To find the quotient of \(5 \frac{2}{7} \div 1 \frac{1}{2}\), we first need to convert the mixed numbers into improper fractions.
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Convert \(5 \frac{2}{7}\): \[ 5 \frac{2}{7} = \frac{5 \times 7 + 2}{7} = \frac{35 + 2}{7} = \frac{37}{7} \]
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Convert \(1 \frac{1}{2}\): \[ 1 \frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2} \]
Now, we can divide the two improper fractions: \[ \frac{37}{7} \div \frac{3}{2} = \frac{37}{7} \times \frac{2}{3} \]
Multiply the fractions: \[ \frac{37 \times 2}{7 \times 3} = \frac{74}{21} \]
Now, we can simplify the result if needed. \(74\) and \(21\) have no common factors, so we can leave it as is.
To express \(\frac{74}{21}\) as a mixed number: \[ 74 \div 21 = 3 \quad \text{(with a remainder of } 11\text{)} \] So, \[ \frac{74}{21} = 3 \frac{11}{21} \]
Thus, the quotient of \(5 \frac{2}{7} \div 1 \frac{1}{2}\) is \(\frac{74}{21}\) or \(3 \frac{11}{21}\).