[tex]\displaystyle\\5\frac{3}{4}\times\left(-2\frac{2}{9}\right)=\\\\\\=-\frac{5\times4+3}{4}\times\frac{2\times9+2}{9}=\\\\\\=-\frac{23}{4}\times\frac{20}{9}=-\frac{460}{36}=-\frac{115}{9}=\boxed{\bf12\frac{7}{9}}[/tex]
