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[tex]\displaystyle8-3\frac{6}{9}=8-3-\frac{6}{9} =5-\frac{6}{9} =\frac{5*9}{9} -\frac{6}{9} =\frac{45}{9} -\frac{6}{9} =\frac{45-6}{9} =\frac{39}{9} =\frac{13*3}{3*3} =\frac{13}{3} =\frac{4*3+1}{3} =4\frac{1}{3}[/tex]