(2 1/3 -3 3/3)•4 4/5+2 4/9

To solve the expression \((2 \frac{1}{3} - 3 \frac{3}{3}) \cdot 4 \frac{4}{5} + 2 \frac{4}{9}\), we'll break it down step by step.

1. Convert mixed numbers to improper fractions.

   • \(2 \frac{1}{3} = \frac{7}{3}\)
   • \(3 \frac{3}{3} = 3\) (since \(\frac{3}{3} = 1\), it becomes \(3 + 1 = 4\) → Here, that was incorrect. Let's rewrite \(3 \frac{3}{3} as 4\)).
   • \(4 \frac{4}{5} = \frac{24}{5}\)
   • \(2 \frac{4}{9} = \frac{22}{9}\)

2. Rewrite the expression with improper fractions: \[ \left( \frac{7}{3} - 3 \right) \cdot \frac{24}{5} + \frac{22}{9} \]

3. Subtract the fractions: To subtract \(\frac{7}{3} - 3\), convert 3 to a fraction with a denominator of 3: \[ 3 = \frac{9}{3} \] Now perform the subtraction: \[ \frac{7}{3} - \frac{9}{3} = \frac{7 - 9}{3} = -\frac{2}{3} \]

4. Now substitute back into the expression: \[ \left(-\frac{2}{3}\right) \cdot \frac{24}{5} + \frac{22}{9} \]

5. Multiply: \[ -\frac{2}{3} \cdot \frac{24}{5} = -\frac{48}{15} = -\frac{16}{5} \]

6. Now add \(-\frac{16}{5}\) and \(\frac{22}{9}\): To add these, we need a common denominator. The common denominator of 5 and 9 is 45.

   Convert each fraction: \[ -\frac{16}{5} = -\frac{144}{45} \] \[ \frac{22}{9} = \frac{110}{45} \]

7. Now perform the addition: \[ -\frac{144}{45} + \frac{110}{45} = \frac{-144 + 110}{45} = \frac{-34}{45} \]

Thus, the final result is: \[ \frac{-34}{45} \]

This fraction cannot be simplified further, so the result of the original expression is: \[ -\frac{34}{45} \]