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Axioms, Properties, Equastions
for test on 9-17-08
31
Mathematics
9th Grade
09/16/2008
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Term
Identity Axiom of Addition
 Definition
2x^2-5x+y=2x^2-5x+1y
Term
Associative Axiom of Addition
 Definition
[3(a+b)+4a]+3a=3(a+b)+[4a+3a]
Term
Associative Axiom of Multiplication
 Definition
(xy)z=x(yz)
Term
Commutative Axiom of Multiplication
 Definition
(ab)c=(ba)c
Term
Transitive Axiom of Equality
 Definition
If x=2a-4 and 2a-4=y then x=y
Term
Reflexive Axiom of Equality
 Definition
a+bc+d=a+bc+d
Term
Commutative Axiom of Addition
 Definition
(3+4y)+5x=(4y+3)+5x
Term
Identity Axiom of Addition
 Definition
ab+d^2=ab+0+d^2
Term
Closure Axiom of Addition
 Definition
The square root of 5 + the square root of 7 is a real number.
Term
Substitution Principle
 Definition
20x+18=(5x+15x)+18
Term
Symmetric Axiom of Equality
 Definition
If 2x-4=18+x^2 then 18+x^2=2x-4
Term
Closure Axiom of Multiplication
 Definition
(-4)(-8) is a real number
Term
Commutative Property of Addition
 Definition
a+b=b+a
Term
Associative Property of Addition
 Definition
(a+b)+c=a+(b+c)
Term
Additive Inverse (Opposite)
 Definition
a+(-a)=0
Term
Additive Identity (Addition Property of Zero)
 Definition
a+0=a
Term
Commutative Property of Multiplication
 Definition
ab=ba
Term
Associative Property of Multiplication
 Definition
a(bc)=b(ac)
Term
Multiplicative Inverse (Reciprocal)
 Definition
a*(1/a)=1
Term
Multiplicative Identity (Multiplication Property of One)
 Definition
a*0=0
Term
Multiplication Property of Zero
 Definition
anything times 0 is 0 (for example, 4*0=0)
Term
Distributive Property of Multiplication with respect to (over) Addition
 Definition
a(b+c)=ab+ac
Term
Reflexive Property of Equality
 Definition
b=b
Term
Symmetric Property of Equality
 Definition
a=b b=a
Term
Transitive Property of Equality
 Definition
a=b, b=c, a=c
Term
Natural (Counting) Numbers
 Definition
start with 1 (2,3,4,etc.)
Term
Whole Numbers
 Definition
start with 0 (1,2,3,etc.)
Term
Integers
 Definition
negative and positive numbers
Term
Rational Numbers
 Definition
numbers that have a pattern, or are terminating (ratio) (1/3) (1/2)
Term
Irrational Numbers
 Definition
go on and on without a pattern (Pi) (square root of 2)
Term
Real Numbers
 Definition
rational/irrational numbers
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