Solve Mixed Number Equation: 2½ + 3¾ - 1½

To solve this problem, we begin by converting each mixed number to an improper fraction:

• $2\frac{1}{2}$: Convert using the formula $\frac{ac + b}{c}$, where $a = 2$, $b = 1$, and $c = 2$. The improper fraction is $\frac{2 \times 2 + 1}{2} = \frac{5}{2}$.
• $3\frac{2}{4}$: Using the same formula, where $a = 3$, $b = 2$, and $c = 4$. The improper fraction is $\frac{3 \times 4 + 2}{4} = \frac{14}{4}$, which simplifies to $\frac{7}{2}$.
• $1\frac{3}{6}$: Again, using the formula, where $a = 1$, $b = 3$, and $c = 6$. The improper fraction is $\frac{1 \times 6 + 3}{6} = \frac{9}{6}$, which simplifies to $\frac{3}{2}$.

Next, we perform the addition and subtraction:

$\frac{5}{2} + \frac{7}{2} - \frac{3}{2}$

All fractions have the common denominator 2, so we can directly add and subtract the numerators:

$(5 + 7 - 3) / 2 = \frac{9}{2}$

Finally, convert the improper fraction $\frac{9}{2}$ back to a mixed number:

$9 \div 2 = 4$ with a remainder of 1, so $\frac{9}{2} = 4\frac{1}{2}$.

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