18 Properties MathScience Innovation Center Mrs. B. Davis.

18 Properties

MathScience Innovation Center

Mrs. B. Davis

18 Properties B. Davis MathScience Innovation Center

Properties of Real Numbers



Property Addition Multiplication




Closure

Commutative

Associative

Identity

Inverse




Closure If a, b are R,Then a+b is R

Commutative

Associative

Identity

Inverse




Closure If,Then

Commutative

Associative

Identity

Inverse

Rba ,Rba




Closure If,Then

If,Then

Commutative

Associative

Identity

Inverse

Rba ,Rba *

Rba ,Rba




Closure If,Then

If,Then

Commutative a + b = b + a

Associative

Identity

Inverse

Rba ,Rba *

Rba ,Rba




Closure If,Then

If,Then

Commutative a + b = b + a ab = ba

Associative

Identity

Inverse

Rba ,Rba *

Rba ,Rba




Closure If,Then

If,Then


Associative a+(b+c)=(a+b)+c

Identity

Inverse

Rba ,Rba *

Rba ,Rba




Closure If,Then

If,Then



a(bc)=(ab)c

Identity

Inverse

Rba ,Rba *

Rba ,Rba




Closure If,Then

If,Then



a(bc)=(ab)c

Identity a + ? = a a * ? =a

Inverse

Rba ,Rba *

Rba ,Rba




Closure If,Then

If,Then



a(bc)=(ab)c

Identity a + 0 = a a * 1=a

Inverse

Rba ,Rba *

Rba ,Rba




Closure If,Then

If,Then



a(bc)=(ab)c


Inverse a + ? = 0 a * ? = 1

Rba ,Rba *

Rba ,Rba




Closure If,Then

If,Then



a(bc)=(ab)c


Inverse a + -a = 0 a * = 1

Rba ,Rba *

Rba ,Rba

a

1


One more property of real numbers… Distributive

Property

a(b+c) = ab + acOrab+ac = a(b + c)


Properties of Equality You may

Add Subtract Multiply Divide ( by anything except 0)

As long as you operate on both sides !


Properties of Equality

Addition

If a = 5, then a + 1 = 5 + 1

Subtraction

If a = 5, then a - 3 = 5 - 3

Multiplication

If a = 5, then a x 9 = 5 x 9

Division

If a = 5, then a /2 = 5 /2


Properties of Equality Reflexive Symmetric Transitive


Properties of Equality Reflexive 1 Symmetric 2 Transitive 3


Properties of Equality Reflexive 1 a= a Symmetric 2 Transitive 3


Properties of Equality Reflexive 1 a= a Symmetric 2 If a = b, then b =

a. Transitive 3


Properties of Equality Reflexive 1 a= a Symmetric 2 If a = b, then b =

a. Transitive 3 If a = b, and b = c, then a = c.


Properties of Equality

Reflexive

a= a

Transitive

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

Symmetric

If a = b, then b = a.


Which property is it?

Distributive Property

a(b+c) = ab + acOrab+ac = a(b + c)



Commutative Property of Multiplicatio

n

a(b+c) = (b+c)a



ReflexiveProperty of

Equality

a(b+c) = a(b+c)



IdentityProperty of Multiplicatio

n1(b+c) = b+ c



Symmetric Property of

Equality

If 2 + 3x = 5Then 5 = 2 +

3x


Which is an example for the property?

Transitive Property of

Equality

If 2 + 3x = 5, and 5 = 6b

Then 2 + 3x= 6b

If 2 + 3x = 5, and 5 = 6b

Then 2 + 3x= 6b

If 2 + 3x = 5y, and x= 2

Then 2 + 3(2)= 5y

Substitution property

If 2 + 3x = 5y, and x= 2

Then 2 + 3(2)= 5y


Which example for the property?

Property of Additive Inverses

4 + -4 = 0And-4 + 4 = 0

4 + 0 = 4 And 0 + 4 = 4

4 + -4 = 0And-4 + 4 = 0

Identity Property

of Addition

4 + 0 = 4 And 0 + 4 = 4


Which is an example for the property?

Commutative Property for Multiplicatio

n

4(x + y)=(x+y)4

4(x+y)=4(y+x)

4(x+y)=(x+y)4

Commutative Property for

Addition4(x+y)=4(y+x)

18 Properties MathScience Innovation Center Mrs. B. Davis.

Documents

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