To divide \( 25 \frac{1}{2} \) by \( 4 \frac{1}{4} \), we first convert the mixed numbers into improper fractions.
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Convert \( 25 \frac{1}{2} \) to an improper fraction: \[ 25 \frac{1}{2} = 25 \times 2 + 1 = 50 + 1 = 51 \] So, \[ 25 \frac{1}{2} = \frac{51}{2} \]
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Convert \( 4 \frac{1}{4} \) to an improper fraction: \[ 4 \frac{1}{4} = 4 \times 4 + 1 = 16 + 1 = 17 \] So, \[ 4 \frac{1}{4} = \frac{17}{4} \]
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Now, we divide the two improper fractions: \[ \frac{51}{2} \div \frac{17}{4} \] Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{51}{2} \times \frac{4}{17} \]
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Multiply the numerators and the denominators: \[ = \frac{51 \times 4}{2 \times 17} \] \[ = \frac{204}{34} \]
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Simplify the fraction: To simplify \( \frac{204}{34} \), we can divide both the numerator and the denominator by 34: \[ = 6 \]
Thus, the quotient of \( 25 \frac{1}{2} \div 4 \frac{1}{4} \) is \( 6 \).