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Basic Rules Of ALGEBRA
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Algebraic Expressions
Before We Begin Algebraic Expressions
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One characteristic of algebra is the use of letters to represent numbers The letters are variables, and combinations of letters and numbers are algebraic expressions. Examples
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An algebraic expression is a collection of letters (variables) and real numbers (constants) combined using the operations of addition, subtraction, multiplication, division and exponentiation.
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Example Has Three Terms
The TERMS of an algebraic expression are those parts that are separated by addition Example Has Three Terms
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Has Three Terms
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Then a can be replaced by b in any expression involving a
When an algebraic expression is evaluated the Substitution Principle is used. If a = b Then a can be replaced by b in any expression involving a Example
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Back To Basic Rules Of ALGEBRA
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Binary Operations Addition Multiplication
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The Commutative Property
Addition Multiplication equals equals
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Postive Integers TABLE
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1 2 3 ……
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1 2 3 …… .
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+ 1 2 3 …… .
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+ 1 2 3 …… 4 5 6 .
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+ 1 2 3 …… 4 5 6 .
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+ 1 2 3 …… 4 5 6 .
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+ 1 2 3 …… 4 5 6 .
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+ …… 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
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What About Multiplication
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x 1 2 3 …… 4 6 9 .
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x 1 2 3 …… 4 6 9 .
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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
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The Associative Property
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The Associative Property
Addition Multiplication equals
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Associative Example for Addition
VS
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Associative Example for Addition
equal ?
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Go Back
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The Associative Property
Addition Multiplication equals equals
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Associative Example for Multiplication
VS
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Associative Example for Multiplication
equal ?
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The Identity Property
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Identity Properties Addition Multiplication ? equals
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Identity Properties Addition Multiplication equals
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Identity Properties Addition Multiplication equals
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Identity Properties equals Addition Multiplication
Identity for Addition equals
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Go Back
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Identity Properties Addition Multiplication ? equals equals
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Identity Properties Addition Multiplication equals equals
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Identity Properties Addition Multiplication equals equals
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Identity Properties Addition Multiplication equals equals
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Identity for Multiplication
Identity Properties Addition Multiplication Identity for Multiplication equals equals
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Next
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The Property of Inverses
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Property of Opposites and Reciprocals
Addition OPPOSITES Multiplication RECIPROCALS ? equals
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Property of Opposites and Reciprocals
Addition OPPOSITES Multiplication RECIPROCALS ? Identity for Addition equals
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Property of Opposites and Reciprocals
Addition OPPOSITES Multiplication RECIPROCALS equals
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Opposites for Addition
Is equal to
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Property of Opposites and Reciprocals
Addition OPPOSITES Multiplication RECIPROCALS ? equals equals
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? Property of Opposites and Reciprocals equals equals Addition
Multiplication RECIPROCALS ? Identity for Multiplication equals equals
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Property of Opposites and Reciprocals
Addition OPPOSITES Multiplication RECIPROCALS equals equals
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Reciprocals for Multiplication
Is equal to
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of Multiplication over Addition
The Distributive Property of Multiplication over Addition
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The Distributive Property
equals
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Distributive Example equal ?
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CAREFUL
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IS NOT THE SAME AS
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Addition Sign NO Addition Sign
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Multiplication over Addition
Distributive Property of Multiplication over Addition NOT THE SAME Associative Property of Multiplication Closure Property of Multiplication
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The Property of Closure
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Property of Closure If a and b are and unique and unique Real Numbers
Addition Multiplication Real Number Real Number and unique and unique
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Closure for Addition Example
Real Number unique
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Closure for Multiplication Example
Real Number unique
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Example 1 Using Properties
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Given
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Given Distributive Property
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Given Distributive Property Identity Property of ? Multiplication
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Given Distributive Property Identity Property of ? Multiplication Commutative Property of ? Addition
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Given Distributive Property Identity Property of ? Multiplication Commutative Property of ? Addition
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Given Distributive Property Identity Property of ? Multiplication Commutative Property of ? Addition Associative Property of ? Addition
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Given Distributive Property Identity Property of ? Multiplication Commutative Property of ? Addition Associative Property of ? Addition Closure Property of ? Addition
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Example 2 Using Properties
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Given Commutative Property of ? Addition Associative Property of ? Addition Property of Opposites Identity Property of ? Addition
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