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 Commutative Property

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

3. 8+0=8 Identity Property of Addition

5. 6 • 4=4 • 6 Commutative Property of Multiplication

11. 5 • 1=5 Identity Property of Multiplication

25. 1 5/ + 0 = 7 1 5/ 7 Identity Property of Addition

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

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