Bot GPT 4-o mini To divide the mixed numbers \(1 \frac{1}{2}\) by \(1 \frac{7}{8}\), we first convert them to improper fractions.
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Convert \(1 \frac{1}{2}\) to an improper fraction: \[ 1 \frac{1}{2} = \frac{2 \times 1 + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2} \]
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Convert \(1 \frac{7}{8}\) to an improper fraction: \[ 1 \frac{7}{8} = \frac{8 \times 1 + 7}{8} = \frac{8 + 7}{8} = \frac{15}{8} \]
Now we can set up the division: \[ \frac{3}{2} \div \frac{15}{8} \] To divide by a fraction, we multiply by its reciprocal: \[ \frac{3}{2} \times \frac{8}{15} \]
Now multiply the numerators and denominators: \[ \frac{3 \times 8}{2 \times 15} = \frac{24}{30} \]
We can simplify \(\frac{24}{30}\) by finding the greatest common divisor (GCD), which is 6: \[ \frac{24 \div 6}{30 \div 6} = \frac{4}{5} \]
Thus, the final answer is: \[ \boxed{\frac{4}{5}} \]
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