To add the mixed number \(2 \frac{3}{5}\) and the fraction \(\frac{9}{10}\), we first convert the mixed number to an improper fraction.
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Convert \(2 \frac{3}{5}\) to an improper fraction: \[ 2 \frac{3}{5} = 2 \times 5 + 3 = 10 + 3 = 13 \] So, \(2 \frac{3}{5} = \frac{13}{5}\).
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Now we can add \(\frac{13}{5}\) and \(\frac{9}{10}\). To do this, we need a common denominator. The least common multiple of 5 and 10 is 10.
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Convert \(\frac{13}{5}\) to have a denominator of 10: \[ \frac{13}{5} = \frac{13 \times 2}{5 \times 2} = \frac{26}{10} \]
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Now we add \(\frac{26}{10}\) and \(\frac{9}{10}\): \[ \frac{26}{10} + \frac{9}{10} = \frac{26 + 9}{10} = \frac{35}{10} \]
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Simplify \(\frac{35}{10}\): \[ \frac{35}{10} = \frac{35 \div 5}{10 \div 5} = \frac{7}{2} \]
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Convert \(\frac{7}{2}\) to a mixed number: \[ \frac{7}{2} = 3 \frac{1}{2} \]
Thus, the final answer in mixed number form is: \[ 3 \frac{1}{2} \]
So, the answer is: \[ [3] [1]/[2] \]
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