Bot GPT 4-o mini To add the mixed numbers \(4\ \frac{1}{6}\) and \(5\ \frac{2}{3}\), we first convert them into improper fractions.
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Convert \(4\ \frac{1}{6}\) into an improper fraction: \[ 4\ \frac{1}{6} = 4 \times 6 + 1 = 24 + 1 = 25 \quad \text{(so it is } \frac{25}{6}) \]
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Convert \(5\ \frac{2}{3}\) into an improper fraction: \[ 5\ \frac{2}{3} = 5 \times 3 + 2 = 15 + 2 = 17 \quad \text{(so it is } \frac{17}{3}) \]
Now we need to add \(\frac{25}{6}\) and \(\frac{17}{3}\). To do this, we need a common denominator. The least common multiple of 6 and 3 is 6.
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Convert \(\frac{17}{3}\) to an equivalent fraction with a denominator of 6: \[ \frac{17}{3} = \frac{17 \times 2}{3 \times 2} = \frac{34}{6} \]
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Now we can add the fractions: \[ \frac{25}{6} + \frac{34}{6} = \frac{25 + 34}{6} = \frac{59}{6} \]
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Convert \(\frac{59}{6}\) back to a mixed number: \[ 59 \div 6 = 9 \quad \text{(with a remainder of } 5\text{)} \] So, \[ \frac{59}{6} = 9\ \frac{5}{6} \]
Thus, the answer is: \[ 4\ \frac{1}{6} + 5\ \frac{2}{3} = 9\ \frac{5}{6} \]
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