1. Properties

2. Properties  Commutative Property  Associative Property  Distributive Property  Additive Identity  Additive Inverse  Multiplicative Identity  Multiplicative Inverse  Substitution  Symmetric Equality  Transitive Equality  Addition Property of Equality  Multiplication Property of Equality  Zero Product Property

3. Commutative Property  a + b = b + a  CO is Change order; move; “commute”  Example: 3 + x = ??? 3 + x = ???

4. Associative Property  (a + b) + c = a + (b + c)  SO is Same Order. Change friends; “associates”.  Numbers stay in the same order, but parenthesis move around.  Example: (6 + x) + 4 = ??? (6 + x) + 4 = ???

5. Distributive Property  a(b + c) = ab + ac OR (b + c)a = ba + ca  a is multiplied by (distributed) everything inside the parentheses.   Taste the Rainbow (draw arrows on top).  Example: 3(x + 2) = ??? 3(x + 2) = ???

6. Additive Identity  a + 0 = a  Adds ZERO  stays the same keeps its “identity” keeps its “identity”  Example: 3 + 0 = ??? 3 + 0 = ???

7. Additive Inverse  a + (-a) = 0  Opposite (inverse) numbers add to 0  Example: 4 + ??? = 0 4 + ??? = 0

8. Multiplicative Identity  a * 1 = a  Multiply by 1  stays the same keeps its “identity” keeps its “identity”  Example: 5 * 1 = ??? 5 * 1 = ???

9. Multiplicative Inverse  2 x 3 = 1 3 2 3 2  Opposite (inverse) numbers multiply to 1  Opposite of multiply is divide.  Also called Reciprocals.  Example: 6 * ??? = 1 6 * ??? = 1

10. Substitution  If a + b = c and b = 2, then a + 2 = c  Substitute given information into equation.  Example: 5 + x = y where x = 4 5 + x = y where x = 4

11. Symmetric Equality  If a = b, then b = a  Switch sides  Example: If 6 = x, then ??? If 6 = x, then ???

12. Transitive Equality  If a = b and b = c, then a = c.  “Great cheese comes from happy cows. Happy cows come from California.” Therefore great cheese comes from California. Therefore great cheese comes from California.  Example: If 4 = x and x = 2y, then ??? If 4 = x and x = 2y, then ???

13. Addition Property of Equality  If a = b, then a + 2 = b + 2  Add the same thing to both sides.  Or Subtract the same thing from both sides.  Example: If 5 = x, then 9 = ??? If 5 = x, then 9 = ???

14. Multiplication Property of Equality  If a = b, then 2a = 2b.  Multiply both sides by the same thing.  Example: If 4 = x, then 12 = ??? If 4 = x, then 12 = ???

15. Zero Product Property  If ab = 0, then a = 0 or b = 0.  If the product of 2 numbers is 0, then one of the numbers must be 0 itself.  Example: If 5x = 0, then ??? If 5x = 0, then ???

17. Properties Examples 2 Block 1 Shown Bl 5 7

18. Commutative Property  1 Equation  CO = Change order;  move numbers; “commute”  Example: 4 * 5 * 7 = 7 * 5 * 4 4 * 5 * 7 = 7 * 5 * 4

19. Associative Property  1 Equation  SO = Same Order.  Change groups or ( )  Example: (1 * 2) * 3 = 1 * (2 * 3) (1 * 2) * 3 = 1 * (2 * 3)

20. Distributive Property  1 Equation  Multiply the outside by everything in the inside.  Example: 6(x - 5) = 6x - 30 6(x - 5) = 6x - 30

21. Additive Identity  Add ZERO  Identity means stays the same  Example: 10 + 0 = 10 10 + 0 = 10

22. Additive Inverse  Inverse means Opposite  Add and Subtract the same number or  Positive and Negative  Adds to ZERO.  Example: -57 + 57 = 0 -57 + 57 = 0

23. Multiplicative Identity  Multiply by 1  Identity means stays the same  Example: 2 * 1 = 2 2 * 1 = 2 Or Or 1 * 15 = 15 1 * 15 = 15

24. Multiplicative Inverse  Inverse means Opposite  Multiply and Divide the same number are opposites  OR Do reciprocal  numbers multiply to 1  Example: 7 * 1/7 = 1 7 * 1/7 = 1 Or * 2/5 becomes * 5/2 Or * 2/5 becomes * 5/2

25. Substitution  Replace a letter with a number  Example: 5 + x = y where x = 4 5 + x = y where x = 4 y = 9 y = 9

26. Symmetric Equality  2 Equations  Switch sides  Example: If 5 + 6 = 11, If 5 + 6 = 11, then 11 = 5 + 6 then 11 = 5 + 6

27. Transitive Equality  3 equations  The middle of the first two are equal.  The ends create the third.  Example: If 4 = x and x = y, then 4 = y If 4 = x and x = y, then 4 = y

28. Addition Property of Equality  Add Equal things to both sides.  Example: If 6 = x If 6 = x Then 14 = x + 8 (Add 8 to both sides) Then 14 = x + 8 (Add 8 to both sides)

29. Multiplication Property of Equality  Multiply Equal things to both sides.  Example: If 10 = x If 10 = x Then 20 = 2x (multiply by 2) Then 20 = 2x (multiply by 2)

30. Zero Product Property  Product is multiply  If 2 numbers multiply to 0, then one of the numbers must be 0.  Example: If (x + 8)(x - 9) = 0, then If (x + 8)(x - 9) = 0, then (x + 8) = 0 or (x - 9) = 0 (x + 8) = 0 or (x - 9) = 0 So (x + 8) gives x = -8 So (x + 8) gives x = -8 And (x – 9) gives x = 9 And (x – 9) gives x = 9

32. Properties Examples 2 Block 5 Shown Bl 1 7

33. Commutative Property  1 Equation  CO = Change order;  move numbers; “commute”  Example: 3 * 5 * 4 * 8 = 8 * 4 * 5 *3 3 * 5 * 4 * 8 = 8 * 4 * 5 *3

34. Associative Property  1 Equation  SO = Same Order.  Change groups or ( )  Example: ( 6 * 3) * 5 = 6 * (3 * 5) ( 6 * 3) * 5 = 6 * (3 * 5)

35. Distributive Property  1 Equation  Multiply the outside by everything in the inside.  Example: 3(x - 8) = 3x - 24 3(x - 8) = 3x - 24

36. Additive Identity  Add ZERO  Identity means stays the same  Example: 5 + 0 = 5 5 + 0 = 5

37. Additive Inverse  Inverse means Opposite  Add and Subtract the same number or  Positive and Negative  Adds to ZERO.  Example: -12 + 12 = 0 -12 + 12 = 0

38. Multiplicative Identity  Multiply by 1  Identity means stays the same  Example: 72 * 1 = 72 72 * 1 = 72 Or Or 1 * 72 = 72 1 * 72 = 72

39. Multiplicative Inverse  Inverse means Opposite  Multiply and Divide the same number are opposites  OR Do reciprocal  numbers multiply to 1  Example: 8 * 1/8 = 1 8 * 1/8 = 1 Or Or * 3/4 becomes * 4/3 * 3/4 becomes * 4/3

40. Substitution  Replace a letter with a number  Example: 5 + x = y where x = 8 5 + x = y where x = 8 y = 13 y = 13

41. Symmetric Equality  2 Equations  Switch sides  Example: If 2 + 3 = 5, If 2 + 3 = 5, then 5 = 2 + 3 then 5 = 2 + 3

42. Transitive Equality  3 equations  The middle of the first two are equal.  The ends create the third.  Example: If 4 = x and x = y, then 4 = y If 4 = x and x = y, then 4 = y

43. Addition Property of Equality  Add Equal things to both sides.  Example: If 9 = x If 9 = x then 12 = x + 3 (Add 3 to both sides.) then 12 = x + 3 (Add 3 to both sides.)

44. Multiplication Property of Equality  Multiply Equal things to both sides.  Example: If 7 = x If 7 = x Then 28 = 4x (Multiply both sides by 4.) Then 28 = 4x (Multiply both sides by 4.)

45. Zero Product Property  Product is multiply  If 2 numbers multiply to 0, then one of the numbers must be 0.  Example: Question: If (x + 6)(x - 4) = 0, then Question: If (x + 6)(x - 4) = 0, then Answer: (x + 6) = 0 or (x - 4) = 0 Answer: (x + 6) = 0 or (x - 4) = 0 So (x + 6) gives x = -6 So (x + 6) gives x = -6 And (x – 4) gives x = 4 And (x – 4) gives x = 4

47. Properties Examples 2 Block 7 Shown Bl 1 5

48. Commutative Property  1 Equation  CO = Change order;  move numbers; “commute”  Example: 3 * 2 * 1 = 1 * 2 * 3 3 * 2 * 1 = 1 * 2 * 3

49. Associative Property  1 Equation  SO = Same Order.  Change groups or ( )  Example: ( 3 * 6 ) * 15 = 3 * ( 6 * 15) ( 3 * 6 ) * 15 = 3 * ( 6 * 15)

50. Distributive Property  1 Equation  Multiply the outside by everything in the inside.  Example: 4 (x - 7) = 4x - 28 4 (x - 7) = 4x - 28

51. Additive Identity  Add ZERO  Identity means stays the same  Example: 21 + 0 = 21 21 + 0 = 21

52. Additive Inverse  Inverse means Opposite  Add and Subtract the same number or  Positive and Negative  Adds to ZERO.  Example: +8 - 8 = 0 +8 - 8 = 0

53. Multiplicative Identity  Multiply by 1  Identity means stays the same  Example: 7 * 1 = 7 7 * 1 = 7 Or Or 1 * 8 = 8 1 * 8 = 8

54. Multiplicative Inverse  Inverse means Opposite  Multiply and Divide the same number are opposites  OR Do reciprocal  numbers multiply to 1  Example: 10 * 1/10 = 1 10 * 1/10 = 1 Or * 7/8 becomes * 8/7 Or * 7/8 becomes * 8/7

55. Substitution  Replace a letter with a number  Example: 5 + x = y where x = 7 5 + x = y where x = 7 y = 12 y = 12

56. Symmetric Equality  2 Equations  Switch sides  Example: If 3 + 4 = 7, If 3 + 4 = 7, then 7 = 3 + 4 then 7 = 3 + 4

57. Transitive Equality  3 equations  The middle of the first two are equal.  The ends create the third.  Example: If 4 = x and x = y, then 4 = y If 4 = x and x = y, then 4 = y

58. Addition Property of Equality  Add Equal things to both sides.  Example: If 8 = x If 8 = x then 15 = x + 7 (Add 7 to both sides.) then 15 = x + 7 (Add 7 to both sides.)

59. Multiplication Property of Equality  Multiply Equal things to both sides.  Example: If 3 = x If 3 = x then 21 = 7x (Multiply both sides by 7) then 21 = 7x (Multiply both sides by 7)

60. Zero Product Property  Product is multiply  If 2 numbers multiply to 0, then one of the numbers must be 0.  Example: If (x + 2)(x - 7) = 0, then If (x + 2)(x - 7) = 0, then (x + 2) = 0 or (x - 7) = 0 (x + 2) = 0 or (x - 7) = 0 So (x + 2) gives x = -2 So (x + 2) gives x = -2 And (x – 7) gives x = 7 And (x – 7) gives x = 7

62. Properties Examples Block 6/7 2011

63. Commutative Property  1 Equation  CO = Change order;  move numbers; “commute”  Example:

64. Commutative Property  1 Equation  CO = Change order;  move numbers; “commute”  Example:

65. Associative Property  1 Equation  SO = Same Order.  Change groups or ( )  Example:

66. Associative Property  1 Equation  SO = Same Order.  Change groups or ( )  Example:

67. Distributive Property  1 Equation  Multiply the outside by everything in the inside.  Example: (x -) = x – (x -) = x – (x + -) = x + - (x + -) = x + -

68. Distributive Property  1 Equation  Multiply the outside by everything in the inside.  Example: (x -) = x – (x -) = x – (x + -) = x + - (x + -) = x + -

69. Additive Identity  Add ZERO  Identity means stays the same  Example: + 0 = + 0 =

70. Additive Identity  Add ZERO  Identity means stays the same  Example: + 0 = + 0 =

71. Additive Inverse  Inverse means Opposite  Add and Subtract the same number or  Positive and Negative  Adds to ZERO.  Example: + = 0 + = 0

72. Additive Inverse  Inverse means Opposite  Add and Subtract the same number or  Positive and Negative  Adds to ZERO.  Example: + = 0 + = 0

73. Multiplicative Identity  Multiply by 1  Identity means stays the same  Example: * 1 = ??? * 1 = ??? Or 1 * = Or 1 * =

74. Multiplicative Identity  Multiply by 1  Identity means stays the same  Example: * 1 = ??? * 1 = ??? Or 1 * = Or 1 * =

75. Multiplicative Inverse  Inverse means Opposite  Multiply and Divide the same number are opposites  OR Do reciprocal  numbers multiply to 1  Example: * 1/ = 1 * 1/ = 1 Or * / becomes * / Or * / becomes * /

76. Multiplicative Inverse  Inverse means Opposite  Multiply and Divide the same number are opposites  OR Do reciprocal  numbers multiply to 1  Example: * 1/ = 1 * 1/ = 1 Or * / becomes * / Or * / becomes * /

77. Substitution  Replace a letter with a number  Example: 5 + x = y where x = 5 + x = y where x = y = y =

78. Substitution  Replace a letter with a number  Example: 5 + x = y where x = 5 + x = y where x = y = y =

79. Symmetric Equality  2 Equations  Switch sides  Example: If + =, If + =, then then

80. Symmetric Equality  2 Equations  Switch sides  Example: If + =, If + =, then then

81. Transitive Equality  3 equations  The middle of the first two are equal.  The ends create the third.  Example: If 4 = x and x = 2y, then ??? If 4 = x and x = 2y, then ???

82. Transitive Equality  3 equations  The middle of the first two are equal.  The ends create the third.  Example: If 4 = x and x = 2y, then ??? If 4 = x and x = 2y, then ???

83. Addition Property of Equality  Add Equal things to both sides.  Example: If 5 = x, then 9 = ??? If 5 = x, then 9 = ???

84. Addition Property of Equality  Add Equal things to both sides.  Example: If 5 = x, then 9 = ??? If 5 = x, then 9 = ???

85. Multiplication Property of Equality  Multiply Equal things to both sides.  Example: If 5 = x, then 9 = ??? If 5 = x, then 9 = ???

86. Multiplication Property of Equality  Multiply Equal things to both sides.  Example: If 5 = x, then 9 = ??? If 5 = x, then 9 = ???

87. Zero Product Property  Product is multiply  If 2 numbers multiply to 0, then one of the numbers must be 0.  Example: If (x + )(x - ) = 0, then If (x + )(x - ) = 0, then (x + ) = 0 or (x - ) = 0 (x + ) = 0 or (x - ) = 0 So (x + ) gives x = So (x + ) gives x = And (x – ) gives x = And (x – ) gives x =

88. Zero Product Property  Product is multiply  If 2 numbers multiply to 0, then one of the numbers must be 0.  Example: If (x + )(x - ) = 0, then If (x + )(x - ) = 0, then (x + ) = 0 or (x - ) = 0 (x + ) = 0 or (x - ) = 0 So (x + ) gives x = So (x + ) gives x = And (x – ) gives x = And (x – ) gives x =

90. Properties Examples 2 Block X Template

91. Commutative Property  1 Equation  CO = Change order;  move numbers; “commute”  Example:

92. Associative Property  1 Equation  SO = Same Order.  Change groups or ( )  Example:

93. Distributive Property  1 Equation  Multiply the outside by everything in the inside.  Example: (x -) = x – (x -) = x – (x + -) = x + - (x + -) = x + -

94. Additive Identity  Add ZERO  Identity means stays the same  Example: + 0 = + 0 =

95. Additive Inverse  Inverse means Opposite  Add and Subtract the same number or  Positive and Negative  Adds to ZERO.  Example: + = 0 + = 0

96. Multiplicative Identity  Multiply by 1  Identity means stays the same  Example: * 1 = ??? * 1 = ??? Or 1 * = Or 1 * =

97. Multiplicative Inverse  Inverse means Opposite  Multiply and Divide the same number are opposites  OR Do reciprocal  numbers multiply to 1  Example: * 1/ = 1 * 1/ = 1 Or * / becomes * / Or * / becomes * /

98. Substitution  Replace a letter with a number  Example: 5 + x = y where x = 5 + x = y where x = y = y =

99. Symmetric Equality  2 Equations  Switch sides  Example: If + =, If + =, then then

100. Transitive Equality  3 equations  The middle of the first two are equal.  The ends create the third.  Example: If 4 = x and x = 2y, then ??? If 4 = x and x = 2y, then ???

101. Addition Property of Equality  Add Equal things to both sides.  Example: If 5 = x, then 9 = ??? If 5 = x, then 9 = ???

102. Multiplication Property of Equality  Multiply Equal things to both sides.  Example: If 5 = x, then 9 = ??? If 5 = x, then 9 = ???

103. Zero Product Property  Product is multiply  If 2 numbers multiply to 0, then one of the numbers must be 0.  Example: If (x + )(x - ) = 0, then If (x + )(x - ) = 0, then (x + ) = 0 or (x - ) = 0 (x + ) = 0 or (x - ) = 0 So (x + ) gives x = So (x + ) gives x = And (x – ) gives x = And (x – ) gives x =

105. Properties Examples 2 Block X Template

106. Commutative Property  1 Equation  CO = Change order;  move numbers; “commute”  Example:

107. Associative Property  1 Equation  SO = Same Order.  Change groups or ( )  Example:

108. Distributive Property  1 Equation  Multiply the outside by everything in the inside.  Example: (x -) = x – (x -) = x – (x + -) = x + - (x + -) = x + -

109. Additive Identity  Add ZERO  Identity means stays the same  Example: + 0 = + 0 =

110. Additive Inverse  Inverse means Opposite  Add and Subtract the same number or  Positive and Negative  Adds to ZERO.  Example: + = 0 + = 0

111. Multiplicative Identity  Multiply by 1  Identity means stays the same  Example: * 1 = ??? * 1 = ??? Or 1 * = Or 1 * =

112. Multiplicative Inverse  Inverse means Opposite  Multiply and Divide the same number are opposites  OR Do reciprocal  numbers multiply to 1  Example: * 1/ = 1 * 1/ = 1 Or * / becomes * / Or * / becomes * /

113. Substitution  Replace a letter with a number  Example: 5 + x = y where x = 5 + x = y where x = y = y =

114. Symmetric Equality  2 Equations  Switch sides  Example: If + =, If + =, then then

115. Transitive Equality  3 equations  The middle of the first two are equal.  The ends create the third.  Example: If 4 = x and x = 2y, then ??? If 4 = x and x = 2y, then ???

116. Addition Property of Equality  Add Equal things to both sides.  Example: If 5 = x, then 9 = ??? If 5 = x, then 9 = ???

117. Multiplication Property of Equality  Multiply Equal things to both sides.  Example: If 5 = x, then 9 = ??? If 5 = x, then 9 = ???

118. Zero Product Property  Product is multiply  If 2 numbers multiply to 0, then one of the numbers must be 0.  Example: If (x + )(x - ) = 0, then If (x + )(x - ) = 0, then (x + ) = 0 or (x - ) = 0 (x + ) = 0 or (x - ) = 0 So (x + ) gives x = So (x + ) gives x = And (x – ) gives x = And (x – ) gives x =