24 terms

# Chapter 1 Test (Lantrip)

This is the first chapter of Algebra 2 with Trigonometry Houghton Mifflin Text Book. This set of flash cards is composed of the axioms which the book indicates in red

#### Terms in this set (...)

a+b is a unique real number
Closure Axiom for Addition
(a+b) + c = a + (b+c)
Associative Axiom for Addition
a+b = b+a
Commutative Axiom for Addition
a+0=a
Identity Axiom for Addition
a + (-a) = 1
Axiom for Additive Inverses
ab is a unique real number
Closure Axiom for Multiplication
(ab)c = a(bc)
Associative Axiom for Multiplication
ab = ba
Commutative Axiom for Multiplication
a * 1 = a
Identity Axiom for Multiplication
b/a * a/b = 1
Axiom for Multiplicative Inverses
a(b+c) = ab + ac
Distributive Axiom for Multiplication with Respect to Addition
if a=b then a+c = b+c
Substitution Principle for Equality
a=a
Reflexive Property for Equality
if a=b then b=a
Symmetric Property for Equality
if a = b and b =c then a = c
Transitive Property for Equality
if a+c = b +c then a=b
Cancellation Axiom for Addition
-(a+b) = (-a) + (-b)
Property for the Opposite for a Sum
-(-a) = a
Cancellation Axiom for Additive Inverses
if ac=bc then a=b
Cancellation Axiom for Multiplication
1/ab = 1/a * 1/b
Property for the reciprocal of a Product
a * 0 = 0
Multiplicative Axiom for Zero
a(-1) = -a
Multiplicative Axiom for -1
(-a)b = -ab or (-a)(-b)=ab
Properties of Opposites in Products
a-b = a+(-b)
Definition of Subtraction