Multiplying and Dividing
Integers
We are learning to…multiply and divide
integers by looking for patterns.
Tuesday, March 22, 2016
Multiplication of Integers
-8
Evaluate: -2 + -2 + -2 + -2 = ________
Multiplication
Repeated addition is the same thing as:__________________
4(-2)
...so -2 + -2 + -2 + -2 can be written:________
-12
Evaluate: -4 + -4 + -4 = ______________
Multiplication
Repeated addition is the same thing as:__________________
.
3(-4)
..so -4 + -4 + -4 can be written:________
Multiplication of Integers
-35
Evaluate: -7 + -7 + -7 + -7 + -7 = ______________
5(-7)
...Rewrite as a multiplication problem:_________
-24
Evaluate: -12 + -12 = ______________
2(-12)
...Rewrite as a multiplication problem:_________
-5
Evaluate: -1 + -1 + -1 + -1 + -1 = ______________
5(-1)
...Rewrite as a multiplication problem:_________
Multiplication of Integers
I know that:
(positive number) × (negative number) =
Negative Number
_______________________________________.
Commutative
The ______________________________
property of
multiplication allows me to multiply in any order.
So I also know that (negative number) × (positive number) =
Negative Number
_______________________________________.
Evaluate the expressions below. When your entire group
is finished share your solutions.
Multiplication of Integers
Negative
Negative
Negative × Positive = _______________
and Positive × Negative = _______________
Negative
If the signs in a multiplication problem are different the solution is:_______________
I know that a:
Positive
positive × positive = ______________
Negative
(+)(–) = ______________
Now follow the pattern:
Negative
(–)(+) = ______________
Positive
(+)(+) = ______________
So…
I know that a:
Positive
(–)(–) = ______________
Positive
negative × negative = _________________________
Positive
If the signs in a multiplication problem are the same the solution is:_______________
7(-8) = _____
A.
B.
C.
D.
56
-56
-1
-15
-6(-7) = _____
A.
B.
C.
D.
49
-42
-13
42
-9(3) = _____
A.
B.
C.
D.
27
-6
-36
-27
Which of the following
statements is NOT true?
A.
B.
C.
D.
A negative multiplied by a
negative is a positive product.
A positive multiplied by a
negative is a negative product.
A negative multiplied by a
negative is a negative product.
A negative multiplied by a
positive is a negative product.
Division of Integers
a
c  ______
b  _______
a
The Division Algorithm: If b  c then ______
Example 1: Negative divided by a Positive:
40
40
-8
-8  5  40
 ______
so… ______
 ? or…
5
5
Negative
Negative divided by a positive will always result in a:______________
Division of Integers
a
c  ______
b  _______
a
The Division Algorithm: If b  c then ______
Example 2: Positive divided by a Negative:
63
?
9
or…
63
-7
 ______
9
-7  (9)  63
so… ______
Negative
Positive divided by a negative will always result in a:______________
Division of Integers
a
c  ______
b  _______
a
The Division Algorithm: If b  c then ______
Example 2: Negative divided by a Negative:
42
?
7
42
6
6  (7)  42
so… ______
or… 7  ______
Positive
Negative divided by a negative will always result in a:______________
Division of Integers
Wait a minute…these look familiar!
Multiplication
These are the same rules as:____________________________
Negative
If the signs in a division problem are different the solution is:______________
Positive
If the signs in a division problem are the same the solution is:_____________
Evaluating Integer Expressions
Tuesday, March 22, 2016
48
Evaluate: 6
A.
B.
C.
D.
8
-8
7
-9
Evaluate:
A.
B.
C.
D.
21
-20
-22
-21
105
5
Evaluate:
A.
B.
C.
D.
-7
7
8
-6
77
11
Evaluating Integer Expression


Today you will use the Order of Operations
and your knowledge about integer operations
to simplify some complex expressions.
Order of Operations:




Parentheses
Exponents
Multiplication and Division
Addition and Subtraction
Evaluate: 2  4  6  1   3  5
A.
B.
C.
D.
-14
-30
20
-8
Evaluate: 7(3)  2  5  8
A.
B.
C.
D.
315
-105
3
-76
2