To add the mixed numbers \( 2 \frac{1}{3} \) and \( 1 \frac{2}{5} \), follow these steps:
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Convert mixed numbers to improper fractions:
- For \( 2 \frac{1}{3} \): \[ 2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3} \]
- For \( 1 \frac{2}{5} \): \[ 1 \frac{2}{5} = \frac{1 \times 5 + 2}{5} = \frac{5 + 2}{5} = \frac{7}{5} \]
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Add the improper fractions:
- To add \( \frac{7}{3} + \frac{7}{5} \), first find a common denominator. The least common multiple of \( 3 \) and \( 5 \) is \( 15 \).
- Convert both fractions: \[ \frac{7}{3} = \frac{7 \times 5}{3 \times 5} = \frac{35}{15} \] \[ \frac{7}{5} = \frac{7 \times 3}{5 \times 3} = \frac{21}{15} \]
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Now add them: \[ \frac{35}{15} + \frac{21}{15} = \frac{35 + 21}{15} = \frac{56}{15} \]
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Convert back to a mixed number:
- Perform the division \( 56 \div 15 = 3 \) with a remainder of \( 11 \).
- So, \( \frac{56}{15} = 3 \frac{11}{15} \).
Thus, \( 2 \frac{1}{3} + 1 \frac{2}{5} = 3 \frac{11}{15} \).