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

18 Properties B. Davis MathScience Innovation Center

Properties of Real Numbers

Property Addition Multiplication

18 Properties B. Davis MathScience Innovation Center

Properties of Real Numbers

Property Addition Multiplication

Closure

Commutative

Associative

Identity

Inverse

18 Properties B. Davis MathScience Innovation Center

Properties of Real Numbers

Property Addition Multiplication

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

Commutative

Associative

Identity

Inverse

18 Properties B. Davis MathScience Innovation Center

Properties of Real Numbers

Property Addition Multiplication

Closure If,Then

Commutative

Associative

Identity

Inverse

Rba ,Rba

18 Properties B. Davis MathScience Innovation Center

Properties of Real Numbers

Property Addition Multiplication

Closure If,Then

If,Then

Commutative

Associative

Identity

Inverse

Rba ,Rba *

Rba ,Rba

18 Properties B. Davis MathScience Innovation Center

Properties of Real Numbers

Property Addition Multiplication

Closure If,Then

If,Then

Commutative a + b = b + a

Associative

Identity

Inverse

Rba ,Rba *

Rba ,Rba

18 Properties B. Davis MathScience Innovation Center

Properties of Real Numbers

Property Addition Multiplication

Closure If,Then

If,Then

Commutative a + b = b + a ab = ba

Associative

Identity

Inverse

Rba ,Rba *

Rba ,Rba

18 Properties B. Davis MathScience Innovation Center

Properties of Real Numbers

Property Addition Multiplication

Closure If,Then

If,Then

Commutative a + b = b + a ab = ba

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

Identity

Inverse

Rba ,Rba *

Rba ,Rba

18 Properties B. Davis MathScience Innovation Center

Properties of Real Numbers

Property Addition Multiplication

Closure If,Then

If,Then

Commutative a + b = b + a ab = ba

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

a(bc)=(ab)c

Identity

Inverse

Rba ,Rba *

Rba ,Rba

18 Properties B. Davis MathScience Innovation Center

Properties of Real Numbers

Property Addition Multiplication

Closure If,Then

If,Then

Commutative a + b = b + a ab = ba

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

a(bc)=(ab)c

Identity a + ? = a a * ? =a

Inverse

Rba ,Rba *

Rba ,Rba

18 Properties B. Davis MathScience Innovation Center

Properties of Real Numbers

Property Addition Multiplication

Closure If,Then

If,Then

Commutative a + b = b + a ab = ba

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

a(bc)=(ab)c

Identity a + 0 = a a * 1=a

Inverse

Rba ,Rba *

Rba ,Rba

18 Properties B. Davis MathScience Innovation Center

Properties of Real Numbers

Property Addition Multiplication

Closure If,Then

If,Then

Commutative a + b = b + a ab = ba

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

a(bc)=(ab)c

Identity a + 0 = a a * 1=a

Inverse a + ? = 0 a * ? = 1

Rba ,Rba *

Rba ,Rba

18 Properties B. Davis MathScience Innovation Center

Properties of Real Numbers

Property Addition Multiplication

Closure If,Then

If,Then

Commutative a + b = b + a ab = ba

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

a(bc)=(ab)c

Identity a + 0 = a a * 1=a

Inverse a + -a = 0 a * = 1

Rba ,Rba *

Rba ,Rba

a

1

18 Properties B. Davis MathScience Innovation Center

One more property of real numbers… Distributive

Property

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

18 Properties B. Davis MathScience Innovation Center

Properties of Equality You may

Add Subtract Multiply Divide ( by anything except 0)

As long as you operate on both sides !

18 Properties B. Davis MathScience Innovation Center

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

18 Properties B. Davis MathScience Innovation Center

Properties of Equality Reflexive Symmetric Transitive

18 Properties B. Davis MathScience Innovation Center

Properties of Equality Reflexive 1 Symmetric 2 Transitive 3

18 Properties B. Davis MathScience Innovation Center

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

18 Properties B. Davis MathScience Innovation Center

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

a. Transitive 3

18 Properties B. Davis MathScience Innovation Center

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.

18 Properties B. Davis MathScience Innovation Center

Properties of Equality

Reflexive

a= a

Transitive

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

Symmetric

If a = b, then b = a.

18 Properties B. Davis MathScience Innovation Center

Which property is it?

Distributive Property

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

18 Properties B. Davis MathScience Innovation Center

Which property is it?

Commutative Property of Multiplicatio

n

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

18 Properties B. Davis MathScience Innovation Center

Which property is it?

ReflexiveProperty of

Equality

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

18 Properties B. Davis MathScience Innovation Center

Which property is it?

IdentityProperty of Multiplicatio

n1(b+c) = b+ c

18 Properties B. Davis MathScience Innovation Center

Which property is it?

Symmetric Property of

Equality

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

3x

18 Properties B. Davis MathScience Innovation Center

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

18 Properties B. Davis MathScience Innovation Center

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

18 Properties B. Davis MathScience Innovation Center

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)