The property of addition that allows two or more

addends to be added in any order

without changing the sum;a + b = b + a

Examples: c + 4 = 4 + c

(2 + 5) + 4r = 4r + (2 + 5)

commutative property of addition

The Product of two numbers is the same

regardless of the order in which they are

multiplied.Examples

A · B = B · A-3 · 2 = 2 · -3

Commutative Property ofMultiplication

Associative Property of Addition

The property which states that for all real numbers a, b, and c, their sum is

always the same, regardless of their

grouping: (a + b) + c = a + (b + c)

Example:(2 + 3) + 4 = 2 + (3 + 4)

The Product of three or more numbers is

the same regardless of the way in which they

are grouped.Examples

(A · B) · C = A · (B · C)(4 · 2) · -3 = 4 · (2 · -3)

Associative Property ofMultiplication

The property which states that the sum of zero and any number

or variable is the number or variable

itself.

For example, 4 + 0 = 4, - 11 + 0 = - 11,

y + 0 = y

Identity property of addition

The product of any number and 1 is the

number.Examples A · 1 = A

-382 · 1= -382

Identity Property ofMultiplication

The product of any fraction and it’s reciprocal is 1.

Examples · = 1 · = 1

Inverse (Reciprocal)

Examples

( ) = ( · ) + ()

distributive Property