Properties of Real Numbers Commutative Associative Distributive Identity

Properties of Real Numbers Commutative Associative Distributive Identity + × Inverse + ×

Commutative Properties Changing 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 ab = ba.

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 (ab)c = a(bc)

Distributive Property Multiplication distributes over addition.

Additive Identity Property There exists a unique number 0 such that zero preserves identities under addition. a + 0 = a and 0 + a = a In other words adding zero to a number does not change its value.

Multiplicative Identity Property There exists a unique number 1 such that the number 1 preserves identities under multiplication. a ∙ 1 = a and 1 ∙ a = a In other words multiplying a number by 1 does not change the value of the number.

Additive Inverse Property For each real number a there exists a unique real number –a such that their sum is zero. a + (-a) = 0 In other words opposites add to zero.

Multiplicative Inverse Property For each real number a there exists a unique real number product is 1. such that their

Let’s play “Name that property!”

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

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

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

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

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

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

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

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

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

3+7=7+3

3+7=7+3 Commutative Property of Addition

8+0=8

8+0=8 Identity Property of Addition

6 • 4=4 • 6 Commutative Property of Multiplication

17 + (-17) = 0

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

2(5) = 5(2)

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

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

even + even = even

3(2 + 5) = 3 • 2 + 3 • 5 Distributive Property

6(7 • 8) = (6 • 7)8 Associative Property of Multiplication

5 • 1=5 Identity Property of Multiplication

(6 – 3)4 = 6 • 4 – 3 • 4 Distributive Property

1(-9) = -9 Identity Property of Multiplication

3 + (-3) = 0 Inverse Property of Addition

1 + [-9 + 3] = [1 + (-9)] + 3 Associative Property of Addition

-3(6) = 6(-3) Commutative Property of Multiplication

-8 + 0 = -8 Identity Property of Addition

3 • 7 – 3 • 4 = 3(7 – 4) Distributive Property

6 + [(3 + (-2)] = (6 + 3) + (- 2) Associative Property of Addition

7 + (-5) = -5 + 7 Commutative Property of Addition

(5 + 4)9 = 45 + 36

(5 + 4)9 = 45 + 36 Distributive Property

-3(5 • 4) = (-3 • 5)4 Associative Property of Multiplication

-8(4) = 4(-8) Commutative Property of Multiplication

1 5/ + 0 = 7 1 5/ 7

1 5/ + 0 = 7 1 5/ 7 Identity Property of Addition

3/ – 4 6/ = – 7 6/ + 7 3/ 4 Commutative Property of Addition

2 1/ • 1 = 5 2 1/ 5

2 1/ • 1 = 5 2 1/ 5 Identity Property of Multiplication

-8 2/ + 0 = -8 5 2/ 5

-8 2/ + 0 = -8 5 2/ 5 Identity Property of Addition

2 [(- / )(5)]9 = 3 2 -/ [(5)(9)] 3 Associative Property of Multiplication

6(3 – 2 n) = 18 – 12 n

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

2 x + 3 = 3 + 2 x

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

ab = ba

ab = ba Commutative Property of Multiplication

a+0=a

a+0=a Identity Property of Addition

a(bc) = (ab)c

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

a • 1 = a Identity Property of Multiplication

a +b = b + a Commutative Property of Addition

a(b + c) = ab + ac

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

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

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

Properties of Real Numbers Commutative Associative Distributive Identity + × Inverse + ×