For any real numbers \(a\) and \(b\)

$$a + b = b + a$$

When we **add** two numbers, the order in which we add them has no effect on the final result, so the **order is unimportant** because the sum will remain the same regardless of the order.

Let's go over a quick example to illustrate the concept of the Commutative Property of Addition.

Suppose we are given the values of \(a\) and \(b\).

$$\eqalign{

& a = 5 \cr

& b = 7 \cr} $$

Substituting the values into the "formula",

$$a + b = b + a$$

We get

$$\displaylines{

a + b = b + a \cr

5 + 7 = 7 + 5 \cr

12 = 12 \cr} $$

As you can see that swapping the addends, \(5\) and \(7\), did not make any difference in the final result. The sum remains the same which is \(12\).