Algebra Properties
• Definition
Numeric Example
Algebraic Example
Commutative Property
of Addition
We can change the order when
adding without affecting the sum.
8 3  38
y 5  5 y
Commutative Property
of Multiplication
We can change the order when
multiplying without affecting the product.
10  4  4 10
xy  yx
Associative Property
of Addition
Numbers can be grouped in any
order for addition.
3  (4  5)  (3  4)  5
7  (2  x)  (7  2)  x
Associative Property
of Multiplication
Numbers can be grouped in any
order for multiplication.
3  (2  4)  (3  2)  4
m  (5  n)  (m  5)  n
Identity Property of
Addition
Adding 0 to any number gives
that number.
15  0  15
0a  a
Identity Property of
Multiplication
Multiplying a number by 1 gives that
number.
7 1  7
1 x  x
Additive Inverse
Property
Two rational numbers whose sum
is 0.
7  (7)  0
 5a  5a  0
Multiplicative Inverse
Property
Two rational numbers whose
product is 1.
1
5  1
5
1
a 1
a
Distributive Property
Multiplying a number over
addition or subtraction.
2  (8  5)  (2  8)  (2  5)
4( x  6)  4 x  24
The Inverse of a Sum
Property
The additive inverse of a sum is
the sum of the additive inverses.
 (6  t )  6  t
 (4a  10)  4a  10
Multiplicative Property
of Zero
The product of 0 and any rational
number is 0.
13(0)  0
0x  0
Multiplicative Property
of -1
Negative one times a is the
additive inverse of a.
1 8  8
1y   y
The Addition Property
of Equality
Adding the same number to both sides of an
equation results in an equivalent equation.
2x  6  18
6 6
The Subtraction
Property of Equality
Subtracting the same number to both sides of
an equation results in an equivalent equation.
12  3 y  6
 12
 12
The Multiplication
Property of Equality
Multiplying the same number to both sides of an
equation results in an equivalent equation.
x
x


388     3
3
3
The Division Property
of Equality
Dividing the same number to both sides of an
equation results in an equivalent equation.
 5m  25
5 5
Symmetric Property
Two equal quantities can be
written in any order.
If x  6  9, then 9  x  6
Transitive Property
If a  b and b  c,
then a  c.