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 PropertyAdditionMultiplication

18 Properties B. Davis MathScience Innovation Center Properties of Real Numbers PropertyAdditionMultiplication Closure Commutative Associative Identity Inverse

18 Properties B. Davis MathScience Innovation Center Properties of Real Numbers PropertyAdditionMultiplication 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 PropertyAdditionMultiplication Closure If, Then Commutative Associative Identity Inverse

18 Properties B. Davis MathScience Innovation Center Properties of Real Numbers PropertyAdditionMultiplication Closure If, Then If, Then Commutative Associative Identity Inverse

18 Properties B. Davis MathScience Innovation Center Properties of Real Numbers PropertyAdditionMultiplication Closure If, Then If, Then Commutative a + b = b + a Associative Identity Inverse

18 Properties B. Davis MathScience Innovation Center Properties of Real Numbers PropertyAdditionMultiplication Closure If, Then If, Then Commutative a + b = b + a ab = ba Associative Identity Inverse

18 Properties B. Davis MathScience Innovation Center Properties of Real Numbers PropertyAdditionMultiplication Closure If, Then If, Then Commutative a + b = b + a ab = ba Associativea+(b+c)= (a+b)+c Identity Inverse

18 Properties B. Davis MathScience Innovation Center Properties of Real Numbers PropertyAdditionMultiplication Closure If, Then If, Then Commutative a + b = b + a ab = ba Associativea+(b+c)= (a+b)+c a(bc)=(ab)c Identity Inverse

18 Properties B. Davis MathScience Innovation Center Properties of Real Numbers PropertyAdditionMultiplication Closure If, Then If, Then Commutative a + b = b + a ab = ba Associativea+(b+c)= (a+b)+c a(bc)=(ab)c Identitya + ? = a a * ? =a Inverse

18 Properties B. Davis MathScience Innovation Center Properties of Real Numbers PropertyAdditionMultiplication Closure If, Then If, Then Commutative a + b = b + a ab = ba Associativea+(b+c)= (a+b)+c a(bc)=(ab)c Identitya + 0 = a a * 1=a Inverse

18 Properties B. Davis MathScience Innovation Center Properties of Real Numbers PropertyAdditionMultiplication Closure If, Then If, Then Commutative a + b = b + a ab = ba Associativea+(b+c)= (a+b)+c a(bc)=(ab)c Identitya + 0 = a a * 1=a Inverse a + ? = 0 a * ? = 1

18 Properties B. Davis MathScience Innovation Center Properties of Real Numbers PropertyAdditionMultiplication Closure If, Then If, Then Commutative a + b = b + a ab = ba Associativea+(b+c)= (a+b)+c a(bc)=(ab)c Identitya + 0 = a a * 1=a Inverse a + -a = 0 a * = 1

18 Properties B. Davis MathScience Innovation Center One more property of real numbers… Distributive Property a(b+c) = ab + ac Or ab+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 = Subtraction If a = 5, then a - 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 + ac Or ab+ac = a(b + c)

18 Properties B. Davis MathScience Innovation Center Which property is it? Commutative Property of Multiplication a(b+c) = (b+c)a

18 Properties B. Davis MathScience Innovation Center Which property is it? Reflexive Property of Equality a(b+c) = a(b+c)

18 Properties B. Davis MathScience Innovation Center Which property is it? Identity Property of Multiplication 1(b+c) = b+ c

18 Properties B. Davis MathScience Innovation Center Which property is it? Symmetric Property of Equality If 2 + 3x = 5 Then 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 = 0 And = = 4 And = = 0 And = 0 Identity Property of Addition = 4 And = 4

18 Properties B. Davis MathScience Innovation Center Which is an example for the property? Commutative Property for Multiplication 4(x + y)=(x+y)4 4(x+y)=4(y+x) 4(x+y)=(x+y)4 Commutative Property for Addition 4(x+y)=4(y+x)