Introduction to Using the Commutative and Associative Properties

What you’ll learn to do: Use the commutative and associative properties to simplify and evaluate expressions

A group of children wearing matching t-shirts at a camp

When adding up the number of kids in a family, does order matter?

Janelle is helping to plan a family reunion, and she wants to order shirts for all the kids who will attend. She starts thinking about the best way to tally up the number of kids in each family. Should she start with the oldest child’s family? Should she add them up alphabetically? Will her method change the total number of shirts she needs to order, or will she arrive at the same number no matter how she does it? In this section, you’ll learn about the commutative and associative properties, which can help Janelle figure out her answer.

Before you get started, try a few practice problems and review prior concepts.

readiness quiz


If you missed this problem, review the following video.


If you missed this problem, review this video.


If you missed this problem, review the video below.

In the next few sections, we will take a look at the properties of real numbers. Many of these properties will describe things you already know, but it will help to give names to the properties and define them formally. This way we’ll be able to refer to them and use them as we solve equations in the next chapter.