What is the quotient of \( 25 \frac{1}{2} \div 4 \frac{1}{4} \) ? Simplify the answer, if possible. (1 point)

To find the quotient of \( 25 \frac{1}{2} \div 4 \frac{1}{4} \), we first convert the mixed numbers to improper fractions. For \( 25 \frac{1}{2} \): \[ 25 \frac{1}{2} = 25 + \frac{1}{2} = \frac{25 \times 2 + 1}{2} = \frac{50 + 1}{2} = \frac{51}{2} \] For \( 4 \frac{1}{4} \): \[ 4 \frac{1}{4} = 4 + \frac{1}{4} = \frac{4 \times 4 + 1}{4} = \frac{16 + 1}{4} = \frac{17}{4} \] Now, we need to divide these two fractions: \[ \frac{51}{2} \div \frac{17}{4} = \frac{51}{2} \times \frac{4}{17} \] Now, we can multiply: \[ \frac{51 \times 4}{2 \times 17} = \frac{204}{34} \] Next, we simplify \( \frac{204}{34} \): \[ 204 \div 34 = 6 \] Thus, the quotient of \( 25 \frac{1}{2} \div 4 \frac{1}{4} \) is \( 6 \).