# Bell Ringer Bell Ringer

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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
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
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.
• -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

• 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.
• 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.
• -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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