Lesson 4-1 Using Properties Designed by Skip Tyler, Varina High School and modified for review in Geometry

Commutative Property ...order does not matter. Addition: a + b = b + a Examples Addition: a + b = b + a 4 + 5 = 5 + 4 Multiplication: a • b = b • a 2 • 3 = 3 • 2 The commutative property does not work for subtraction or division.

Associative Property ...grouping does not matter Examples Addition: (a + b) + c = a + (b + c) (1 + 2) + 3 = 1 + (2 + 3) Multiplication: (ab) c = a (bc) (2•3)•4 = 2•(3•4) The associative property does not work for subtraction or division.

Properties for ADDITION Additive Identity a + = a “0”is the identity element for addition (-a) a + = 0 Additive Inverse a and (-a) are called opposites

Properties for MULTIPLICATION Multiplicative Identity a • = a 1 “1”is the identity element for multiplication Multiplicative Inverse a • = 1 a and are called reciprocals

Properties for MULTIPLICATION Multiplicative Property of Zero a • 0 = ___ Multiplicative Property of -1 -a a • -1 = ___

The Distributive Property The process of distributing the number on the outside of the parentheses to each term on the inside. a(b + c) = ab + ac a(b - c) = ab - ac and (b + c) a = ba + ca (b - c) a = ba - ca 5(x + 7) Example 5 • x + 5 • 7 5x + 35

Name the property 1) 5a + (6 + 2a) = 5a + (2a + 6) commutative (switching order) 2) 5a + (2a + 6) = (5a + 2a) + 6 associative (switching groups) 3) 2(3 + a) = 6 + 2a distributive

Properties of Equality x  0 If a = b, then Addition a + c = b + c Subtraction a - c = b - c Multiplication a • c = b • c Division a / c = b / c Substitution: If a = b, then a can be replaced by b Example: (5 + 2)x = 7x

Properties of Equality Reflexive: a = a 5 = 5 Symmetric: If a = b then b = a If 4 = 2 + 2 then 2 + 2 = 4 Transitive: If a=b and b=c, then a=c If 4 = 2 + 2 and 2 + 2 = 3 + 1, then 4 = 3 + 1

Properties of Congruence Reflexive: a  a A  B Symmetric: If a  b then b  a If C  D, then D  C Transitive: If ab and bc, then ac If XY and YZ, then XZ