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

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

5. 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)

6. Distributive Property
Multiplication distributes over addition.

7. 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.

8. 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.

9. 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.

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

11. Let’s play “Name that property!”

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

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

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

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

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

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

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

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

20. Identity Property of Multiplication
11.
Which Property?
5 • 1 = 5
Identity Property of Multiplication

21. Identity Property of Addition
25.
Which Property?
51/7 + 0 = 51/7
Identity Property of Addition

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

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