To add the mixed numbers \(1 \frac{1}{2}\) and \(4 \frac{5}{6}\), we can first convert them into 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 \(4 \frac{5}{6}\) to an improper fraction: \[ 4 \frac{5}{6} = \frac{6 \times 4 + 5}{6} = \frac{24 + 5}{6} = \frac{29}{6} \]
Next, we need to add the two improper fractions: \[ \frac{3}{2} + \frac{29}{6} \]
To add these fractions, we need a common denominator. The least common multiple of 2 and 6 is 6. Now we will convert \(\frac{3}{2}\) to have a denominator of 6: \[ \frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6} \]
Now we can add the two fractions together: \[ \frac{9}{6} + \frac{29}{6} = \frac{9 + 29}{6} = \frac{38}{6} \]
We can simplify \(\frac{38}{6}\): \[ \frac{38}{6} = \frac{19}{3} \]
Next, we convert \(\frac{19}{3}\) back to a mixed number: \[ 19 \div 3 = 6 \quad \text{remainder } 1 \] So, as a mixed number, \(\frac{19}{3} = 6 \frac{1}{3}\).
The answer in mixed number form is: \[ 6 \frac{1}{3} \]
To complete your request, the whole number is: \[ \text{Whole number: } 6 \]
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