739124064-Grade-7-Real-Numbers.pptxREAL NUMBERS

REAL NUMBERS

1. Grade 7 MATH MS. MELANIE E. VENTURA

2. Subsets of Real Numbers

3. Subsets of Real Numbers – Natural Numbers

4. Subsets of Real Numbers – Natural Numbers Also called counting numbers N = { 1, 2, 3, 4, 5, 6, . . .}

5. Subsets of Real Numbers – Whole Numbers

6. Subsets of Real Numbers – Whole Numbers Formed by adding 0 to the set of N W = { 0, 1, 2, 3, 4, 5, 6, . . .}

7. Subsets of Real Numbers – Integers

8. Subsets of Real Numbers – Integers Formed by adding negatives of the set of N to the set of W Z = { . . . – 6, – 5, – 4, – 3, – 2, – 1, 0, 1, 2, 3, 4, 5, 6, . . .}

9. Subsets of Real Numbers – Rational Numbers

10. Subsets of Real Numbers – Rational Numbers Set of all numbers which can be represented in the form , where and are integers, and . Decimal representation either terminates or repeats. Q = { . . . – 6, , – 5, – , – 3, – 2, – 1, 0, 1, 2, 3, 3.75, 4, 5, 6, . . .}  

11. Subsets of Real Numbers – Irrational Numbers

12. Subsets of Real Numbers – Irrational Numbers Set of numbers which decimal representations are NON-TERMINATING and NON-REPEATING. Cannot be expressed as or a quotient of integers. = { . . . , П . . .}  

13. Subsets of Real Numbers ‘

14. Subsets of Real Numbers N ⊆ W ⊆ Z ⊆ Q ⊆ R

15. Subsets of Real Numbers N ⊆ W ⊆ Z ⊆ Q ⊆ R Q’ ⊆ R

16. Real Numbers   ________________________ 1) This set is the union of rational and irrational numbers.  ________________________ 2) This is the set of numbers that can be expressed as a quotient of 2 integers . ________________________ 3) This is the set of numbers that represent non – terminating and non – repeating decimals. ________________________ 4) This set is represented by the set .  

17. Real Numbers     Natural Whole Integers Rational Irrational Real                                                   Natural Whole Integers Rational Irrational Real                                    

18. Real Numbers     Natural Whole Integers Rational Irrational Real                                   Natural Whole Integers Rational Irrational Real                        

19. Real Numbers     Natural Whole Integers Rational Irrational Real                                                   Natural Whole Integers Rational Irrational Real                                    

20. Properties of Real Numbers Closure Property of Addition = a real number  

21. Properties of Real Numbers Closure Property of Multiplication = a real number  

22. Properties of Real Numbers Commutative Property of Addition  

23. Properties of Real Numbers Commutative Property of Multiplication  

24. Properties of Real Numbers Associative Property of Addition  

25. Properties of Real Numbers Associative Property of Multiplication  

26. Properties of Real Numbers Distributive Property of Multiplication over Addition  

27. Properties of Real Numbers Distributive Property of Multiplication over Addition  

28. Properties of Real Numbers Distributive Property of Multiplication over Addition - Useful for decimals  

29. Properties of Real Numbers Distributive Property of Multiplication over Subtraction  

30. Properties of Real Numbers Distributive Property of Multiplication over Subtraction  

31. Properties of Real Numbers Identity Property of Addition  

32. Properties of Real Numbers Identity Property of Addition Additive identity: 0  

33. Properties of Real Numbers Identity Property of Multiplication  

34. Properties of Real Numbers Identity Property of Multiplication Multiplicative identity: 1  

35. Properties of Real Numbers Inverse Property of Addition  

36. Properties of Real Numbers Inverse Property of Addition Additive inverse: the real number’s NEGATIVE or OPPOSITE  

37. Properties of Real Numbers Inverse Property of Multiplication  

38. Properties of Real Numbers Inverse Property of Multiplication Multiplicative inverse: the real number’s RECIPROCAL  

39. Properties of Real Numbers   ______________________________________ Multiplication distributes over addition.   ______________________________________ Any number added to 0 will result in the same real number.   ______________________________________ If three real numbers are multiplied, it makes no difference which two are multiplied first.   ______________________________________ The sum of any two real numbers is a real number.   ______________________________________ The sum of any real number and its opposite is 0. ______________________________________ Two real numbers can be added in any order.    

40. Properties of Real Numbers   ______________________________________ The product of any two real numbers is a real number.   ______________________________________ Any number multiplied by 1 will result in the same real number.   ______________________________________ If three real numbers are added, it makes no difference which two are added first.   ______________________________________ The product of a number and its reciprocal is 1.   ______________________________________ Two real numbers can be multiplied in any order

41. Properties of Real Numbers   ______________________________________   ______________________________________   ______________________________________   ______________________________________  

42. Integers

43. Integers Characteristics of integers: Smallest positive integer: 1 Largest negative integer: –1 Integer that is neither positive nor negative: 0

44. Integer Number Line

45. Integer Number Line – Inequalities ‘

46. Integer Number Line – Absolute Value

47. Integer Number Line – Absolute Value Absolute value = distance of the integers from 0

48. Integer Number Line – Absolute Value Absolute value = distance of the integers from 0 Ex: point A = 3

49. Integer Number Line – Absolute Value Absolute value = distance of the integers from 0 Ex: point A = 3 distance of the integer from 0 is 3

50. Integer Number Line – Absolute Value Absolute value = distance of the integers from 0 Ex: point B = –3

51. Integer Number Line – Absolute Value Absolute value = distance of the integers from 0 Ex: point B = –3 distance of the integer from 0 is 3

52. Integer Number Line

53. Operations on Integers – Addition

54. Operations on Integers – Addition  

55. Operations on Integers – Addition  

56. Operations on Integers – Addition  

57. Operations on Integers – Addition  

58. Operations on Integers – Addition  

59. Operations on Integers – Addition  

60. Operations on Integers – Addition

61. Operations on Integers – Addition - Same sign Ex: - Different sign Ex:  

62. Operations on Integers – Addition - Same sign: add the absolute values and use the same sign Ex: - Different sign Ex:  

63. Operations on Integers – Addition - Same sign: add the absolute values and use the same sign Ex: - Different sign: subtract the absolute values and use the sign of the greater absolute value Ex:  

64. Operations on Integers – Addition  

65. Operations on Integers – Addition  

66. Operations on Integers – Addition  

67. Operations on Integers – Addition  

68. Operations on Integers – Subtraction

69. Operations on Integers – Subtraction  

70. Operations on Integers – Subtraction  

71. Operations on Integers – Subtraction  

72. Operations on Integers – Subtraction  

73. Operations on Integers – Subtraction  

74. Operations on Integers – Addition and Subtraction 1. 2. 3. 4. 5. 6.  

75. Operations on Integers – Multiplication

76. Operations on Integers – Division

77. Operations on Integers – PEMDAS