Commutative Property of Addition

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 review a brief example to demonstrate 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 \(12\).