32 terms

8th Grade - All Algebra Properties

Properties to learn for Honors Algebra

Terms in this set (...)

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
Property of the Opposite of a Sum
a/b = a*(1/b)
Definition of Division
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
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
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
Commutative Property of Addition
Commutative Property of Mult.
Associative Property of Addition
Associative Property of Mult.
Identity Property of Addition
Identity Property of Multiplication
Additive Inverse Property
a * (1/a)=1
Multiplicative Inverse Property
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