\( 2 \frac{1}{2} \) \( +5 \frac{1}{4} \) \( =\square \) (Simplify your answer. Type an integer, fraction, or a mixed number.)

To add the mixed numbers \( 2 \frac{1}{2} \) and \( 5 \frac{1}{4} \), first convert them to improper fractions. \( 2 \frac{1}{2} = \frac{5}{2} \) and \( 5 \frac{1}{4} = \frac{21}{4} \). Now, to add \( \frac{5}{2} \) and \( \frac{21}{4} \), we need a common denominator. The least common denominator (LCD) of 2 and 4 is 4. Convert \( \frac{5}{2} \) to \( \frac{10}{4} \). Now add the fractions: \[ \frac{10}{4} + \frac{21}{4} = \frac{31}{4} \] Convert \( \frac{31}{4} \) back to a mixed number: \[ 31 \div 4 = 7 \text{ remainder } 3 \Rightarrow 7 \frac{3}{4} \] So, \( 2 \frac{1}{2} + 5 \frac{1}{4} = 7 \frac{3}{4} \). Final answer: \( 7 \frac{3}{4} \)