The Commutative Property of Addition and Multiplication is a fairly simple and straight forward property for developing number sense and understanding. The property simply states that in addition expressions and multiplication expressions, numbers can travel (or commute) to either side of the operation symbol (the ‘+’ or the ‘x’). What this means is:

Notice how the ‘2’ and the ‘3’ changed locations around the addition symbol. The sum (total) will be the same (which is 5). Why does this property exist? It simply proves that we can add numbers in any order to get the same total.

The property also applies to multiplication expressions. Consider the following:

Both expressions have a product (multiplication answer) of 24. The order of the numbers in the expression make no difference.

One reason we use the Commutative Property is to assist with number sense and mental math calculations. Reordering the numbers in a string of addition or multiplication problems gives me the flexibility to move numbers around in the expression to make numbers that are more compatible with one another for quick mental math calculations. Consider this example:

2 + 9 + 8 + 1

While mathematically, this seems like a simple problem, our brain can execute the application of the Commutative Property of Addition and move the numbers in this expression around to place numbers that will make tens (I will replace the ‘9 + 8’ with ‘8 + 9’) closer together:

2 + 8 + 9 + 1

Now, my brain processes this expression by grouping ‘2 + 8’ and ‘9 + 1,’ which are two groups that have sums of 10 each, making a sum total of 20 for the expression.

This is how the Commutative Property applies to number sense and mental math.

This is what I am here to help you with. I am here to help you learn Mathanese, because I speak Mathanese, and you will, too. The focus of my blog is to present you with strategies to practice computational facts, explanations of number sense reasoning to understand computational processes, and teach you the Mathanese terms you need to succeed as a mathematician. Choose a topic that is listed in the menu to learn more. If a topic you want to learn about isn’t available, send me an email and ask me to write something about it.

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Mr. H.