Download 2.1 Lesson

Lesson
Opener
2-1 The Real Number Line
• Real Numbers = the set of all positive and
negative numbers and zero
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–
–
–
The point labeled zero is the ORIGIN
Negative numbers = the points to the left of zero
Positive numbers = the points to the right of zero
Real number line:
•
-5 -4 -3 -2 -1 0 1 2 3 4 5 6
• Plotting points = putting a dot on the number
line where the given number would be
• Opposites = two points that are the same
distance from the origin but on opposite sides
– Ex: Opposite of 3 = -3
Opposite of –8 = 8
• Absolute value = the distance between the
origin and the point representing the real
number
– Symbol = a
– Ex:
8  8
8 8
-a  a
• Counterexample = you come up with one
example to prove that a statement is false
Practice
Graph the numbers on a number line. Then
write two inequalities that compare the two
numbers.
• 1.) 3, -5, 0
• 2.) -0.1, -1.1, -1
• 3.)  1 ,  3 , 1
2
4 4
Practice 2
Find the opposites of the number
1.) 3.8
2.) -16
3.) 0
4.) -2.04
5.) 3 1
6.)  2
6
3
Evaluate the expression by finding absolute value
1
1.) 12
2.) 4.1
3.) 5
4.) -103
5.) 7.8
6.) -6.1  6.01
When
will I
use this?
Summary
• The set of numbers consisting of the positive numbers,
the negative numbers, and zero are called
___________ ___________.
• The point labeled zero on the number line is called the
_______________.
• You can graph or plot points on a ___________
______________.
• The distance between the origin and the point
representing the real number is called the___________
___________.
• Two points that are the same distance from the origin
but on different sides are called___________.
Check Yourself
• Pg. 67-70 # 20-52 eoe, 54-60, 88-102 e
• # 20-26: graph numbers on a number line
• #28-32: write the number in increasing
order
• #34-48: find the opposite or absolute value
of each number
• #54-56: write counterexamples if the
statement is false
• #88-102: mixed review