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					Bell Ringer          5. Evaluate g – h
     Subtract        if g = -2 and h = -7

1.    2 – 15         6.   In Mongolia, the
2.    -13 - 8             temperature can dip
3.    Find 12 – (-6)      down to -45oC in
4.    Find 21 – (-8)      January. The
                          temperature in July
                          may reach 40oC. What
                          is the temperature
                          range in Mongolia?
3-6 Multiplying Integers

• For the first activity we are going to need
  the following items:

  • Some type of counter Counter can be anything
  • 1 Paper towel         with different colors:
                              M & M’s, Skittles,
                             Reese’s Pieces, etc.
  Mini Lab
• Counters can be used to 1. 4(-2)
  multiply positive and
  negative integers. Here’s               Write a rule for finding
                              2. 3(-2)
  how we are going to                     the sign of the product
                                             of a positive and
  multiply integers.                         negative integer.
   • Pick a counter color for 3. 4(-3)
     positive and negative
     integers
                               4. 1(-7)
   • The first number is the
     amount of sets you will
     have                      5. 5(-2)

     LET’S TRY IT OUT!!!
Using a Number line

   Remember that
  multiplication is the
    same as repeated            -2   -2     -2    -2
      addition. The
     multiplication     -9   -8 -7 -6 -5 -4 -3 -2 -1 0   1
   expression 4(-2) in
  the Mini Lab means
  that -2 is used as an
   addend four times.
  Multiplying Integers with Different
                 Signs
• The product of two integers with
  different signs is negative

• Examples:
              6(-4) = -24
              -5(7) = -35
Multiplying Integers with Different
               Signs
• 3(-5)
  3(-5) = -15
          The integers have different signs. The product is negative.


• -6(8)
  -6(8) = -48
          The integers have different signs. The product is negative.
Multiplying Integers with Same Signs


 • The product of two integers with
   the same signs is positive

 • Examples:
   • 2(6) = 12
   • -10(-6) = 60
Multiplying Integers with Same Signs

 • -11(-9)
                        The integers have same signs. The product is positive.
   -11(-9) = 99

 • (-4)2
   (-4)2 = (-4)(-4) There are two factors of -4.
         = 16     The product is positive.
Your Turn
• -12(-4)



• (-5)2



• (-2)3
Simplify and Evaluate Expressions

• Simplify -2(3x)
  -2(3x) = (-2 * 3)x           Associative Property of Multiplication
        = -6x                  Simplify


• Evaluate pqr if p = -3, q = 4, and r = -1
  pqr = (-3)(4)(-1) Replace p with -3, q with 4, and r with -1
     = (-12)(-1)     Multiply -3 and 4

     =12             Multiply -12 and -1
Your Turn

• Simplify -5(2y)



• Evaluate xyz if x = -7, y = -4, and z = 2
3-7 Dividing Integers

• For the first activity we are going to need
  the following items:

  • Some type of counter Counter can be anything
  • 1 Paper towel         with different colors:
                              M & M’s, Skittles,
                             Reese’s Pieces, etc.
     Mini Lab
• We are going to use the counters
  similar to how we used them when             Your Turn
  multiplying integers. This time we are
  going to use the steps to find -10 .
                                5
                                           •   -6
• Place 10 negative counters on your           2
  towel
• Separate the counters into 5 equal
  groups                                   •   -12
• There are 2 negative counters in each         3
  group. So, -10 = -2.
               5
         Division and Multiplication
         Relationship
              Division of integers is related to multiplication.
                 When finding the quotient of two integers,
               you can use a related multiplication sentence.

                                       -12
                     2(-6) = -12           = -6
 The factor is in                       2
                                                  … is the quotient in
the multiplication   4(-5) = -20       -20            the division
   sentence…                               = -5
                                        4               sentence
 Division and Multiplication
 Relationship
Since multiplication and division sentences are
related, you can use them to find the quotient of
          integers with different signs.
                                  different signs

                       -72
      8(-9) = -72          = -9
                        8
      -8(-9) = 72       72
                           = -9
                        -8

                                  different signs
 Dividing Integers with Different Signs


• The quotient of two integers with
  different signs is negative

• Examples: 33 = -3       -64= -8
            -11            8
Dividing Integers with Different Signs


 • 80                                    • -55
   -10 The integers have different signs. 11      The integers have different signs.



     80 = -8                              -55
                                              = -5
    -10 The quotient is negative.          11    The quotient is negative.
Your Turn
 • 20
   -4

 • -81
    9

 • -45
    9
 Dividing Integers with Same Signs


• The quotient of two integers with
  the same signs is positive

• Examples: 15 = 3       -21 = 7
            5             -3
  Dividing Integers with Same Signs

• -14
           The integers have same signs.
   -7
  -14
   -7 =2   The product is positive.
 Your Turn
• -24
   -4

• -9
  -3

• -28
   -7
Ticket out Door


           Page 571
       Lesson 3-6 & 3-7
   #2-28 even and #2-32 even

				
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