$$ 3 \frac { 1 } { 9 } - \frac { 5 \frac { 2 } { 5 } } { } + 4 \frac { 1 } { 18 } $$

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Let's simplify the expression $$ 3 \frac{1}{9} - \frac{5 \frac{2}{5}}{} + 4 \frac{1}{18} $$ step by step.

1. Convert the mixed numbers to improper fractions:
   - $$ 3 \frac{1}{9} = \frac{3 \times 9 + 1}{9} = \frac{27 + 1}{9} = \frac{28}{9} $$
   - $$ 5 \frac{2}{5} = \frac{5 \times 5 + 2}{5} = \frac{25 + 2}{5} = \frac{27}{5} $$
   - $$ 4 \frac{1}{18} = \frac{4 \times 18 + 1}{18} = \frac{72 + 1}{18} = \frac{73}{18} $$

2. Now, we can rewrite the expression:
   $$
   \frac{28}{9} - \frac{27}{5} + \frac{73}{18}
   $$

3. To perform the addition and subtraction, we need a common denominator. The least common multiple of $$ 9, 5, $$ and $$ 18 $$ is $$ 90 $$.

4. Convert each fraction to have a denominator of $$ 90 $$:
   - $$ \frac{28}{9} = \frac{28 \times 10}{90} = \frac{280}{90} $$
   - $$ \frac{27}{5} = \frac{27 \times 18}{90} = \frac{486}{90} $$
   - $$ \frac{73}{18} = \frac{73 \times 5}{90} = \frac{365}{90} $$

5. Now, substitute back into the expression:
   $$
   \frac{280}{90} - \frac{486}{90} + \frac{365}{90}
   $$

6. Combine the fractions:
   $$
   \frac{280 - 486 + 365}{90} = \frac{159}{90}
   $$

7. Finally, simplify $$ \frac{159}{90} $$ if possible.

Now, let's calculate the final result.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{159}{90}$$
- step1: Reduce the fraction:
  $$\frac{53}{30}$$
The simplified result of the expression $$ 3 \frac{1}{9} - \frac{5 \frac{2}{5}}{} + 4 \frac{1}{18} $$ is $$ \frac{53}{30} $$ or as a mixed number, $$ 1 \frac{23}{30} $$.
The simplified result is $$ \frac{53}{30} $$ or $$ 1 \frac{23}{30} $$.

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