Gabriel and his sister have arrived at expressions that give the same result when evaluated (except on some computers for some values of x and y*). We have no basis for deciding which of the two equivalent expressions is "correct."

The distributive property lets you "collect terms" by adding the coefficients of terms with the same variable:

x + x + 0.5x = x(1 + 1 + 0.5) = 2.5x . . . . for example

When we collect terms in the sister's expression, we find it is identical to Gabriel's expression.



* About computer evaluation

The internal representation of numbers in binary computers is such that many numbers cannot be represented exactly. As a consequence, the order in which numbers get added can make a difference in the resulting value. In some cases, it may be preferable to compute x+x+0.5x, rather than 2.5x. This can depend, too, on the precise computer language used and the manner in which it is translated to the machine language actually exe