2⅔2222+22222

To simplify the expression \( 2\frac{2}{3}222 + 22222 \), we first convert the mixed number \( 2\frac{2}{3} \) into an improper fraction:

1. Convert \( 2\frac{2}{3} \): \[ 2\frac{2}{3} = 2 + \frac{2}{3} = \frac{6}{3} + \frac{2}{3} = \frac{8}{3} \]

2. So now the expression becomes: \[ \frac{8}{3} \cdot 222 + 22222 \]

3. Next, calculate \( \frac{8}{3} \cdot 222 \): \[ \frac{8 \cdot 222}{3} = \frac{1776}{3} = 592 \]

4. Now add \( 592 + 22222 \): \[ 592 + 22222 = 22814 \]

Therefore, the final answer is: \[ \boxed{22814} \]