Решение и ответ:

[tex]\displaystyle \left({10-1\frac{{17}}{{27}}\div\frac{{22}}{{45}}}\right)\div 4\frac{4}{9}\cdot 2=3[/tex]

[tex]\displaystyle 1)\;\;1\frac{{17}}{{27}}\div\frac{{22}}{{45}}=\frac{{44}}{{27}}\div\frac{{22}}{{45}}=\frac{{44}}{{27}}\cdot\frac{{45}}{{22}}=\frac{{10}}{3}[/tex]

[tex]\displaystyle 2)\;\;10-\frac{{10}}{3}=\frac{{20}}{3}[/tex]

[tex]\displaystyle 3)\;\;\frac{{20}}{3}\div4\frac{4}{9}=\frac{{20}}{3}\div\frac{{40}}{9}=\frac{{20}}{3}\cdot\frac{9}{{40}}=\frac{3}{2}[/tex]

[tex]\displaystyle 4)\;\;\frac{3}{2}\cdot 2=3[/tex]