Commutative Property of Multiplication

One of the first things I remember learning in school, during math class is the concept of multiplying numbers and working to memorize multiplication tables. One of the most basic of mathematical operations, multiplication is one of the most essential subjects of study. Even if you don't plan to make a career in pure mathematics, there is a basic level of math, which we all must know about, if we are to survive the real world and be able to calculate our taxes! Addition, multiplication, subtraction and division are the four operations, which need to be a part of your mathematical arsenal. The aim of this article is to bring multiplication operation under the scanner and explain the commutative property of addition.

I assume that you are already familiar with how multiplication is carried out. A knowledge of multiplication tables will make it easier for you to easily multiply numbers. Let me define what is the commutative property of multiplication for you and then illustrate it with some examples.

Definition

When you multiply two numbers and change the order, does the end product change? Or in other words, does order matter when multiplying numbers? That's the question which this property deals with. In simple words, the property is stated as follows -

'Irrespective of the order in which, you multiply the numbers, the end product remains the same.'

In terms of an equation, it states that, for any two variables or numbers - a and b,

(a x b) = (b x a)

It could be restated in the following way - for the variables or numbers p,1 and r,

(p x q) = r = (q x p)

This is perhaps the most important property of multiplication which you need to know about. The math term - 'commutative' itself means 'independent of factor order'. Multiplying numbers is actually carrying out addition in another way. Since addition shows the property of commutativity, multiplication, as a form of addition, inherits this property. Let us take a look at some examples of that demonstrate the implications of this property.

Examples

Here are some examples that will demonstrate the property:

• m x n = n x m
• 5 x 8 = 8 x 5 = 40
• 3/5 x 2/9 = 2/9 x 3/5 = 2/15
• a x b x c = b x c x a = c x a x b = b x a x c
• 2.3 x 10 = 10 x 2.3 = 23
• 7.8 x 2/39 = 2/39 x 7.8 = 0.4

Thus the commutative property of addition makes it possible to factorize a number in any order. As discussed before, if you delve into it deeply, you will realize that multiplication is actually addition in another form. That's the reason why multiplication and addition have a commutative property, while subtraction and division don't have this property. In the latter two operations, order matters. To sum it all up, this property lets you multiply numbers in any order.