2 1/2 + 3/4 = to the lowest terms

1. **Convert Mixed Number to Improper Fraction:**

2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}

2. **Addition of Fractions:**

Find a common denominator. The least common denominator of 2 and 4 is 4.

3. **Convert Fractions to Have Common Denominator:**

\frac{5}{2} = \frac{5 \times 2}{2 \times 2} = \frac{10}{4}

4. **Add the Fractions:**

\frac{10}{4} + \frac{3}{4} = \frac{10+3}{4} = \frac{13}{4}

5. **Simplify the Fraction (if necessary):**

\frac{13}{4} \text{ is already in its simplest form.}

6. **Convert Back to Mixed Number (Optional):**

\frac{13}{4} = 3 \frac{1}{4}

The answer as an improper fraction is:

\frac{13}{4}

In lowest terms, there is no further simplification, so our final answer can also be considered simply as the improper fraction:

\frac{13}{4}