[tex]3\frac{2}{9} +6\frac{5}{7} +4\frac{11}{13} +4\frac{7}{9}

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To add these mixed numbers, we first convert them to improper fractions:

3\frac{2}{9} = \frac{29}{9}

6\frac{5}{7} = \frac{47}{7}

4\frac{11}{13} = \frac{57}{13}

4\frac{7}{9} = \frac{43}{9}

Now add the fractions together:

\frac{29}{9} + \frac{47}{7} + \frac{57}{13} + \frac{43}{9}

To add fractions with different denominators, we first find a common denominator. In this case, the common denominator is 819 (9 x 7 x 13).

Rewrite each fraction with the common denominator:

\frac{29 \times 91}{9 \times 91} + \frac{47 \times 117}{7 \times 117} + \frac{57 \times 63}{13 \times 63} + \frac{43 \times 91}{9 \times 91}

Now we add the numerators together:

\frac{2639 + 5499 + 3591 + 3913}{819}

\frac{15642}{819}

Now we simplify the fraction:

15642 ÷ 819 = 19

So, 3\frac{2}{9} + 6\frac{5}{7} + 4\frac{11}{13} + 4\frac{7}{9} = 19.