What does the associative property illustrate in an equation?

The associative property illustrates that the way in which numbers are grouped in an addition (or multiplication) operation does not change the result. In the case of option A, it shows that whether you add 'a' and 'b' first and then add 'c', or add 'b' and 'c' first and then add 'a', the sum will remain the same. This property is fundamental in mathematics because it allows flexibility in calculations, making it easier to simplify expressions or solve equations.

The other options refer to different mathematical properties. Option B also describes the associative property but is written in a less standard format. Option C represents the associative property of multiplication, not addition, and while it demonstrates a similar concept, it is not the correct choice for this specific question about the associative property in an addition context. Option D denotes the distributive property, which involves multiplying a single term by a sum and demonstrating how it can distribute across addition, thereby illustrating a different mathematical principle.