Solve Mixed Number Subtraction: 6½ minus 1¾

Let's work through the problem:

Step 1: Convert to improper fractions.
The mixed number $6\frac{1}{2}$ is converted to an improper fraction as follows:

• Multiply the whole number 6 by the denominator 2: $6 \times 2 = 12$.

• Add the numerator 1: $12 + 1 = 13$.

• The improper fraction is $\frac{13}{2}$.

The mixed number $1\frac{3}{4}$ is converted to an improper fraction as follows:

• Multiply the whole number 1 by the denominator 4: $1 \times 4 = 4$.

• Add the numerator 3: $4 + 3 = 7$.

• The improper fraction is $\frac{7}{4}$.

Step 2: Find a common denominator.
The denominators are 2 and 4. The least common denominator is 4.

Step 3: Adjust fractions to have the common denominator.
$\frac{13}{2}$ needs to be adjusted to have a denominator of 4:

• Multiply both the numerator and the denominator by 2: $\frac{13 \times 2}{2 \times 2} = \frac{26}{4}$.

Step 4: Perform the subtraction.
Subtract $\frac{7}{4}$ from $\frac{26}{4}$:

• $\frac{26}{4} - \frac{7}{4} = \frac{26 - 7}{4} = \frac{19}{4}$.

Step 5: Convert the improper fraction back to a mixed number.
Divide the numerator by the denominator:

• $19 \div 4 = 4$ with a remainder of 3.

• The mixed number is $4\frac{3}{4}$.

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