Simplify: \(2 \frac{1}{2} + 3 \frac{1}{4} - 1 \frac{1}{3}\)
Answer: A
First, convert the mixed fractions to improper fractions.
\(2 \frac{1}{2} = \frac{5}{2}\)
\(3 \frac{1}{4} = \frac{13}{4}\)
\(1 \frac{1}{3} = \frac{4}{3}\)
The expression is \(\frac{5}{2} + \frac{13}{4} - \frac{4}{3}\).
The LCM of the denominators (2, 4, 3) is 12.
\(\frac{5 \times 6}{12} + \frac{13 \times 3}{12} - \frac{4 \times 4}{12} = \frac{30 + 39 - 16}{12} = \frac{53}{12}\).
Converting back to a mixed fraction: \(53 \div 12\) gives a quotient of 4 and a remainder of 5. So, \(4 \frac{5}{12}\).