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.

Identity and Equality PropertiesIdentity and Equality Properties

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

Identity and Equality PropertiesIdentity and Equality Properties

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

+

Identity and Equality PropertiesIdentity and Equality Properties

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

4 + r = 4

+

Identity and Equality PropertiesIdentity and Equality Properties

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

4 + r = 4

+

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

Identity and Equality PropertiesIdentity and Equality Properties

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

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.

Identity and Equality PropertiesIdentity and Equality Properties

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

Identity and Equality PropertiesIdentity and Equality Properties

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

Identity and Equality PropertiesIdentity and Equality Properties

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

a + 0 = 0 + a = ___.

Identity and Equality PropertiesIdentity and Equality Properties

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

a + 0 = 0 + a = ___.a

Identity and Equality PropertiesIdentity and Equality Properties

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

a + 0 = 0 + a = ___.a

7 + 0 = 0 + 7 = ___.

Identity and Equality PropertiesIdentity and Equality Properties

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

a + 0 = 0 + a = ___.a

7 + 0 = 0 + 7 = ___.7

Identity and Equality PropertiesIdentity and Equality Properties

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

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 _______________.

Identity and Equality PropertiesIdentity and Equality Properties

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

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

Identity and Equality PropertiesIdentity and Equality Properties

There are also special properties associated with multiplication.

Identity and Equality PropertiesIdentity and Equality Properties

There are also special properties associated with multiplication.

77 n

Identity and Equality PropertiesIdentity and Equality Properties

There are also special properties associated with multiplication.

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

_____________________

Identity and Equality PropertiesIdentity and Equality Properties

There are also special properties associated with multiplication.

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

_____________________multiplicative identity

Identity and Equality PropertiesIdentity and Equality Properties

There are also special properties associated with multiplication.

77 n 08 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

_____________________multiplicative identity

Identity and Equality PropertiesIdentity and Equality Properties

There are also special properties associated with multiplication.

77 n 08 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

_____________________multiplicative identity

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

and 0 is equal to 0.This is called the

_____________________

Identity and Equality PropertiesIdentity and Equality Properties

There are also special properties associated with multiplication.

77 n 08 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

_____________________multiplicative identity

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

Identity and Equality PropertiesIdentity and Equality Properties

There are also special properties associated with multiplication.

1551

Identity and Equality PropertiesIdentity and Equality Properties

There are also special properties associated with multiplication.

1551

Two numbers whose product is 1 are called

_____________________ or ____________.

Identity and Equality PropertiesIdentity and Equality Properties

There are also special properties associated with multiplication.

1551

Two numbers whose product is 1 are called

_____________________ or ____________.multiplicative inverses reciprocals

Identity and Equality PropertiesIdentity and Equality Properties

There are also special properties associated with multiplication.

1551

Two numbers whose product is 1 are called

_____________________ or ____________.multiplicative inverses reciprocals

51

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

Identity and Equality PropertiesIdentity and Equality Properties

There are also special properties associated with multiplication.

1551

Two numbers whose product is 1 are called

_____________________ or ____________.multiplicative inverses reciprocals

51

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

51

5 is the multiplicative inverse (or reciprocal) of

Identity and Equality PropertiesIdentity and Equality Properties

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

Identity and Equality PropertiesIdentity and Equality Properties

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

xx 1*

Identity and Equality PropertiesIdentity and Equality Properties

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

xx 1* 131*13

Identity and Equality PropertiesIdentity and Equality Properties

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

xx 1* 131*13

00* y

Identity and Equality PropertiesIdentity and Equality Properties

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

xx 1* 131*13

00* y 00*7

Identity and Equality PropertiesIdentity and Equality Properties

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

xx 1* 131*13

00* y 00*7

1

y

x

x

y

Identity and Equality PropertiesIdentity and Equality Properties

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

xx 1* 131*13

00* y 00*7

1

y

x

x

y1

1

2

2

1

Identity and Equality PropertiesIdentity and Equality Properties

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

xx 1* 131*13

00* y 00*7

1

y

x

x

y1

1

2

2

1

17

3

3

7

Identity and Equality PropertiesIdentity and Equality Properties

Property Words Symbols Examples

Reflexive

Symmetric

Any quantity is equalto itself.

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

Identity and Equality PropertiesIdentity and Equality Properties

Property Words Symbols Examples

Reflexive

Symmetric

Any quantity is equalto itself.

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

For any number a,

a = a

Identity and Equality PropertiesIdentity and Equality Properties

Property Words Symbols Examples

Reflexive

Symmetric

Any quantity is equalto itself.

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

For any number a,

a = a 99

Identity and Equality PropertiesIdentity and Equality Properties

Property Words Symbols Examples

Reflexive

Symmetric

Any quantity is equalto itself.

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

For any number a,

a = a 99

For any numbers

a and b,

If a = b then b = a

Identity and Equality PropertiesIdentity and Equality Properties

Property Words Symbols Examples

Reflexive

Symmetric

Any quantity is equalto itself.

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

For any number a,

a = a 99

For any numbers

a and b,

If a = b then b = a

8311then

1183 If

Identity and Equality PropertiesIdentity and Equality Properties

Property Words Symbols Examples

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.

Identity and Equality PropertiesIdentity and Equality Properties

Property Words Symbols Examples

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.

For any numbers

a, b, and c,

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

Identity and Equality PropertiesIdentity and Equality Properties

Property Words Symbols Examples

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.

For any numbers

a, b, and c,

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

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

then 8 = 6 + 2.

Identity and Equality PropertiesIdentity and Equality Properties

Property Words Symbols Examples

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.

For any numbers

a, b, and c,

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

Identity and Equality PropertiesIdentity and Equality Properties

Property Words Symbols Examples

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.

For any numbers

a, b, and c,

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