The Basic Properties of

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Presentation transcript:

The Basic Properties of REAL NUMBERS

Binary Operations Addition Multiplication

The Commutative Property Addition Multiplication equals equals

Postive Integers TABLE

1 2 3 ……

1 2 3 …… .

+ 1 2 3 …… .

+ 1 2 3 …… 4 5 6 .

+ 1 2 3 …… 4 5 6 .

+ 1 2 3 …… 4 5 6 .

+ 1 2 3 …… 4 5 6 .

+ …… Keep Testing The Set of Real Numbers is Commutative 1 2 3 4 5 6 1 2 3 …… 4 5 6 . The Set of Real Numbers is Commutative with respect to ADDITION

What About Multiplication

x 1 2 3 …… 4 6 9 .

x 1 2 3 …… 4 6 9 .

x …… Keep Testing The Set of Real Numbers is Commutative 1 2 3 4 6 9 1 2 3 …… 4 6 9 . The Set of Real Numbers is Commutative with respect to MULTIPLICATION

The Associative Property

The Associative Property Addition Multiplication equals

Associative Example for Addition VS

Associative Example for Addition equal ?

Go Back

The Associative Property Addition Multiplication equals equals

Associative Example for Multiplication VS

Associative Example for Multiplication equal ?

The Identity Property

Identity Properties Addition Multiplication ? equals

Identity Properties Addition Multiplication equals

Identity Properties Addition Multiplication equals

Go Back

Identity Properties Addition Multiplication ? equals equals

Identity Properties Addition Multiplication equals equals

Identity Properties Addition Multiplication equals equals

Identity Properties Addition Multiplication equals equals

Next

The Property of Inverses

Property of Opposites and Reciprocals Addition OPPOSITES Multiplication RECIPROCALS ? equals Identity for Addition

Property of Opposites and Reciprocals Addition OPPOSITES Multiplication RECIPROCALS equals

Opposites for Addition Is equal to

Property of Opposites and Reciprocals Addition OPPOSITES Multiplication RECIPROCALS ? equals equals Identity for Multiplication

Property of Opposites and Reciprocals Addition OPPOSITES Multiplication RECIPROCALS equals equals

Reciprocals for Multiplication Is equal to

of Multiplication over Addition The Distributive Property of Multiplication over Addition

The Distributive Property equals

Distributive Example equal ?

CAREFUL

IS NOT THE SAME AS

Addition Sign NO Addition Sign

Multiplication over Addition Distributive Property of Multiplication over Addition NOT THE SAME Associative Property of Multiplication Closure Property of Multiplication

The Property of Closure

Property of Closure If a and b are and unique and unique Real Numbers Addition Multiplication Real Number Real Number and unique and unique

Closure for Addition Example Real Number unique

Closure for Multiplication Example Real Number unique

Example 1 Using Properties

Given

Given Distributive Property

Given Distributive Property Identity Property of ? Multiplication

Given Distributive Property Identity Property of ? Multiplication Commutative Property of ? Addition

Given Distributive Property Identity Property of ? Multiplication Commutative Property of ? Addition

Given Distributive Property Identity Property of ? Multiplication Commutative Property of ? Addition Associative Property of ? Addition

Given Distributive Property Identity Property of ? Multiplication Commutative Property of ? Addition Associative Property of ? Addition Closure Property of ? Addition

Example 2 Using Properties

Given Commutative Property of ? Addition Associative Property of ? Addition Property of Opposites Identity Property of ? Addition