To add the mixed numbers \( 2 \frac{1}{3} \) and \( 1 \frac{4}{5} \), we can follow these steps:
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Convert the mixed numbers to improper fractions.
- \( 2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3} \)
- \( 1 \frac{4}{5} = \frac{1 \times 5 + 4}{5} = \frac{5 + 4}{5} = \frac{9}{5} \)
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Now add the two fractions, \( \frac{7}{3} \) and \( \frac{9}{5} \).
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To do this, we need a common denominator. The least common multiple of 3 and 5 is 15.
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Convert each fraction:
- \( \frac{7}{3} = \frac{7 \times 5}{3 \times 5} = \frac{35}{15} \)
- \( \frac{9}{5} = \frac{9 \times 3}{5 \times 3} = \frac{27}{15} \)
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Now add the two fractions: \[ \frac{35}{15} + \frac{27}{15} = \frac{35 + 27}{15} = \frac{62}{15} \]
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Convert \( \frac{62}{15} \) back to a mixed number:
- Divide 62 by 15. The quotient is 4 and the remainder is 2.
- Thus, \( \frac{62}{15} = 4 \frac{2}{15} \).
So, \( 2 \frac{3}{3} + 1 \frac{4}{5} = 4 \frac{2}{15} \).