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					Properties
                     Properties
   Commutative Property         Substitution
   Associative Property         Symmetric Equality
   Distributive Property        Transitive Equality
   Additive Identity            Addition Property of
   Additive Inverse              Equality
   Multiplicative Identity      Multiplication Property
   Multiplicative Inverse        of Equality
                                 Zero Product Property
         Commutative Property
a    +b=b+a

 CO   is Change order; move; “commute”

 Example:
     3 + x = ???
           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 = ???
            Distributive Property
 a(b    + c) = ab + ac OR (b + c)a = ba + ca

a    is multiplied by (distributed) everything
    inside the parentheses.

      the Rainbow (draw arrows on top).
 Taste
 Example:
       3(x + 2) = ???
               Additive Identity
a    +0=a

 Adds  ZERO
 stays the same
     keeps its “identity”


 Example:
     3 + 0 = ???
              Additive Inverse
a    + (-a) = 0

 Opposite    (inverse) numbers add to 0

 Example:
     4 + ??? = 0
          Multiplicative Identity
a    *1=a

 Multiplyby 1
 stays the same
     keeps its “identity”


 Example:
     5 * 1 = ???
           Multiplicative Inverse

  1                2 x 3 =1
 a  1
   a •              3   2

 Opposite  (inverse) numbers multiply to 1
 Opposite of multiply is divide.
 Also called Reciprocals.
 Example:
       6 * ??? = 1
                  Substitution
 If   a + b = c and b = 2, then a + 2 = c

 Substitute    given information into equation.

 Example:
      5 + x = y where x = 4
             Symmetric Equality
 If   a = b, then b = a

 Switch     sides

 Example:
      If 6 = x, then ???
             Transitive Equality
 If   a = b and b = c, then a = c.

 “Greatcheese comes from happy cows.
  Happy cows come from California.”
      Therefore great cheese comes from
       California.

 Example:
      If 4 = x and x = 2y, then ???
       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 = ???
 Multiplication Property of Equality
 If   a = b, then 2a = 2b.

 Multiply    both sides by the same thing.

 Example:
      If 4 = x, then 12 = ???
          Zero Product Property
 If   ab = 0, then a = 0 or b = 0.

 Ifthe product of 2 numbers is 0, then one
  of the numbers must be 0 itself.

 Example:
      If 5x = 0, then ???
Properties
Examples 2
  Block 1
    Shown Bl 5 7
        Commutative Property
1    Equation

 CO = Change order;
 move numbers; “commute”


 Example:
     4*5*7=7*5*4
           Associative Property
1    Equation

 SO = Same Order.
 Change groups or ( )


 Example:
     (1 * 2) * 3 = 1 * (2 * 3)
           Distributive Property
1    Equation

 Multiply   the outside by everything in the
 inside.

 Example:
     6(x - 5) = 6x - 30
             Additive Identity
 Add ZERO
 Identity means stays the same


 Example:
     10 + 0 = 10
             Additive Inverse
 Inverse means Opposite
 Add and Subtract the same number or
 Positive and Negative
 Adds to ZERO.


 Example:
     -57 + 57 = 0
          Multiplicative Identity
 Multiply by 1
 Identity means stays the same


 Example:
     2*1=2
     Or
     1 * 15 = 15
         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
     Or * 2/5 becomes * 5/2
                 Substitution
 Replace    a letter with a number

 Example:
     5 + x = y where x = 4
     y=9
           Symmetric Equality
2    Equations

 Switch   sides

 Example:
     If 5 + 6 = 11,
     then 11 = 5 + 6
            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
  Addition Property of Equality
 Add   Equal things to both sides.

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

 Example:
     If   10 = x
     Then 20 = 2x (multiply by 2)
         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
     (x + 8) = 0 or (x - 9) = 0
     So (x + 8) gives x = -8
     And (x – 9) gives x = 9
Properties
Examples 2
  Block 5
    Shown Bl 1 7
         Commutative Property
1    Equation

 CO = Change order;
 move numbers; “commute”


 Example:
     3 * 5 * 4 * 8 = 8 * 4 * 5 *3
           Associative Property
1    Equation

 SO = Same Order.
 Change groups or ( )


 Example:
     ( 6 * 3) * 5 = 6 * (3 * 5)
           Distributive Property
1    Equation

 Multiply   the outside by everything in the
 inside.

 Example:
     3(x - 8) = 3x - 24
             Additive Identity
 Add  ZERO
 Identity means stays the same


 Example:
     5+0=5
             Additive Inverse
 Inverse means Opposite
 Add and Subtract the same number or
 Positive and Negative
 Adds to ZERO.


 Example:
     -12 + 12 = 0
          Multiplicative Identity
 Multiply by 1
 Identity means stays the same


 Example:
     72 * 1 = 72
     Or
     1 * 72 = 72
         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
     Or
     * 3/4 becomes * 4/3
                 Substitution
 Replace    a letter with a number

 Example:
     5 + x = y where x = 8
     y = 13
           Symmetric Equality
2    Equations

 Switch   sides

 Example:
     If 2 + 3 = 5,
     then 5 = 2 + 3
            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
  Addition Property of Equality
 Add   Equal things to both sides.

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

 Example:
     If     7 =x
     Then   28 = 4x (Multiply both sides by 4.)
         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
     Answer: (x + 6) = 0 or (x - 4) = 0
     So (x + 6) gives x = -6
     And (x – 4) gives x = 4
Properties
Examples 2
  Block 7
    Shown Bl 1 5
        Commutative Property
1    Equation

 CO = Change order;
 move numbers; “commute”


 Example:
     3*2*1=1*2*3
          Associative Property
1    Equation

 SO = Same Order.
 Change groups or ( )


 Example:
     ( 3 * 6 ) * 15 = 3 * ( 6 * 15)
           Distributive Property
1    Equation

 Multiply   the outside by everything in the
 inside.

 Example:
     4 (x - 7) = 4x - 28
             Additive Identity
 Add ZERO
 Identity means stays the same


 Example:
     21 + 0 = 21
             Additive Inverse
 Inverse means Opposite
 Add and Subtract the same number or
 Positive and Negative
 Adds to ZERO.


 Example:
     +8 - 8 = 0
        Multiplicative Identity
 Multiply by 1
 Identity means stays the same


 Example:
     7*1=7
     Or
     1*8=8
         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
     Or * 7/8 becomes * 8/7
                 Substitution
 Replace    a letter with a number

 Example:
     5 + x = y where x = 7
     y = 12
           Symmetric Equality
2    Equations

 Switch   sides

 Example:
     If 3 + 4 = 7,
     then 7 = 3 + 4
            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
  Addition Property of Equality
 Add   Equal things to both sides.

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

 Example:
     If    3= x
     then 21 = 7x (Multiply both sides by 7)
         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
     (x + 2) = 0 or (x - 7) = 0
     So (x + 2) gives x = -2
     And (x – 7) gives x = 7
  Properties
  Examples
Block 6/7 2011
        Commutative Property
1    Equation

 CO = Change order;
 move numbers; “commute”


 Example:
  
        Commutative Property
1    Equation

 CO = Change order;
 move numbers; “commute”


 Example:
  
        Associative Property
1   Equation

 SO = Same Order.
 Change groups or ( )


 Example:
        Associative Property
1   Equation

 SO = Same Order.
 Change groups or ( )


 Example:
           Distributive Property
1    Equation

 Multiply   the outside by everything in the
 inside.

 Example:
      (x -) = x –
     (x + -) = x + -
           Distributive Property
1    Equation

 Multiply   the outside by everything in the
 inside.

 Example:
      (x -) = x –
     (x + -) = x + -
             Additive Identity
 Add ZERO
 Identity means stays the same


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


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


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


 Example:
     + =0
          Multiplicative Identity
 Multiply by 1
 Identity means stays the same


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


 Example:
     * 1 = ???
     Or 1 * =
         Multiplicative Inverse
 Inverse  means Opposite
 Multiply and Divide the same number are
  opposites
 OR Do reciprocal
 numbers multiply to 1
 Example:
     * 1/ = 1
     Or * / becomes * /
         Multiplicative Inverse
 Inverse  means Opposite
 Multiply and Divide the same number are
  opposites
 OR Do reciprocal
 numbers multiply to 1
 Example:
     * 1/ = 1
     Or * / becomes * /
                 Substitution
 Replace    a letter with a number

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

 Example:
     5 + x = y where x =
     y=
           Symmetric Equality
2    Equations

 Switch   sides

 Example:
     If   +=,
     then
           Symmetric Equality
2    Equations

 Switch   sides

 Example:
     If   +=,
     then
            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 ???
            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 ???
  Addition Property of Equality
 Add   Equal things to both sides.

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

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

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

 Example:
     If 5 = x, then 9 = ???
         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
     (x + ) = 0 or (x - ) = 0
     So (x + ) gives x =
     And (x – ) gives x =
         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
     (x + ) = 0 or (x - ) = 0
     So (x + ) gives x =
     And (x – ) gives x =
   Properties
   Examples 2
Block X Template
        Commutative Property
1    Equation

 CO = Change order;
 move numbers; “commute”


 Example:
  
        Associative Property
1   Equation

 SO = Same Order.
 Change groups or ( )


 Example:
           Distributive Property
1    Equation

 Multiply   the outside by everything in the
 inside.

 Example:
      (x -) = x –
     (x + -) = x + -
             Additive Identity
 Add ZERO
 Identity means stays the same


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


 Example:
     + =0
          Multiplicative Identity
 Multiply by 1
 Identity means stays the same


 Example:
     * 1 = ???
     Or 1 * =
         Multiplicative Inverse
 Inverse  means Opposite
 Multiply and Divide the same number are
  opposites
 OR Do reciprocal
 numbers multiply to 1
 Example:
     * 1/ = 1
     Or * / becomes * /
                 Substitution
 Replace    a letter with a number

 Example:
     5 + x = y where x =
     y=
           Symmetric Equality
2    Equations

 Switch   sides

 Example:
     If   +=,
     then
            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 ???
  Addition Property of Equality
 Add   Equal things to both sides.

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

 Example:
     If 5 = x, then 9 = ???
         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
     (x + ) = 0 or (x - ) = 0
     So (x + ) gives x =
     And (x – ) gives x =
   Properties
   Examples 2
Block X Template
        Commutative Property
1    Equation

 CO = Change order;
 move numbers; “commute”


 Example:
  
        Associative Property
1   Equation

 SO = Same Order.
 Change groups or ( )


 Example:
           Distributive Property
1    Equation

 Multiply   the outside by everything in the
 inside.

 Example:
      (x -) = x –
     (x + -) = x + -
             Additive Identity
 Add ZERO
 Identity means stays the same


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


 Example:
     + =0
          Multiplicative Identity
 Multiply by 1
 Identity means stays the same


 Example:
     * 1 = ???
     Or 1 * =
         Multiplicative Inverse
 Inverse  means Opposite
 Multiply and Divide the same number are
  opposites
 OR Do reciprocal
 numbers multiply to 1
 Example:
     * 1/ = 1
     Or * / becomes * /
                 Substitution
 Replace    a letter with a number

 Example:
     5 + x = y where x =
     y=
           Symmetric Equality
2    Equations

 Switch   sides

 Example:
     If   +=,
     then
            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 ???
  Addition Property of Equality
 Add   Equal things to both sides.

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

 Example:
     If 5 = x, then 9 = ???
         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
     (x + ) = 0 or (x - ) = 0
     So (x + ) gives x =
     And (x – ) gives x =

				
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posted:8/5/2012
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