Properties of Real Numbers 1.Objective: To apply the properties of operations. 2.Commutative Properties 3.Associative Properties 4.Identity Properties 5.Inverse Properties 6.Distributive Property

On Tab 2: Commutative Properties  Changing the order of the numbers in addition or multiplication will not change the result.  Commutative Property of Addition states: = or a + b = b + a  Commutative Property of Multiplication states: 4 5 = 5 4 or a b = b a.

On Tab 3: Associative Properties  Changing the grouping of the numbers in addition or multiplication will not change the result.  Associative Property of Addition states: 3 + (4 + 5) = (3 + 4)+ 5 or a + (b + c) = (a + b)+ c  Associative Property of Multiplication states: (2 3) 4 = 2 (3 4) or (a b) c = a (b c)

On Tab 4: Identity Properties  Adding zero to a number does not change its value = 2 & = 2 a + 0 = a & 0 + a = a  Multiplying a number by 1 does not change the value of the number. 5 ∙ 1 = 5 & 1 ∙ 5 = 5 a ∙ 1 = a & 1 ∙ a = a Addition Multiplication

On Tab 5: Inverse Properties  Opposites add to zero = 0 a + (-a) = 0  A number multiplied by its reciprocal is always 1. Addition Multiplication

On Tab 6: Distributive Property  Multiplication distributes over addition & subtraction.

Let’s play “Name that property!”

State the property or properties that justify the following = Commutative Property

State the property or properties that justify the following. 10(1/10) = 1 Inverse Property of Multiplication

State the property or properties that justify the following. 3(x – 10) = 3x – 30 Distributive Property

State the property or properties that justify the following. 3 + (4 + 5) = (3 + 4) + 5 Associative Property

State the property or properties that justify the following. (5 + 2) + 9 = (2 + 5) + 9 Commutative Property

(2 + 1) + 4 = 2 + (1 + 4) Associative Property of Addition 1.

3 + 7 = Commutative Property of Addition 2.

8 + 0 = 8 Identity Property of Addition 3.

6 4 = 4 6 Commutative Property of Multiplication 5.

17 + (-17) = 0 Inverse Property of Addition 6.

2(5) = 5(2) Commutative Property of Multiplication 7.

even + even = even Closure Property 8.

3(2 + 5) = Distributive Property 9.

6(78) = (67)8 Associative Property of Multiplication 10.

5 1 = 5 Identity Property of Multiplication 11.

6(3 – 2n) = 18 – 12n Distributive Property 12.

2x + 3 = 3 + 2x Commutative Property of Addition 13.

ab = ba Commutative Property of Multiplication 14.

a + 0 = a Identity Property of Addition 15.

a(bc) = (ab)c Associative Property of Multiplication 16.

a1 = a Identity Property of Multiplication 17.

a +b = b + a Commutative Property of Addition 18.

a(b + c) = ab + ac Distributive Property 19.

a + (b + c) = (a +b) + c Associative Property of Addition 20.

a + (-a) = 0 Inverse Property of Addition 21.

Properties of Real Numbers 1.Objective: To apply the properties of operations. 2.Commutative Properties 3.Associative Properties 4.Identity Properties 5.Inverse Properties 6.Distributive Property