To divide \( 5 \frac{2}{7} \) by \( 1 \frac{1}{2} \), we first convert both mixed numbers to 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 have: \[ 5 \frac{2}{7} \div 1 \frac{1}{2} = \frac{37}{7} \div \frac{3}{2} \]
To divide by a fraction, we multiply by its reciprocal: \[ \frac{37}{7} \div \frac{3}{2} = \frac{37}{7} \times \frac{2}{3} \]
Now, we perform the multiplication: \[ \frac{37 \times 2}{7 \times 3} = \frac{74}{21} \]
Finally, we simplify if necessary. The fraction \( \frac{74}{21} \) cannot be simplified further because 74 and 21 have no common factors.
Thus, the quotient \( 5 \frac{2}{7} \div 1 \frac{1}{2} \) is: \[ \frac{74}{21} \]
If you want to convert it back to a mixed number: \[ 74 \div 21 = 3 \quad \text{(since \( 21 \times 3 = 63 \))} \] The remainder is: \[ 74 - 63 = 11 \]
So, we can write \( \frac{74}{21} \) as: \[ 3 \frac{11}{21} \]
In conclusion, the answer is: \[ \frac{74}{21} \quad \text{or} \quad 3 \frac{11}{21} \]
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