Solve Mixed Number Expression: 2¾ - ¼ + 3½ Step by Step

To solve the problem, we need to first convert the mixed numbers $2\frac{3}{4}$ and $3\frac{1}{2}$ to improper fractions and then perform the operations.

Step 1: Convert the mixed numbers to improper fractions.

• $2\frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4}$
• $3\frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2}$

Step 2: Find a common denominator for all fractions involved, which is $4$.

• $\frac{11}{4}$ is already expressed with the denominator $4$.
• $\frac{1}{4}$ is already expressed with the denominator $4$.
• $\frac{7}{2} = \frac{7 \times 2}{2 \times 2} = \frac{14}{4}$

Step 3: Perform the operations.

• $\frac{11}{4} - \frac{1}{4} + \frac{14}{4}$
• Perform subtraction: $\frac{11}{4} - \frac{1}{4} = \frac{11 - 1}{4} = \frac{10}{4}$.
• Perform addition: $\frac{10}{4} + \frac{14}{4} = \frac{10 + 14}{4} = \frac{24}{4}$.

Step 4: Simplify the resulting fraction.

• $\frac{24}{4} = 6$

The final result of $2\frac{3}{4} - \frac{1}{4} + 3\frac{1}{2} = 6$.

Therefore, the solution to the problem is $6$.