Bot GPT 4-o mini To multiply the mixed numbers \(3 \frac{1}{3}\) and \(5 \frac{1}{2}\), we first convert them into improper fractions.
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Convert \(3 \frac{1}{3}\): \[ 3 \frac{1}{3} = 3 \times 3 + 1 = 9 + 1 = 10, \text{ so } \frac{10}{3} \]
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Convert \(5 \frac{1}{2}\): \[ 5 \frac{1}{2} = 5 \times 2 + 1 = 10 + 1 = 11, \text{ so } \frac{11}{2} \]
Now we can multiply the two improper fractions: \[ \frac{10}{3} \times \frac{11}{2} = \frac{10 \times 11}{3 \times 2} = \frac{110}{6} \]
Next, we simplify \(\frac{110}{6}\): \[ \frac{110 \div 2}{6 \div 2} = \frac{55}{3} \]
Finally, we convert \(\frac{55}{3}\) back to a mixed number: \[ 55 \div 3 = 18 \quad \text{(with a remainder of 1)} \] So, \(55 = 3 \times 18 + 1\), resulting in: \[ 18 \frac{1}{3} \]
Thus, the final answer is: \[ 3 \frac{1}{3} \times 5 \frac{1}{2} = 18 \frac{1}{3} \]
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