1. The Basic Properties of
REAL NUMBERS

2. Binary Operations
Addition
Multiplication

3. The Commutative Property
Addition
Multiplication
equals
equals

4. Postive Integers
TABLE

6. 1 2 3 ……

7. 1 2 3 …… .

8. + 1 2 3 …… .

9. + 1 2 3 …… 4 5 6 .

10. + 1 2 3 …… 4 5 6 .

11. + 1 2 3 …… 4 5 6 .

12. + 1 2 3 …… 4 5 6 .

13. + …… Keep Testing The Set of Real Numbers is Commutative 1 2 3 4 5 61 2 3 …… 4 5 6 .
The Set of Real Numbers is Commutative
with respect to ADDITION

14. What About Multiplication

15. x 1 2 3 …… 4 6 9 .

16. x 1 2 3 …… 4 6 9 .

17. x …… Keep Testing The Set of Real Numbers is Commutative 1 2 3 4 6 91 2 3 …… 4 6 9 .
The Set of Real Numbers is Commutative
with respect to MULTIPLICATION

18. The Associative Property

19. The Associative Property
Addition
Multiplication
equals

20. Associative Example for AdditionVS

21. Associative Example for Addition
equal ?

22. Go Back

23. The Associative Property
Addition
Multiplication
equals
equals

24. Associative Example for MultiplicationVS

25. Associative Example for Multiplication
equal ?

26. The Identity Property

27. Identity Properties
Addition
Multiplication ?
equals

28. Identity Properties
Addition
Multiplication
equals

29. Identity Properties
Addition
Multiplication
equals

30. Go Back

31. Identity Properties
Addition
Multiplication ?
equals
equals

32. Identity Properties
Addition
Multiplication
equals
equals

33. Identity Properties
Addition
Multiplication
equals
equals

34. Identity Properties
Addition
Multiplication
equals
equals

35. Next

36. The Property of Inverses

37. Property of Opposites and Reciprocals
Addition
OPPOSITES
Multiplication
RECIPROCALS ?
equals
Identity for Addition

38. Property of Opposites and Reciprocals
Addition
OPPOSITES
Multiplication
RECIPROCALS
equals

39. Opposites for AdditionIs
equal to

40. Property of Opposites and Reciprocals
Addition
OPPOSITES
Multiplication
RECIPROCALS ?
equals
equals
Identity for Multiplication

41. Property of Opposites and Reciprocals
Addition
OPPOSITES
Multiplication
RECIPROCALS
equals
equals

42. Reciprocals for MultiplicationIs
equal to

43. of Multiplication over Addition
The Distributive Property
of Multiplication over Addition

44. The Distributive Property
equals

45. Distributive Example
equal ?

46. CAREFUL

47. IS NOT THE SAME AS

48. Addition Sign
NO Addition Sign

49. Multiplication over Addition
Distributive Property of
Multiplication over Addition
NOT THE SAME
Associative Property of Multiplication
Closure Property of Multiplication

50. The Property of Closure

51. Property of Closure If a and b are and unique and unique Real Numbers
Addition
Multiplication
Real Number
Real Number
and unique
and unique

52. Closure for Addition Example
Real Number
unique

53. Closure for Multiplication Example
Real Number
unique

54. Example 1
Using Properties

55. Given

56. Given
Distributive Property

57. Given
Distributive Property
Identity Property of ?
Multiplication

58. Given
Distributive Property
Identity Property of ?
Multiplication
Commutative Property of ?
Addition

59. Given
Distributive Property
Identity Property of ?
Multiplication
Commutative Property of ?
Addition

60. Given
Distributive Property
Identity Property of ?
Multiplication
Commutative Property of ?
Addition
Associative Property of ?
Addition

61. Given
Distributive Property
Identity Property of ?
Multiplication
Commutative Property of ?
Addition
Associative Property of ?
Addition
Closure Property of ?
Addition

62. Example 2
Using Properties

63. Given
Commutative Property of ?
Addition
Associative Property of ?
Addition
Property of Opposites
Identity Property of ?
Addition