1. 2.1 Properties of Real Numbers
Commutative
Associative
Identity + ×

2. Commutative Properties
Changing the order of the numbers in addition or multiplication will not change the result.
Commutative Property of Addition states:
2 + 3 = a + b = b + a.
Commutative Property of Multiplication states:
4 • 5 = 5 • ab = ba.

3. 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)

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

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

6. Let’s play “Name that property!”

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

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

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

10. EXAMPLES

11. Commutative Property of Addition2.
Which Property?
3 + 7 = 7 + 3
Commutative Property of Addition

12. Identity Property of Addition3.
Which Property?
8 + 0 = 8
Identity Property of Addition

13. Commutative Property of Multiplication5.
Which Property?
6 • 4 = 4 • 6
Commutative Property of Multiplication