To divide \( 14 \) by \( 5 \frac{5}{6} \), we first need to convert the mixed number into an improper fraction.
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Convert \( 5 \frac{5}{6} \) into an improper fraction: \[ 5 \frac{5}{6} = 5 \times 6 + 5 = 30 + 5 = 35 \quad \text{(the numerator)} \] So, \[ 5 \frac{5}{6} = \frac{35}{6} \]
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Now, we can express the division as: \[ 14 \div 5 \frac{5}{6} = 14 \div \frac{35}{6} \]
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Dividing by a fraction is the same as multiplying by its reciprocal: \[ 14 \div \frac{35}{6} = 14 \times \frac{6}{35} \]
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Now, we can multiply: \[ 14 \times \frac{6}{35} = \frac{14 \times 6}{35} = \frac{84}{35} \]
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Simplify \( \frac{84}{35} \):
- The greatest common divisor (GCD) of 84 and 35 is 7.
- Divide both the numerator and the denominator by 7: \[ \frac{84 \div 7}{35 \div 7} = \frac{12}{5} \]
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Convert \( \frac{12}{5} \) to a mixed number: \[ 12 \div 5 = 2 \quad \text{remainder } 2 \] So, \[ \frac{12}{5} = 2 \frac{2}{5} \]
Therefore, the final answer is: \[ \frac{12}{5} \text{ or } 2 \frac{2}{5} \]
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