To simplify the division of mixed numbers \(25 \frac{1}{2}\) and \(4 \frac{1}{4}\), first convert them to improper fractions.
-
Convert \(25 \frac{1}{2}\) to an improper fraction: \[ 25 \frac{1}{2} = \left(25 \times 2 + 1\right) / 2 = \frac{50 + 1}{2} = \frac{51}{2} \]
-
Convert \(4 \frac{1}{4}\) to an improper fraction: \[ 4 \frac{1}{4} = \left(4 \times 4 + 1\right) / 4 = \frac{16 + 1}{4} = \frac{17}{4} \]
-
Now perform the division: \[ \frac{51}{2} \div \frac{17}{4} \] To divide by a fraction, multiply by its reciprocal: \[ \frac{51}{2} \times \frac{4}{17} \]
-
Multiply the fractions: \[ = \frac{51 \times 4}{2 \times 17} = \frac{204}{34} \]
-
Simplify the fraction: \[ \frac{204 \div 34}{34 \div 34} = \frac{6}{1} = 6 \]
Thus, \(25 \frac{1}{2} \div 4 \frac{1}{4} = 6\).