Transcript Integers and Absolute Values

Objective: Graph integers on a number line and find
absolute value.
Example 1.
Study the pattern of the following subtraction sentences.
5–1=4
5–2=3
5–3=2
5–4=1
5–5=0
5–6=?
Example 1.
Study the pattern of the following subtraction sentences.
5–1=4
5–2=3
5–3=2
5–4=1
5–5=0
5 – 6 = -1
This is an example of a negative number. A
negative number is less than zero.
Integers
Integers
Numbers to the left of zero
are less than zero.
Integers
Numbers to the left of zero
are less than zero.
Numbers to the right of
zero are more than zero.
Integers
Numbers to the left of zero
are less than zero.
The numbers –1, -2, -3,…
are called negative
integers. The number
negative 3 is written –3.
Numbers to the right of
zero are more than zero.
Integers
Numbers to the left of zero
are less than zero.
The numbers –1, -2, -3,…
are called negative
integers. The number
negative 3 is written –3.
Numbers to the right of
zero are more than zero.
The numbers 1, 2, 3, … are
called positive integers.
The number positive 4 is
written +4 or 4.
Integers
Numbers to the right of
zero are more than zero.
Numbers to the left of zero
are less than zero.
The numbers –1, -2, -3,…
are called negative
integers. The number
negative 3 is written –3.
Zero is neither negative nor
positive.
The numbers 1, 2, 3, … are
called positive integers.
The number positive 4 is
written +4 or 4.
Example 2a: Name the coordinates of D, E, and B
A
E
-6 -5 -4 -3 -2 -1
C
0
1
B
2
3
D
4
5
6
Example 2b: Graph points F, U, and N on a number line if F has
coordinate 1, U has coordinate –3, and N has coordinate 4.
-6 -5 -4 -3 -2 -1
0
1
2
3
4
5
6
Absolute Value
Absolute Value
In words: The absolute value of a number is the distance the
number is from the zero point on the number line.
In symbols: |4| = 4 and |-4| = 4
Example 3: Simplify
a. |9| + |-9|
Example 3: Simplify
a. |9| + |-9|
|9| + |-9| = 9 + 9
Example 3: Simplify
a. |9| + |-9||
|9| + |-9| = 9 + 9
= 18
Example 3: Simplify
a. |9| + |-9||
|9| + |-9| = 9 + 9
= 18
b. |13| - |-2|
Example 3: Simplify
a. |9| + |-9||
|9| + |-9| = 9 + 9
= 18
b. |13| - |-2|
|13| - |-2| = 13 – 2
Example 3: Simplify
a. |9| + |-9||
|9| + |-9| = 9 + 9
= 18
b. |13| - |-2|
|13| - |-2| = 13 – 2
= 11
Example 4: Evaluate the expression
|x| - 7 if x = - 13
Example 4: Evaluate the expression
|x| - 7 if x = - 13
|x| - 7 = |-13| - 7
Example 4: Evaluate the expression
|x| - 7 if x = - 13
|x| - 7 = |-13| - 7
= 13 – 7
Example 4: Evaluate the expression
|x| - 7 if x = - 13
|x| - 7 = |-13| - 7
= 13 – 7
=6
Assignment: Page 12 (1-31)