To add \( 4 \frac{2}{3} \) and \( \frac{2}{3} \), first convert the mixed number to an improper fraction.
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Convert \( 4 \frac{2}{3} \) to an improper fraction: \[ 4 \frac{2}{3} = \frac{4 \times 3 + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3} \]
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Now, add \( \frac{14}{3} \) and \( \frac{2}{3} \): \[ \frac{14}{3} + \frac{2}{3} = \frac{14 + 2}{3} = \frac{16}{3} \]
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Convert \( \frac{16}{3} \) back to a mixed number: \[ \frac{16}{3} = 5 \frac{1}{3} \]
So, \( 4 \frac{2}{3} + \frac{2}{3} = 5 \frac{1}{3} \).