At the beggining the ratio of cats to dogs is
[tex]\frac{12}{9}=\frac{4}{3}[/tex]because ratio indicates a fraction (12 cats divided by 9 dogs)
After the adoption there were 11 cats and 8 dogs, then the ratio is
[tex]\frac{11}{8}[/tex]Since
[tex]\frac{4}{3}\ne\frac{11}{8}[/tex]