Drill #11 Write each expression in simplest form:

Drill #12 Evaluate each expression: Simplify: 3.

1-6 Commutative and Associative Properties Objective: To recognize and use the commutative and associative properties to simplify expressions.

Adding ages Mr. Todaro wants to know the sum of the ages of his students… Does it matter what order he adds them up in? Why?

Launch Open books to page 33 ATLANTA SUBWAY “The South Line of the Atlanta subway …”

(32.) Commutative Property** Definition: a + b = b + a  ADDITION a(b) = b(a)  MULTIPLICATION NOTE:In this property the numbers are changing (commuting) position. Example: = = 11 6(5) = 5(6) = 30 3xy + 5x + 4xy = 3xy + 4xy + 5x = 7xy + 5x

(33.) Associative Property** Definition: For any numbers, a, b, and c, (a + b) + c = a + ( b + c ) and (ab)c = a(bc) In this property the numbers stay in the same place, but they way they are associated changes. Example: 5 + (6 + 7) = (5 + 6) + 7 = 18 (5 * 6) * 7 = 5 * (6 * 7) = 210

Use Addition Properties Example # = ? ex 1A = ? ex 1B.

Classwork 1-6 Study Guide # 1, 2

Using Multiplication Properties Example #2 Evaluate: 8(2)(3)(5) = ex 2A: 2.9(4)(10) = ? ex 2B:

Classwork 1-6 Study Guide # 3, 4

Examples: In the commutative property the numbers are moving (commuting) a b c d e = e b d c a = a b c = c a b 12 – = 6 + (12 – 5)

Examples: In the associative property the grouping symbols are moving. (the way the numbers are associated is changing) a b c d e = a b c d e (5 + 10) + ( ) = ( ) + (16 + 2) a b c = a b c (12 – 5 ) + 6 = 12 + (-5 + 6)

Write and Simplify an Expression Example #3 a. Write an algebraic expression for the verbal expression below: Four times the sum of a and b increased by twice the sum of a and 2b b. Simplify the expression above and indicate the properties used.

Writing Algebraic Expressions* The sum of two and the square of t increased by the difference of t squared and 3.

Properties Mini-Quiz* Fill out the following table using the variables a, b, and c: AdditionMultiplication Commutative Associative Identity Mult. Prop of Zero Distributive Substitution

Name the property* 1.Transitive 2.Symmetric 3.Reflexive 4.Substitution a.If a = b then b=a b.If a = b and b = c then a = c c.a = a d.If 2x = 5 and x = y then 2y = 5

Classwork 1-6 Study Guide # 5 – 10

Properties Quiz Tomorrow Homework: 1-6 Practice #1-19 (ODD)