Transcript 1.4 Integer Basics and Absolute Value

Integers and Absolute Value
1.4
Text p. 18
This is where numbers become
magical. You will learn new rules
that govern how we evaluate
numbers !!!
Mastery of integer rules is
required for successful
completion of this class.
Concentrate…….Ask Questions….
MEMORIZE integer rules and
operations !!
Naming the numbers we know …
What are Integers?
•
Counting Numbers
are used to count. They are also called natural
numbers. {1, 2, 3, …..}
This set is found inside the set of . . . .
Whole numbers
{0, 1, 2, 3, …}
This set of whole numbers is found inside the set of . . .
Integers.
Integers are WHOLE NUMBERS AND
THEIR OPPOSITES.
{ . . . -4, -3, -2, -1, 0 , 1, 2, 3, …}
THE BIGGER “BARRELS” WILL COME LATER!!
Vocabulary
Integers:
Whole numbers and their opposites
Opposites:
Numbers the same distance from 0 on a number
line, on opposite sides of 0
Absolute value:
Distance from 0 on a number line – a statement of
distance, NEVER negative….
Zero Pair: An integer and its opposite
Important! The literal definition of a negative sign is
“the opposite of.”
Add this to your notes!!!!!!!!!!!!!
We have two main objectives in this lesson.
Each objective has multiple parts.
Learn to represent, graph, and order
integers
1
Learn to find opposites and absolute 2
value of integers…..this will add another
grouping symbol
1
Learn to represent, graph, and order
integers
Representing an integer means to give a
situation that can be described with a
positive or negative value.
For example, walking up 5 steps would be a +5.
Walking back down those steps would be a -5.
Depositing $75 in the bank would be +75. Spending
$30 of the money would be -30.
Describing Integer Values:
+50
Earning $50.00_________
-30
Having a $30 debt ________
-7
7 o below 0 _______
-300
300 ft. below sea level ________
Hiking to an altitude of 4000’ _______
+4000
-30
30 sec. before liftoff _____
+40
Completing a 40 yd. pass _________
Sacking the quarterback 15 yds. behind
-15
the line of scrimmage _____
You can graph positive and negative numbers on a number
line. This means to make a dot on the value.
On a number line, opposites are the same
distance from 0 but on different sides of 0.
Integers are the set of all whole numbers and
their opposites.
Opposites
–5
–4 –3 –2
–1
Negative Integers
0 +1 +2 +3 +4 +5
Positive Integers
0 is neither negative nor positive.
Turn your notes over.
Graph each integer on the number line. Then
use a X to indicate the opposite. You notes say to
use a square…..it doesn’t matter.
2
4, -3, 0, -1, 2
–5
–4
–3 –2
–1
0
+1 +2
+3 +4
+5
The absolute value of an integer is its
distance from 0 on a number line. The
symbol for absolute value is | |.
|–3| = 3
|3| = 3
3 units
3 units
–5
–4
–3 –2
–1
0
+1 +2
+3 +4
+5
Opposites are the same distance from
0. This means they have the same absolute
value. Opposites create a ZERO PAIR.
• Absolute values are never negative.
• Opposite integers have the same
absolute value.
• |0| = 0
Reading in Math
Read |3| as “the absolute value of 3.”
Read |–3| as “the absolute value of negative 3.”
Comparing Integers
•
•
•
•
Any + is greater than any –
Any + is greater than 0
0 is greater than any –
The farther an integer is to the right on a
number line, the greater its value
≤,
≥, =
≥
-2 ____
-4
8 ____
-9
≥
≤
-12 ____
-9
≥
0 _____
-6
|-5| _____4
≥
5 _____
4
* - |-9| _____ | -1|
≤
-9 ____
1
The “opposite”
of |9| is -9
Lesson Quiz
Name a positive or negative number to
represent each situation.
1. A profit of $250 +250
2. 18 degrees below 0 –18
3. 40 sec. before launch? -40
4. What is the opposite of 4? -4
5. What is the opposite of -9? +9
6. |-8| =
8
7. |-3| =
3
Did we…………
1
Learn to represent, graph, and order
integers?
2
Learn to find opposites and absolute
value of integers…..this will add another
grouping symbol?