To add the mixed numbers \(2 \frac{2}{5}\) and \(2 \frac{7}{10}\), follow these steps:
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Convert the mixed numbers to improper fractions:
- \(2 \frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{10 + 2}{5} = \frac{12}{5}\)
- \(2 \frac{7}{10} = \frac{2 \times 10 + 7}{10} = \frac{20 + 7}{10} = \frac{27}{10}\)
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Find a common denominator: The denominators are 5 and 10. The least common multiple of 5 and 10 is 10.
- Convert \(\frac{12}{5}\) to have a denominator of 10: \[ \frac{12}{5} = \frac{12 \times 2}{5 \times 2} = \frac{24}{10} \]
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Add the fractions: Now, add \(\frac{24}{10}\) and \(\frac{27}{10}\): \[ \frac{24}{10} + \frac{27}{10} = \frac{24 + 27}{10} = \frac{51}{10} \]
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Convert back to a mixed number: To convert \(\frac{51}{10}\) back to a mixed number, divide the numerator by the denominator: \[ 51 \div 10 = 5 \text{ remainder } 1 \] Thus, \(\frac{51}{10} = 5 \frac{1}{10}\).
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Final answer: The final answer in simplest form is: \[ 5 \frac{1}{10} \] In the requested format, that would be:
\[ 5 \quad 1 \quad 10 \]