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 ?
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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
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Identity Properties Addition Multiplication ? equals equals
Identity Properties Addition Multiplication equals equals
Identity Properties Addition Multiplication equals equals
Identity Properties Addition Multiplication equals equals
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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