Question

xplain why the ratio 2 to 5 is different from the ratio 5 to 2 if both represent the ratio of cats to dogs.

Answer 1

Cats to dogs means that the first number is cats and the second number is dogs. Thus, you have the ratios 2 cats to 5 dogs and 5 cats to 2 dogs which are different.

Answer 2

If they are both ratios of cats to dogs, with the ratio 2 to 5 it would mean there are 2.5x more dogs then there are cats, but with the ratio 5 to 2 it would mean there are 2.5x more cats than there are dogs, in which they are both different.