To divide \( 6 \frac{3}{8} \) by \( 3 \), you can first convert the mixed number into an improper fraction.
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Convert \( 6 \frac{3}{8} \) to an improper fraction: \[ 6 \frac{3}{8} = 6 + \frac{3}{8} = \frac{6 \times 8 + 3}{8} = \frac{48 + 3}{8} = \frac{51}{8} \]
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Now, divide this improper fraction by \( 3 \): \[ \frac{51}{8} \div 3 = \frac{51}{8} \div \frac{3}{1} = \frac{51}{8} \times \frac{1}{3} = \frac{51 \times 1}{8 \times 3} = \frac{51}{24} \]
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Now, simplify \( \frac{51}{24} \):
- Find the greatest common divisor (GCD) of \( 51 \) and \( 24 \). The GCD is \( 3 \).
- Divide both the numerator and the denominator by their GCD: \[ \frac{51 \div 3}{24 \div 3} = \frac{17}{8} \]
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Convert \( \frac{17}{8} \) back to a mixed number:
- \( 17 \div 8 = 2 \) remainder \( 1 \), so: \[ \frac{17}{8} = 2 \frac{1}{8} \]
Therefore, the quotient when \( 6 \frac{3}{8} \) is divided by \( 3 \) is \( 2 \frac{1}{8} \).