2.1 Properties of Real Numbers Commutative Associative Identity + ×

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 a + b = b + a. Commutative Property of Multiplication states: 4 • 5 = 5 • 4 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 a + (b + c)= (a + b)+ c Associative Property of Multiplication states: (2 • 3) • 4 = 2 • (3 • 4) (ab)c = a(bc)

Additive Identity Property There exists a unique number 0 such that zero preserves identities under addition. a + 0 = a 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 1 ∙ a = a In other words multiplying a number by 1 does not change the value of the number.

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. 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

EXAMPLES

Commutative Property of Addition 2. Which Property? 3 + 7 = 7 + 3 Commutative Property of Addition

Identity Property of Addition 3. Which Property? 8 + 0 = 8 Identity Property of Addition

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