Properties
 Commutative Property
Order doesn’t make any difference in multiplication or addition.
Examples:
4+3=3+4
a+b=b+a
ab = ba
Note: This property was especially useful when you were memorizing your addition and
multiplication facts.
 Associative Property
When the operations of addition or multiplication are grouped using parentheses, the placement
of the parentheses doesn’t matter.
Examples:
(6 + 2) + 3 = 6 + (2 + 3)
(a + b) +c = a + (b + c)
Note: When multiplying or adding a group of numbers, you can group them any way you want
(or add them in any order)--this is often helpful when you want to add or multiply to multiples
of ten.
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3. Identity Property of Addition
The sum of any number and zero is that number.
Examples:
4+0= 4
-2 = -2 + 0
0+a=a
Note: This property will prove useful when solving equations (while maintaining equality).
4. Identity Property of Multiplication
The product of any number and one is that number.
Examples:
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 Equality Property of Addition
You can add the same number to both sides of an equation, and the statement will still be true,
equality will be maintained.
Example:
 Equality Property of Subtraction
You can subtract the same number from both sides of an equation, and the statement will still
be true, equality will be maintained.
Example:
 Equality Property of Multiplication
You can multiply by the same number on both sides of an equation, and the statement will still
be true, equality will be maintained.
Example:
 Equality Property of Division
You can divide by the same number on both sides of an equation, and the statement will still be
true, equality will be maintained.
Example:
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 Inverse Property of Addition
Any number added to its opposite (called the additive inverse) equals zero
Examples:
22 + (-22) = 0
a + (-a) = 0
a–a=0
 Inverse Property of Multiplication
Any non-zero number multiplied by its reciprocal (also called the multiplicative inverse) equals
one.
Examples:
or
as long as a ≠ 0 and b ≠ 0
Properties
 Distributive Property
When a number or variable (or both) is multiplied by a series of terms in parentheses, it is
multiplied by each of the terms in parentheses.
Examples:
6(99)  6(100  1)  6 100  6 1  600  6  594
5 (x + 2) = 5x + 10
a (b + c) = ab + ac
5 (x – 2) = 5x – 10
a (b - c) = ab - ac
-5 (x + 2) = -5x – 10
-3x (2x – 4) = -6x2 – 12x
 Zero Property of Multiplication
Any number multiplied by zero equals zero.
Examples:
22 (0) = 0