Lesson 5 Introductory Algebra Number Properties

Warm-Up 5 × (3 × 4) (5 × 3) × 4 82 + 32 32 + 82

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

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

Example 1a Determine if the expressions are equal. If so, name the property. (3 + 2) + 9 3 + (2 + 9) Solve each expression. (3 + 2) + 9 = 5 + 9 = 14 3 + (2 + 9) = 3 + 11 = 14 They are the same. Associative Property – They are grouped differently.

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

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.

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

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?

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