1. Lesson 5
Introductory Algebra
Number Properties

2. Warm-Up
5 × (3 × 4)
(5 × 3) × 4

3. Target: Recognize and use the Commutative and Associative Properties.
Number Properties
Target:
Recognize and use the Commutative
and Associative Properties.

6. Properties of Addition and Multiplication
Commutative Property: The order in which numbers are added or multiplied does not change the value of an expression = × 6 = 6 × 4
Associative Property: The way in which numbers are grouped in addition and multiplication expressions does not change the value of the expression (4 + 7) = (2 + 4) × (8 × 3) = (5 × 8) × 3

7. Example 1a Determine if the expressions are equal. If so, name the
property.
(3 + 2) (2 + 9)
Solve each expression. (3 + 2) + 9 = = (2 + 9) = = 14
They are the same.
Associative Property – They are grouped differently.

8. Example 1b Determine if the expressions are equal. If so, name the
property.
8 ÷ ÷ 8
Solve each expression. 8 ÷ 4 = 2 4 ÷ 8 = 0.5
They are not the same.
The Commutative Property does not work with division.

9. Example 1c Determine if the expressions are equal. If so, name the
property.
10 × (4 – 2) (10 × 4) – 2
Solve each expression. 10 × (4 – 2) = 10 × 2 = 20 (10 × 4) – 2 = 40 – 2 = 38
They are not the same.
The Associative Property only works when using one operation at a time.

10. Example 1d Determine if the expressions are equal. If so, name the
property.
5 × × 5
Solve each expression. 5 × 11 = × 5 = 55
They are the same.
Commutative Property – The numbers changed places.

11. Exit Problems Identify the property shown: 8 + 11 = 11 + 8
Rewrite 7 × (3 × 2) in a different way using the Associative Property.
What two operations do the Associative and Commutative Property work for?

12. Communication Prompt
Describe a real-world situation in which it would be helpful to rearrange numbers before adding them.