To add the mixed number \( 2 \frac{1}{3} \) and the fraction \( \frac{8}{9} \), we first convert the mixed number into an improper fraction.
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Convert \( 2 \frac{1}{3} \) to an improper fraction: \[ 2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3} \]
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Now we need to add \( \frac{7}{3} \) and \( \frac{8}{9} \). To do this, we need a common denominator. The least common denominator (LCD) of 3 and 9 is 9.
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Convert \( \frac{7}{3} \) to have a denominator of 9: \[ \frac{7}{3} = \frac{7 \times 3}{3 \times 3} = \frac{21}{9} \]
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Now we can add the two fractions: \[ \frac{21}{9} + \frac{8}{9} = \frac{21 + 8}{9} = \frac{29}{9} \]
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Convert \( \frac{29}{9} \) back to a mixed number:
- Divide 29 by 9, which equals 3 with a remainder of 2.
- Thus, \( \frac{29}{9} = 3 \frac{2}{9} \).
The final answer in mixed number form is: \[ 3 \frac{2}{9} \]
To fill in your format: [3] [2]/[9]