To find the quotient of \( 6 \div 3 \frac{1}{5} \), we first need to convert the mixed number \( 3 \frac{1}{5} \) into an improper fraction.
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Convert \( 3 \frac{1}{5} \):
- Multiply the whole number (3) by the denominator (5): \( 3 \times 5 = 15 \)
- Add the numerator (1) to this result: \( 15 + 1 = 16 \)
- Therefore, \( 3 \frac{1}{5} = \frac{16}{5} \).
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Now perform the division: \[ 6 \div \frac{16}{5} = 6 \times \frac{5}{16} \]
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Convert 6 to a fraction: \[ 6 = \frac{6}{1} \] So, \[ 6 \times \frac{5}{16} = \frac{6 \times 5}{1 \times 16} = \frac{30}{16} \]
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Simplify \( \frac{30}{16} \):
- Both 30 and 16 can be divided by 2: \[ \frac{30 \div 2}{16 \div 2} = \frac{15}{8} \]
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Convert \( \frac{15}{8} \) to a mixed number:
- Divide 15 by 8, which gives 1 with a remainder of 7, leading to: \[ 1 \frac{7}{8} \]
Thus, the quotient of \( 6 \div 3 \frac{1}{5} \) is \( 1 \frac{7}{8} \).
The answer is: 1 7/8.