2 1 Properties of Real Numbers Commutative Associative

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

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