To calculate \( 6 \div 3 \frac{1}{5} \), we first need to convert the mixed number \( 3 \frac{1}{5} \) into an improper fraction.
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Convert \( 3 \frac{1}{5} \): \[ 3 \frac{1}{5} = 3 + \frac{1}{5} = \frac{3 \times 5}{5} + \frac{1}{5} = \frac{15}{5} + \frac{1}{5} = \frac{16}{5} \]
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Now, rewrite the division: \[ 6 \div 3 \frac{1}{5} = 6 \div \frac{16}{5} \]
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To divide by a fraction, we multiply by its reciprocal: \[ 6 \div \frac{16}{5} = 6 \times \frac{5}{16} \]
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Convert 6 into a fraction: \[ 6 = \frac{6}{1} \]
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Now perform the multiplication: \[ \frac{6}{1} \times \frac{5}{16} = \frac{6 \times 5}{1 \times 16} = \frac{30}{16} \]
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Simplify \( \frac{30}{16} \): \[ \frac{30}{16} = \frac{15}{8} \]
So, the quotient of \( 6 \div 3 \frac{1}{5} \) is \( \frac{15}{8} \) or \( 1 \frac{7}{8} \) in mixed number form.