24 terms

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

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