Properties of Real Numbers 1.Objective: To apply the properties of operations. 2.Commutative Properties 3.Associative Properties 4.Identity Properties.

Properties of Real NumbersObjective: To apply the properties of operations.Commutative PropertiesAssociative PropertiesIdentity Properties Inverse Properties Distributive Property

On Tab 2: Commutative PropertiesChanging the order of the numbers in addition or multiplication will not change the result.

Commutative Property of Addition states: 2 + 3 = 3 + 2 or a + b = b + a

Commutative Property of Multiplication states: 4 5 = 5 4 or a b = b a.

On Tab 3: Associative PropertiesChanging 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 PropertiesAdding zero to a number does not change its value.2 + 0 = 2 & 0 + 2 = 2a + 0 = a & 0 + a = aMultiplying a number by 1 does not change the value of the number.5 1 = 5 & 1 5 = 5 a 1 = a & 1 a = aAdditionMultiplication

On Tab 5: Inverse PropertiesOpposites add to zero. 3 + -3 = 0 a + (-a) = 0A number multiplied by its reciprocal is always 1. AdditionMultiplication

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

Lets play Name that property!

State the property or properties that justify the following.3 + 2 = 2 + 3Commutative Property

State the property or properties that justify the following.10(1/10) = 1Inverse 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 Addition1.

3 + 7 = 7 + 3Commutative Property of Addition2.

8 + 0 = 8Identity Property of Addition3.

6 4 = 4 6Commutative Property of Multiplication5.

17 + (-17) = 0Inverse Property of Addition6.

2(5) = 5(2)Commutative Property of Multiplication7.

even + even = evenClosure Property8.

3(2 + 5) = 32 + 35Distributive Property9.

6(78) = (67)8Associative Property of Multiplication10.

5 1 = 5Identity Property of Multiplication11.

6(3 2n) = 18 12nDistributive Property12.

2x + 3 = 3 + 2xCommutative Property of Addition13.

ab = baCommutative Property of Multiplication14.

a + 0 = aIdentity Property of Addition15.

a(bc) = (ab)cAssociative Property of Multiplication16.

a1 = aIdentity Property of Multiplication17.

a +b = b + aCommutative Property of Addition18.

a(b + c) = ab + acDistributive Property19.

a + (b + c) = (a +b) + cAssociative Property of Addition20.

a + (-a) = 0Inverse Property of Addition21.

Properties of Real NumbersObjective: To apply the properties of operations.Commutative PropertiesAssociative PropertiesIdentity Properties Inverse Properties Distributive Property