Bot GPT 4-o mini To divide \( \frac{8}{9} \) by \( 1 \frac{1}{3} \), we first need to convert the mixed number \( 1 \frac{1}{3} \) into an improper fraction.
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Convert \( 1 \frac{1}{3} \) to an improper fraction: \[ 1 \frac{1}{3} = 1 + \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3} \]
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To divide by a fraction, we multiply by its reciprocal. Thus, we divide \( \frac{8}{9} \) by \( \frac{4}{3} \) as follows: \[ \frac{8}{9} \div \frac{4}{3} = \frac{8}{9} \times \frac{3}{4} \]
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Multiply the fractions: \[ \frac{8 \times 3}{9 \times 4} = \frac{24}{36} \]
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Simplify \( \frac{24}{36} \) by finding the greatest common divisor (GCD), which is 12: \[ \frac{24 \div 12}{36 \div 12} = \frac{2}{3} \]
Thus, \( \frac{8}{9} \div 1 \frac{1}{3} = \frac{2}{3} \).
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