Properties of Real NumbersCommutative Property of

AdditionCommutative Property of Multiplication

Associative Property of Addition

Associative Property of Multiplication

Distributive Property

Additive Identity Property

Multiplicative Identity Property

Additive Inverse Property

Multiplicative Inverse Property

Zero Property

Commutative Property of Addition

Commutative Property of Multiplication

When two numbers are added, the order can be switched and the sum will still be

the same.

When two numbers are multiplied, the order can be switched and the product will still be the same.

Subtraction is NOT

Commutative

Division is NOT

Commutative

Associative Property of AdditionWhen three or more numbers are added, any two or

more can be grouped together and the sum will still be the same.

Associative Property of MultiplicationWhen three or more numbers are multiplied, any two or more can be grouped together and the product will still be

the same.

Subtraction is NOT

Associative

Division is NOT

Associative

Additive Identity PropertyWhen zero is added to any number,

the sum is the original number.

Multiplicative Identity PropertyWhen any number is multiplied by

one, the product is the original number.

13 10 3 07 7

Zero is the Identity

Element of Addition

4 41 16 6

One is the Identity

Element of Multiplication

Additive Inverse PropertyWhen the opposite of a number is

added to it the sum is zero.

Multiplicative Inverse PropertyWhen any number is multiplied by its

reciprocal the product is one.

10 1( ) 00 )5 0(5

Zero is the Identity

Element of Addition

2 112

23 2

13

One is the

Identity Element of

Multiplication

Distributive PropertyAny number outside parenthesis can be

distributed to the numbers inside the parenthesis.

2(5 )3 ( )2 5 )32( 10 6 1643( )x 4)3( ) (3x 3 12x

Zero PropertyWhen any number is

multiplied by zero the product is zero.

19(0) 0 027

(0)

Binary Operatio

ns

In a Binary Operation, two elements from a set are replaced by exactly one

element from the same set.

Property of ClosureA set is Closed under a binary operation when every pair of

elements from the set, under the given operation, yields an element from that set.

The following sets of numbers are closed under the indicated operation.

Addition

Natural Numbers

Whole Numbers

Integers

Rational Numbers

Real Numbers

Subtraction

Integers

Rational Numbers

Real Numbers

Multiplication

Natural Numbers

Whole Numbers

Integers

Rational Numbers

Real Numbers

Division

Non-Zero Rational Numbers

Non-Zero Real

Numbers