Section 1.3 Properties

Properties of Equality

Reflexive Property: a=a

Symmetric Property: If 3=x, then x=3

Transitive Property: If x=y and y=4 then x=4

Addition Property: If x=3, then x+4=3+4

Multiplication Property: If x=7, then 2x=14

Closure Property

a+b and ab are unique real numbers. The sum of 3 and 5 is only 8 The product of 3 and 5 is only 15

Commutative Property

“Order changes” a + b = b + a ab=ba 3+4=4+3 xyz=yxz Order can NOT change for subtraction or

division

Associative Property

Order stays the same. Parentheses move. (a + b) + c = a + (b +c) (ab)c=a(bc)

Identity Properties

Identity property of addition

(additive identity): a + 0 = a 4 + 0 = 4

Identity property of multiplication (Multiplicative Identity): a•1=a 5•1=5

Inverse Properties

Property of Opposites: a + (-a) = 0 7 + (-7) = 0

Property of Reciprocals:

11

a

a

18

18

Distributive Property

a(b + c) = ab + ac “To give out”

Name the property illustrated.

Using the Properties to Simplify & Solve Equations

)4(4

14

4

1 xxxx

44

1 xx

404

1

44

1

1

Commutative of +

Associative of +

Property of Opposites

Additive Identity

Property of Reciprocals

t

33

11

3

1

t 113

1

t3

1

)3(3

11

3

1)31(

3

1tt

Associative of multiplication

Property of Reciprocals

Distributive Property of + wrt multiplication

Multiplicative Identity