Relationships that are always true for real numbers are called _____________, which are rules used to rewrite and compare expressions. properties

PROPERTYDEFINITIONEXAMPLE Commutative Property Addition Multiplication Associative Property Addition Multiplication Distributive Property Changing Order does not change the outcome = a + b = b + a 1 ● 2 = 2 ● 1 a b = b a (8 + 6) + 7 = 8 + (6 + 7) (a + b) + c = a + (b + c) 4 ● (5 ●9) = (4 ●5) ● 9 (ab) ● c = a ● (bc ) 10 (1 + 7) = 10 ● ●7 15(x - 4) = 15 ● x – 15 ●4 Regrouping Order stays the same only ( ) move (Change who you associate [hang out] with) a(b + c) = ab + ac a(b - c) = ab - ac

PropertyDefinitionExample Identity Properties Addition Multiplication Inverse Properties Addition Multiplication Adding “0” = no change Multiply by 1= no change a + (-a) = = ● 99y = 99y 14 + (-14) = 0

PropertyDefinitionExample Zero Property of Multiplication Multiplication Property of – 1 Multiply by 0, you get 0 Multiply by -1, you change the sign (7003)(0) = 0 -1(a) = -a -1(2) = -2 -1(-5) = 5

Zero Property of Multiplication Associative Prop. of Addition Identity of Addition (Additive Identity) Identity of Multiplication (Multiplicative Identity) Commutative Prop. (Addition) The “z” and the √ y have been switched.

F. A movie ticket costs $7.75. A drink costs $2.40. Popcorn costs $1.25. What is the total cost for a ticket, a drink, and popcorn? Use mental math. G. A can hold 3 tennis balls. A box holds 4 cans. A case holds 6 boxes. How many tennis balls are in 10 cases? Use mental math. $ $ $1.25 = ( ) = = ●4 ●6 ●10 = 720 Using Properties for Mental Calculations

Writing Equivalent Expressions (5 ● 3)n 15n (7b + 4 ) + 8 7b + ( 4 + 8) 7b x (2.1 ● 4.5)x 9.45x 6 + (3 + 4h)(6 + 3) + 4h9+ 4h