18 properties mathscience innovation center mrs. b. davis
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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)