Transcript Integers and Absolute Value

Integers and Absolute Value
#37
Vocabulary
• Positive numbers are greater than 0. They may be
written with a positive sign (+), but they are usually
written without it.
• 2
• Negative numbers are less than 0. They are always
written with a negative sign (–).
– Ex:-2
• Integers is a member of a set of whole numbers and
their opposites.
– Ex:…-3,-2,-1,0,1,2,3,4…
• Absolute Value is the distance of a number from zero
on a number line; shown by I I.
– Ex: I-5I=5
You can graph positive and negative numbers on a
number line.
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.
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--> |
–5
–4
–3 –2
–1
0
<--3 units-->|
+1 +2
+3 +4
+5
• Absolute values are never negative.
• Opposite integers have the same absolute value.
• |0| = 0
Identifying Positive and Negative Numbers in the
Real World
Name a positive or negative number to represent
each situation.
A. a jet climbing to an altitude of 20,000 feet
B. taking $15 out of the bank
C. 7 degrees below zero
Example 1
Name a positive or negative number to
represent each situation.
A. 300 feet below sea level
B. a hiker hiking to an altitude of 4,000 feet
C. spending $34
Example 2: Graphing Integers
Graph each integer and its opposite on a
number line.
A. +2
–5
–4
–3 –2
–1
0
+1 +2
+3 +4
+5
B. –5
–5
–4
–3 –2
–1
0
+1 +2
+3 +4
+5
Additional Example 2 Continued
Graph each integer and its opposite on a
number line.
C. +1
–5
–4
–3 –2
–1
0
+1 +2
+3 +4
+5
Additional Example 3: Finding Absolute Value
Use a number line to find the absolute value of
each integer.
A. |–2|
–5
–4
–3 –2
–1
0
+1 +2
+3 +4
+5
Additional Example 3: Finding Absolute Value
Continued
Use a number line to find the absolute value of
each integer.
B. |8|
–1
0
1
2
3
4
5
6
7
8
9
Additional Example 3: Finding Absolute Value
Continued
Use a number line to find the absolute value of
each integer.
A. |6|
–1
0
1
2
3
4
5
6
7
8
9
Additional Example 3: Finding Absolute Value
Continued
Use a number line to find the absolute value of
each integer.
B. |–4|
–5
–4
–3 –2
–1
0
+1 +2
+3 +4
+5