In this prealgebra lesson from OpenStax Prealgebra 2E, students learn the commutative and associative properties of addition and multiplication, including why these properties do not apply to subtraction or division. Students practice using these properties to rewrite and simplify expressions involving real numbers. The lesson builds foundational algebraic reasoning skills that support solving equations.
Section 1
📘 Commutative and Associative Properties
This lesson introduces two key rules for addition and multiplication: the Commutative and Associative Properties. You'll learn how reordering and regrouping numbers can make simplifying expressions and solving problems faster and easier.
Next, you'll apply these rules on practice cards and see them used in worked examples to simplify tricky expressions.
Section 2
Commutative properties
Commutative Property of Addition: If and are real numbers, then
Commutative Property of Multiplication: If and are real numbers, then
The commutative properties have to do with order. If you change the order of the numbers when adding or multiplying, the result is the same. Subtraction and division are not commutative.
Section 3
Associative properties
Associative Property of Addition: If , , and are real numbers, then
Associative Property of Multiplication: If , , and are real numbers, then
When adding or multiplying three numbers, changing the grouping of the numbers does not change the result.
Section 4
Evaluate expressions using properties
The commutative and associative properties can make it easier to evaluate some algebraic expressions. Since order does not matter when adding or multiplying three or more terms, we can rearrange and re-group terms to make our work easier.
Section 5
Simplify expressions using properties
When we have to simplify algebraic expressions, we can often make the work easier by applying the Commutative or Associative Property first. We can rearrange an expression so the like terms are together. For example, we simplify by rewriting it as and then combining like terms to get . We were using the Commutative Property of Addition.
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Section 1
📘 Commutative and Associative Properties
This lesson introduces two key rules for addition and multiplication: the Commutative and Associative Properties. You'll learn how reordering and regrouping numbers can make simplifying expressions and solving problems faster and easier.
Next, you'll apply these rules on practice cards and see them used in worked examples to simplify tricky expressions.
Section 2
Commutative properties
Commutative Property of Addition: If and are real numbers, then
Commutative Property of Multiplication: If and are real numbers, then
The commutative properties have to do with order. If you change the order of the numbers when adding or multiplying, the result is the same. Subtraction and division are not commutative.
Section 3
Associative properties
Associative Property of Addition: If , , and are real numbers, then
Associative Property of Multiplication: If , , and are real numbers, then
When adding or multiplying three numbers, changing the grouping of the numbers does not change the result.
Section 4
Evaluate expressions using properties
The commutative and associative properties can make it easier to evaluate some algebraic expressions. Since order does not matter when adding or multiplying three or more terms, we can rearrange and re-group terms to make our work easier.
Section 5
Simplify expressions using properties
When we have to simplify algebraic expressions, we can often make the work easier by applying the Commutative or Associative Property first. We can rearrange an expression so the like terms are together. For example, we simplify by rewriting it as and then combining like terms to get . We were using the Commutative Property of Addition.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter