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 Identity property of multiplication (Multiplicative Identity): a1=a  51=5

Inverse Properties Property of Opposites: a + (-a) = 0  7 + (-7) = 0 Property of Reciprocals: 

Distributive Property a(b + c) = ab + ac “To give out”

Name the property illustrated.

Using the Properties to Simplify & Solve Equations Commutative of + Associative of + Property of Opposites Additive Identity Property of Reciprocals

Associative of multiplication Property of Reciprocals Distributive Property of + wrt multiplication Multiplicative Identity