$$2 \frac { 2 } { 9 } \times 3 \frac { 4 } { 5 } \times 2 \frac { 3 } { 4 }$$
$\frac{209}{9}\approx 23.222222222$
$$\frac{18+2}{9}\times \frac{3\times 5+4}{5}\times \frac{2\times 4+3}{4}$$
$$\frac{20}{9}\times \frac{3\times 5+4}{5}\times \frac{2\times 4+3}{4}$$
$$\frac{20}{9}\times \frac{15+4}{5}\times \frac{2\times 4+3}{4}$$
$$\frac{20}{9}\times \frac{19}{5}\times \frac{2\times 4+3}{4}$$
$$\frac{20\times 19}{9\times 5}\times \frac{2\times 4+3}{4}$$
$$\frac{380}{45}\times \frac{2\times 4+3}{4}$$
$$\frac{76}{9}\times \frac{2\times 4+3}{4}$$
$$\frac{76}{9}\times \frac{8+3}{4}$$
$$\frac{76}{9}\times \frac{11}{4}$$
$$\frac{76\times 11}{9\times 4}$$
$$\frac{836}{36}$$
$$\frac{209}{9}$$
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$\frac{11 \cdot 19}{3 ^ {2}} = 23\frac{2}{9} = 23.22222222222222$
