Bot GPT 4-o mini To divide the mixed numbers \(4 \frac{1}{3}\) and \(2 \frac{5}{6}\), we first convert them to improper fractions.
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Convert \(4 \frac{1}{3}\): \[ 4 \frac{1}{3} = \frac{4 \times 3 + 1}{3} = \frac{12 + 1}{3} = \frac{13}{3} \]
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Convert \(2 \frac{5}{6}\): \[ 2 \frac{5}{6} = \frac{2 \times 6 + 5}{6} = \frac{12 + 5}{6} = \frac{17}{6} \]
Now we need to divide \(\frac{13}{3}\) by \(\frac{17}{6}\). Dividing by a fraction is the same as multiplying by its reciprocal:
\[ \frac{13}{3} \div \frac{17}{6} = \frac{13}{3} \times \frac{6}{17} \]
Now we multiply the fractions:
\[ \frac{13 \times 6}{3 \times 17} = \frac{78}{51} \]
Next, we simplify \(\frac{78}{51}\). The greatest common divisor (GCD) of 78 and 51 is 3. Thus, we simplify it:
\[ \frac{78 \div 3}{51 \div 3} = \frac{26}{17} \]
Finally, we can convert \(\frac{26}{17}\) back to a mixed number:
\[ 26 \div 17 = 1 \quad \text{remainder } 9 \] So, \[ \frac{26}{17} = 1 \frac{9}{17} \]
Therefore, \(4 \frac{1}{3} \div 2 \frac{5}{6} = 1 \frac{9}{17}\).
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