3.1 Commutative Associate and Distributive Properties + - x

Commutative Property (The #’s move) Comm. Prop. Of Add Comm. Prop. Of mult. In a sum, you can add terms in any order In a product, you can mult. Factors in any order Algebra: a + b=b + a Algebra: ab = ba Ex: = Ex: 4·7 = 7·4

Associative Property (The parentheses move) Asso. Prop. Of Add Asso. Prop. Of Mult. Changing the grouping of the terms won’t change the sum Changing the grouping of the factors won’t change the product Algebra: (a+b)+c = a+(b+c) Algebra: (ab)c = a(bc) Ex: (9+5)+6=9+(5+6) Ex: (5·10)3=5(10·3)

Distributive Property Definitions: Equivalent numerical expressions: Definitions: Equivalent numerical expressions: Expressions that have the same value Distributive Property: Algebra: a(b + c) = ab + ac Arithmetic: 4(3 + 8) = 4(3) + 4(8) Arithmetic: 4(3 - 8) = 4(3) - 4(8)

Examples: Identify the Properties a) (5+7)+13 = 5+(7+13) b) 34 ● 6 = 6 ● 34 c) = d) 23(8 ●5)= (23 ●8)5 The parentheses moved Asso. Prop. Of Add. The #’s movedComm. Prop. of Mult. The #’s movedComm. Prop. Of Add The parentheses movedAsso. Prop. Of Mult.

Examples Justify each step a) = =(43+7) + 29 =50+29=79 Comm. Prop. of Add. Asso. Prop. of Add. Add. Comm. Prop. Of Mult. Asso. Prop. Of Mult. Multiply

Examples Rewrite 43 as a sum Distributive Prop. Mult. Then add. 5(43)=5(40+3) =5(40)+5(3) = = 215 Write each product using Distribute Prop. 5(43)