Commutative
Property o f
Symmetric
Property
Multiplication
of Equality
Additive
Identity
Transitive
Property o f
Property
Equality
Multiplication
Identity
Substitution
Property o f
Property
Equality
Multiplication
Property o f
Zero
Additive
Distributive
Property
Inverse
Commutative
Property o f
Property
Addition
For any numbers
if
a and b ,
a = b , then b = a .
For any numbers
a , b , and c ,
For any numbers
a and b ,
a◊b = b◊a
For any number
a,
if
a + 0 = 0 + a = a.
a = b , then
a may be replaced by b
For any number
a,
For any number
a,
a = b and b = c ,
then a = c .
If
in any expression.
For any numbers a , b , and c ,
a) a( b + c ) = ab + ac and
(b + c)a = ba + ca ;
b) a( b - c ) = ab - ac and
(b - c)a = ba - ca ;
a ◊1 = 1 ◊ a = a .
a ◊0 = 0 ◊ a = 0.
a
For any numbers
a and b ,
a + b = b + a.
,
For every number
there is exactly one number
such that
-a
a + ( - a) = 0 .
Subtraction
Property f o r
Multiplication
Inverse
Inequalities
Property
Multiplication
Property f o r
Reflexive
Property o f
Inequalities
Equality
Associative
Property o f
Zero
Product
Addition
Property
Associative
Property o f
Trichotomy
Property
Multiplication
Addition
Property
of
Equality
Addition
Property
for
Inequalities
For every nonzero number
a
, where a π 0
b
there’s exactly one number
b
a
Equivalently, for every
For any number
If
such that
a π 0,
a,
and
b π 0,
a b
◊ = 1.
b a
1
a ◊ = 1.
a
a ◊ b = 0 , then either
a = 0 or b = 0 .
For any two real numbers, a and b , exactly
one of the following statements is true:
For any real numbers,
or
a>b
a , b , and c ,
a > b , then a + c > b + c ,
if a < b , then a + c < b + c .
if
a , b , and c ,
a > b , then a - c > b - c ,
if a < b , then a - c < b - c .
if
For any real numbers, a , b , and c ,
if c is positive and a) a > b , then
ac > bc b) a < b , then ac < bc .
If c is negative and a) a > b , then
ac < bc b) a < b , then ac > bc .
a = a.
a < b, a = b ,
For any real numbers,
For any numbers
a , b , and c ,
For any numbers
a , b , and c ,
For any numbers
a , b , and c ,
( a + b) + c = a + (b + c) .
( ab)c = a(bc) .
if
a = b , then a + c = b + c .
Subtraction
Property o f
Equality
Multiplication
Property o f
Equality
Division
Property
of
Equality
Division
Property
for
Inequalities
For any numbers
if
a = b , then a - c = b - c .
For any numbers
if
a , b , and c ,
a , b , and c ,
a = b , then ac = bc .
For any numbers
a , b , and c ,
a = b and c π 0 , then
if
a b
= .
c c
For any real numbers, a , b , and c ,
if c is positive and a) a > b , then a
b) a < b , then
if
c
a
b
< ,
c
c
c is negative and
b) a < b , then
b
,
c
and
a) a > b , then
a
b
> .
c
c
>
a
b
< ,
c
c