You have to be a bit more specific with your question. But I guess a good example would relate to integrals. When you have an even or odd (a property) function and you integrate it over an anti-symmetric or symmetric domain, you would get 0 as a result. read more
Well,properties can help you because you can shorten or make an equation more understandable, like using distributive property in the example 2(5x-3), you can rewrite it as 10x-6. read more