identity & equality properties (algebra1 1_4)

1) additive identity2) multiplicative identity3) multiplicative inverse4) reciprocal

Identity and Equality PropertiesIdentity and Equality Properties

Recognize the properties of identity and equality.

Use the properties of identity and equality.


The open sentence belowrepresents the change in rank of Oregon State from December 11to the final rank.



11 Dec.

onRank

plus rankin

increase

equals season

forrank final

+



11 Dec.

onRank

plus rankin

increase

equals season

forrank final

4 + r = 4

+



11 Dec.

onRank

plus rankin

increase

equals season

forrank final

4 + r = 4

+

The solution of this equation is 0. Oregon State’s rank changed by 0 fromDecember 11 to the final rank.



11 Dec.

onRank

plus rankin

increase

equals season

forrank final

4 + r = 4

+

The solution of this equation is 0. Oregon State’s rank changed by 0 fromDecember 11 to the final rank. In other words, 4 + 0 = 4.


For any number a, the sum of a and 0 is ___.


For any number a, the sum of a and 0 is ___.a



a + 0 = 0 + a = ___.



a + 0 = 0 + a = ___.a



a + 0 = 0 + a = ___.a

7 + 0 = 0 + 7 = ___.



a + 0 = 0 + a = ___.a

7 + 0 = 0 + 7 = ___.7



a + 0 = 0 + a = ___.a

7 + 0 = 0 + 7 = ___.7

The sum of any number and 0 is equal to the number.

This is called the _______________.



a + 0 = 0 + a = ___.a

7 + 0 = 0 + 7 = ___.7

The sum of any number and 0 is equal to the number.

This is called the _______________.additive identity


There are also special properties associated with multiplication.



77 n



77 n

The solution of the equation is 1.Since the product of any number

and 1 is equal to the number,1 is called the

_____________________



77 n



_____________________multiplicative identity



77 n 08 n






77 n 08 n




The solution of the equation is 0.The product of any number

and 0 is equal to 0.This is called the

_____________________



77 n 08 n




The solution of the equation is 0.The product of any number

and 0 is equal to 0.This is called the

_____________________Multiplicative Property

of Zero



1551



1551

Two numbers whose product is 1 are called

_____________________ or ____________.



1551


_____________________ or ____________.multiplicative inverses reciprocals



1551



51

is the multiplicative inverse (or reciprocal) of 5, and



1551



51

is the multiplicative inverse (or reciprocal) of 5, and

51

5 is the multiplicative inverse (or reciprocal) of


Property Words Symbols Examples

Multiplicative

Identity

Multiplicative

Property

of Zero

Multiplicative

Inverse

For any number a, theproduct of a and 1 is a.

For any number a, theproduct of a and 0 is 0.

1. is ab

and ba

ofproduct thesuch that ab

number oneexactly

is there,0b a, where

,ba

number any For



Multiplicative

Identity

Multiplicative

Property

of Zero

Multiplicative

Inverse



1. is ab

and ba


number oneexactly


,ba

number any For

xx 1*



Multiplicative

Identity

Multiplicative

Property

of Zero

Multiplicative

Inverse



1. is ab

and ba


number oneexactly


,ba

number any For

xx 1* 131*13



Multiplicative

Identity

Multiplicative

Property

of Zero

Multiplicative

Inverse



1. is ab

and ba


number oneexactly


,ba

number any For

xx 1* 131*13

00* y



Multiplicative

Identity

Multiplicative

Property

of Zero

Multiplicative

Inverse



1. is ab

and ba


number oneexactly


,ba

number any For

xx 1* 131*13

00* y 00*7



Multiplicative

Identity

Multiplicative

Property

of Zero

Multiplicative

Inverse



1. is ab

and ba


number oneexactly


,ba

number any For

xx 1* 131*13

00* y 00*7

1

y

x

x

y



Multiplicative

Identity

Multiplicative

Property

of Zero

Multiplicative

Inverse



1. is ab

and ba


number oneexactly


,ba

number any For

xx 1* 131*13

00* y 00*7

1

y

x

x

y1

1

2

2

1



Multiplicative

Identity

Multiplicative

Property

of Zero

Multiplicative

Inverse



1. is ab

and ba


number oneexactly


,ba

number any For

xx 1* 131*13

00* y 00*7

1

y

x

x

y1

1

2

2

1

17

3

3

7



Reflexive

Symmetric

Any quantity is equalto itself.

If one quantity equals a second quantity, thenthe second quantityequals the first.



Reflexive

Symmetric



For any number a,

a = a



Reflexive

Symmetric



For any number a,

a = a 99



Reflexive

Symmetric



For any number a,

a = a 99

For any numbers

a and b,

If a = b then b = a



Reflexive

Symmetric



For any number a,

a = a 99

For any numbers

a and b,

If a = b then b = a

8311then

1183 If



Transitive

Substitution

If one quantity equalsa second quantity, andthe second quantityequals a third quantity,then the first quantityequals the third quantity.

A quantity may be substituted for its equalin any expression.



Transitive

Substitution



For any numbers

a, b, and c,

If a = b and b = c,then a = c.



Transitive

Substitution



For any numbers

a, b, and c,


If 8 = 5 + 3 and 5 + 3 = 6 + 2,

then 8 = 6 + 2.



Transitive

Substitution



For any numbers

a, b, and c,


For any numbers

a and b,

If a = b then a may be

replaced by b in any expression.

If 8 = 5 + 3 and 5 + 3 = 6 + 2,

then 8 = 6 + 2.



Transitive

Substitution



For any numbers

a, b, and c,


For any numbers

a and b,

If a = b then a may be

replaced by b in any expression.

If 8 = 5 + 3 and 5 + 3 = 6 + 2,

then 8 = 6 + 2.

If n = 12,

then 3n = 36

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identity & equality properties (algebra1 1_4)

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