We are asked to evaluate the expression: $-1\frac{4}{9} + \frac{7}{9} - \frac{2}{9} + 2\frac{1}{9}$.

1. Problem Description

We are asked to evaluate the expression:

$-1\frac{4}{9} + \frac{7}{9} - \frac{2}{9} + 2\frac{1}{9}$.

2. Solution Steps

First, we convert the mixed numbers to improper fractions:

$-1\frac{4}{9} = -\frac{(1 \times 9) + 4}{9} = -\frac{9+4}{9} = -\frac{13}{9}$

$2\frac{1}{9} = \frac{(2 \times 9) + 1}{9} = \frac{18+1}{9} = \frac{19}{9}$

Now, we rewrite the original expression with the improper fractions:

$-\frac{13}{9} + \frac{7}{9} - \frac{2}{9} + \frac{19}{9}$

Since all the fractions have the same denominator, we can combine the numerators:

$\frac{-13 + 7 - 2 + 19}{9}$

Now we simplify the numerator:

$-13 + 7 - 2 + 19 = -6 - 2 + 19 = -8 + 19 = 11$

Therefore, the expression simplifies to:

$\frac{11}{9}$

Now we convert the improper fraction back to a mixed number:

$\frac{11}{9} = 1\frac{2}{9}$

3. Final Answer

$1\frac{2}{9}$