To solve \(1 \frac{1}{2} + 1 \frac{1}{5}\), we first convert the mixed numbers to improper fractions.
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Convert \(1 \frac{1}{2}\): \[ 1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} \]
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Convert \(1 \frac{1}{5}\): \[ 1 \frac{1}{5} = 1 + \frac{1}{5} = \frac{5}{5} + \frac{1}{5} = \frac{6}{5} \]
Now we can add the two improper fractions: \[ \frac{3}{2} + \frac{6}{5} \]
To add these fractions, we need a common denominator. The least common multiple (LCM) of 2 and 5 is 10.
Convert each fraction to have the denominator of 10: \[ \frac{3}{2} = \frac{3 \times 5}{2 \times 5} = \frac{15}{10} \] \[ \frac{6}{5} = \frac{6 \times 2}{5 \times 2} = \frac{12}{10} \]
Now we can add the two fractions: \[ \frac{15}{10} + \frac{12}{10} = \frac{27}{10} \]
Next, we convert the improper fraction \(\frac{27}{10}\) back to a mixed number: \[ 27 \div 10 = 2 \quad \text{(whole number)} \] \[ \text{Remainder: } 27 - 20 = 7 \] So, \(\frac{27}{10} = 2 \frac{7}{10}\).
Thus, the answer in mixed number form is \(2 \frac{7}{10}\).
The whole number is: \[ \boxed{2} \]
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