Commutative Property of Multiplication

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

$$a \times b = b \times a$$

When we multiply two numbers, the sequence in which they are multiplied does not affect the final result. Therefore, the order is irrelevant, as the product will be the same no matter how the numbers are arranged.

Let’s go over a quick example to illustrate the concept of the Commutative Property of Multiplication.

Suppose we have the values for \(a\) and \(b\)

$$\displaylines{
  a = 3 \cr 
  b = 9 \cr} $$

Let’s plug them into the “formula”:

$$a \times b = b \times a$$

We obtain

$$\displaylines{
  3 \times 9 = 9 \times 3 \cr 
  27 = 27 \cr} $$

As you can see, swapping the positions of the factors, (3) and (9), does not change the final result. The product remains \(27\).