Integer Operations and Integer Operations and Absolute ValueAbsolute Value
Lesson 2Lesson 2
WarmupComplete the multiplication table.
0 1 2 3 4 5-1-2-3-4-5-6 6
Number Line
•Integers are positive & negative numbers.
•Is 0 positive or negative?
Neither!
Ordering Integers.
0 1 2 3 4 5-1-2-3-4-5-6 6
least greatest
Put the following numbers in order from least to greatest.Ex. 5, -2, -4, 3, 0, -1
-4…-2…-1…0…3…5
On your own…Order from least to greatest1. 10, 8, -5, 0, -2.5, -4, 92. -6.2, -7, 5.4, 12, 1
Order from greatest to least.1. 5, -3, 4, -4, 2, -22. 10, 8, -5, 0, -2.5, -4, 9
-5, -4, -2.5, 0, 8, 9, 10
10, 9, 8, 0, -2.5, -4, -5
-7, -6.2, 1, 5.4, 12
5, 4, 2, -2, -3, -4
They look like equations but are separated with these symbols.
reater than
ess than
reater than or equal to
ess than or equal to
Use <, >, = to complete the
problem.
5 4
>Hold up 1 for > and 2 for <.
Use <, >, = to complete the
problem.
-2 -3
>Hold up 1 for > and 2 for <.
Use <, >, = to complete the
problem.
0 -1
>Hold up 1 for > and 2 for <.
True or False?-6 < -2
0 42-6 -4 -2 6
True
Hold up 1 for true and 2 for false.
True or False?-5 < 7
0 42-6 -4 -2 6
True
Hold up 1 for true and 2 for false.
True or False?6 < 0
0 42-6 -4 -2 6
False
Hold up 1 for true and 2 for false.
True or False?-6 > 5
0 42-6 -4 -2 6
False
Hold up 1 for true and 2 for false.
Absolute Value: The number of units a number is from zero on the number line. (Always Positive)
0 42-6 -4 -2 6
|-4| = 4
Abso ute Va ue
Is written using these brackets.
Not to be confused with (parenthesis)
Absolute Value
|6| = 6 and |-6| = 6
Greater than or less than
Using the number line to determine which sign would make this true.
|-4| |2|0 1 2 3 4 5-1-2-3-4-5-6 6
>
-|5| |-2|<
5- 2
Greater than or less than
On your own…1.|-3| ___ |-2|
2.|-8| ___ |-4|
3.|-1| ___ |1|
4.-|-4| ___ |-8|
5.-|-3| ___ -|-2|
6.-|-4| ___ |0|
>
>
=
<
<
<
|5| + |-2|
5 2+
7
|5| - |-2|
5 2-
3
Integer Addition
Adding Two Positive Integers Add the absolute values and keep the sign. The sum is positive.
Adding Two Negative Integers Add the absolute values and keep the sign. The sum is negative.
Adding a Positive Integer and a Negative Integer
Add the absolute values and keep the sign from the greater absolute value. The sum is the same sign as the number with the greatest absolute value.
Adding Integer Video Adding Integers Interactive
Integer Subtraction
Subtraction is like adding the opposite.
Rewrite subtraction as addition, changing the subtraction sign and write the additive inverse of the subtrahend (second value in problem).
8 – 5 = 8 + (-5) =
4 – (-3) = 4 + (___) =
-6 – 2 = ___ + (___) =
-3 – (-4) = ____ + (____) =
Subtracting Integer Video
Subtracting Integer Interactive (counters)Subtracting Integer Interactive (number line)
Addition/Subtraction
1) 13 + (-8) =
3) 17 – (-3) =
4) 5 + (-10) + (-11) =
5) -3 – 5 + (-7) – (-4) =
2) (-3) + (-12) =
+
+
-
-
-
5
15
16
20
11
813
13 8
105
11
5 21
34
5
4 15
7
- -+Multiplying and Dividing
Integers VideoMultiplying and Dividing Integers Game
What rules can we create based on the last 6
problems?
Integer Multiplication
Multiplying Two Positive Integers
The product is positive.
Multiplying Two Negative Integers
The product is positive.
Multiplying a Positive Integer and a Negative Integer
The product is negative.
- -
+Ex. 1) (-5)(3)
XX
= -15
- -
+Ex. 2) (-12)(-3)= 36
- -
+Ex. 3) (9)(-9)= -81
- -
+Ex. 1) (-7)(3)
= -21
- -
+Ex. 2) (-9)(-8) = 72
- -
+Ex. 3) (5)(-6)= -30
Multiplying Three or More Integers
Count the number of negative signs.
If there is an odd number, the product is negative.
If it is an even number of negative signs, your answer is positive.
25243
Multiplying Three or More Integers
Example 5: Find the producta. 2( -3)(4)b. 3(-2)(-5)c. (-3)(-4)(-2)(-1)d. (-1)(-1)(-1)(-1)(-1) o
Integer Division
Dividing Two Positive Integers The quotient is positive.
Dividing Two Negative Integers The quotient is positive.
Dividing a Positive Integer and a Negative Integer
The quotient is negative.
- -
+X
X
- -
+
- -
+
= -32
= 6
= -97
63)4
848
)3
3216
)2
84)1
= -24
Multiply/Divide
1) 4(-5) =
3) (-5)(-3)(2) =
4) –(-2)(-4)(6) =
5) (-3)(-2)(3)
2) (-3)(-8) =
-
+
-
+
+
20
24
48
30
189
=9
= 2
You Try
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