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 Addition6.
Which Property?
3 + 7 = 7 + 3
Commutative Property of Addition

18. Identity Property of Addition7.
Which Property?
8 + 0 = 8
Identity Property of Addition

19. Commutative Property of Multiplication8.
Which Property?
6 • 4 = 4 • 6
Commutative Property of Multiplication

20. Inverse Property of Addition9.
Which Property?
17 + (-17) = 0
Inverse Property of Addition

21. Commutative Property of Multiplication
10.
Which Property?
2(5) = 5(2)
Commutative Property of Multiplication

22. Associative Property of Addition
11.
Which Property?
(2 + 1) + 4 = 2 + (1 + 4)
Associative Property of Addition

23. Associative Property of Multiplication
12.
Which Property?
6(7•8) = (6•7)8
Associative Property of Multiplication

24. Identity Property of Multiplication
13.
Which Property?
5 • 1 = 5
Identity Property of Multiplication

25. Distributive Property
14.
Which Property?
(6 – 3)4 = 6•4 – 3•4
Distributive Property

26. Identity Property of Multiplication
15.
Which Property?
1(-9) = -9
Identity Property of Multiplication

27. Inverse Property of Addition
16.
Which Property?
3 + (-3) = 0
Inverse Property of Addition

28. Associative Property of Addition
17.
Which Property?
1 + [-9 + 3]
= [1 + (-9)] + 3
Associative Property of Addition

29. Commutative Property of Multiplication
18.
Which Property?
-3(6) = 6(-3)
Commutative Property of Multiplication

30. Identity Property of Addition
19.
Which Property?
= -8
Identity Property of Addition

31. Distributive Property
20.
Which Property?
3•7 – 3•4 = 3(7 – 4)
Distributive Property

32. Associative Property of Addition
21.
Which Property?
6 + [3 + (-2)]
= (6 + 3) + (- 2)
Associative Property of Addition

33. Commutative Property of Addition
22.
Which Property?
7 + (-5) =
Commutative Property of Addition

34. Distributive Property
23.
Which Property?
(5 + 4)9 =
Distributive Property

35. Associative Property of Multiplication
24.
Which Property?
-3(5 • 4) = (-3 • 5)4
Associative Property of Multiplication

36. Commutative Property of Multiplication
25.
Which Property?
-8(4) = 4(-8)
Commutative Property of Multiplication

37. Identity Property of Addition
26.
Which Property?
51/7 + 0 = 51/7
Identity Property of Addition

38. Commutative Property of Addition
27.
Which Property?
3/4 – 6/7 = – 6/7 + 3/4
Commutative Property of Addition

39. Identity Property of Multiplication
28.
Which Property?
12/5 • 1 = 12/5
Identity Property of Multiplication

40. Identity Property of Addition
29.
Which Property?
-8 2/5 + 0 = -8 2/5
Identity Property of Addition

41. Associative Property of Multiplication
30.
Which Property?
[(-2/3)(5)]9 = -2/3[(5)(9)]
Associative Property of Multiplication

42. Distributive Property
31.
Which Property?
6(3 – 2n) = 18 – 12n
Distributive Property

43. Commutative Property of Addition
32.
Which Property?
2x + 3 = 3 + 2x
Commutative Property of Addition

44. Commutative Property of Multiplication
33.
Which Property?
ab = ba
Commutative Property of Multiplication

45. Identity Property of Addition
34.
Which Property?
a + 0 = a
Identity Property of Addition

46. Associative Property of Multiplication
35.
Which Property?
a(bc) = (ab)c
Associative Property of Multiplication

47. Identity Property of Multiplication
36.
Which Property?
a•1 = a
Identity Property of Multiplication

48. Commutative Property of Addition
37.
Which Property?
a +b = b + a
Commutative Property of Addition

49. Distributive Property
38.
Which Property?
a(b + c) = ab + ac
Distributive Property

50. Associative Property of Addition
39.
Which Property?
a + (b + c) = (a +b) + c
Associative Property of Addition

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

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