$, $4$, and $3$. The least common multiple of these is $12$.
Convert each fraction:
$\frac{11}{2} = \frac{11 \times 6}{2 \times 6} = \frac{66}{12}$
$\frac{11}{4} = \frac{11 \times 3}{4 \times 3} = \frac{33}{12}$
$\frac{13}{3} = \frac{13 \times 4}{3 \times 4} = \frac{52}{12}$

Step 3: Perform the operations
First, perform the subtraction:
$\frac{66}{12} - \frac{33}{12} = \frac{33}{12}$

Now, add $\frac{33}{12}$ and $\frac{52}{12}$:
$\frac{33}{12} + \frac{52}{12} = \frac{85}{12}$

Step 4: Convert back to a mixed number
$\frac{85}{12}$ as a mixed number is $7\frac{1}{12}$ because:
$\frac{85}{12} = 7$ remainder $1$, thus $7\frac{1}{12}$.

Step 5: Simplify
The fraction $\frac{1}{12}$ is already in its simplest form.

Therefore, the correct answer is $7\frac{1}{12}$.