32 terms

8th Grade - All Algebra Properties

Properties to learn for Honors Algebra
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if a>b and b>c, then a>c
Transitive Property of Inequality
if a=b, then ac=bc
Multiplication Property of Equality
-(-a) = a
The -(-a) = a property
1/(1/a) = a
The 1/(1/a) = a property
-(a+b)=-a+(-b)
Property of the Opposite of a Sum
a/b = a*(1/b)
Definition of Division
a-b=a+(-b)
Definition of Subtraction
The abs. value of a = a if a >= 0
The abs. value of a = -a if a < 0
Definition of Absolute Value
A Set S is closed under operation # if for every a,b that are members of set S, a#b is also a member of S.
Definition of Closure
a=a
Reflexive Property of Equality
if a=b, then b=a
Symmetric Property of Equality
if a=b and b=c, then a=c
Transitive Property of Equality
if a=b, then a can be substituted for b at any time
Substitution
if a=b, then a+c=b+c
Addition Property of Equality
if a=b, then a-c=b-c
Subtraction Property of Equality
if a=b, then ac = bc
Multiplication Property of Equality
if a=b, then a/c=b/c
Division Property of Equality
a+b=b+a
Commutative Property of Addition
ab=ba
Commutative Property of Mult.
(a+b)+c=a+(b+c)
Associative Property of Addition
(ab)c=a(bc)
Associative Property of Mult.
x+0=x
Identity Property of Addition
x*1=x
Identity Property of Multiplication
a+(-a)=0
Additive Inverse Property
a * (1/a)=1
Multiplicative Inverse Property
a*0=0
Multiplicative Property of Zero
if ab=0, then a=0 or b=0 or both a&b=0
Zero Product Property
a(b+c) = ab + ac
Distributive Property
a-b = a+ (-b)
Definition of Subtraction
between any two rational numbers, there are many other rational numbers (true for irrationals/reals too)
Density Property
Rules for A
a > 0 --> 1/a > 0
a < 0 --> 1/a < 0

a > b --> 1/a < 1/b
* true if a and b are the same sign
Property of Squares
a^2 ≥ 0