Transcript Incredible Integers

Integers & Absolute
Value
What is an
integer?
Integers are the set
of all whole numbers
and their opposites.
Okay…but what
does that mean?
Integers
Negative numbers are numbers
to the left or below zero
and are less than zero.
Integers
The numbers –1, -2, 3,… are called negative
integers. The number
negative 3 is written –3.
Integers
Positive numbers are
numbers to the right of
zero and are more than
zero.
Integers
The numbers 1, 2, 3, …
are called positive
integers. The number
positive 4 is written +4 or
4.
Integers
Zero is neither negative
nor positive.
Opposites are two numbers that
are the same distance from zero
Let’s look at some
examples of opposites!
• -4 and +4
• -2 and +2
• -5 and +5
But what about zero?
What is the
opposite of
0?
0
Zero is neither positive or
negative
Integers can also
represent situations
Here are some examples:
• Sarah went up four
steps
• +4
• The temperature is
twelve below zero.
• -12
• The elevation of the
mountain is 52,000
feet
• +52,000
And a few more…
• The football team
lost 8 yards
• -8
• Anne gained 10
pounds
• +10
• Tara spent $20 of
her checking
account.
• -$20
Representing a situation with an
integer: (see notes)
Example: Dry ice is solid carbon dioxide, which
freezes at about 109 degrees below zero
Fahrenheit. Use an integer to represent this
situation.
Step 1: Identify key words:
below and zero
Step 2: Write the integer:
-109
You try:
The lowest elevation in New Orleans, LA, is 8
feet below sea level. Use an integer to
represent this elevation.
-8
More (not on notes)…
• The stock market
showed a gain of 212
points today
• +212
• Death Valley,
California is 282
feet below sea level
• -282
• The elevator went
down two floors.
• -2
Identifying Opposite
Remember opposites are two numbers that are
the same distance from zero.
Example: Write the opposite of 3
So, the opposite of 3 is -3.
You Try:
1. Write the opposite
of -5
• 5
2. Write the opposite
of -100
• 100
3. Write the opposite
of 1,999
• -1,999
4. Write the opposite
of 209
• -209
Now let’s talk
about
Absolute Value
Absolute Value
is…
The distance a number is from
zero on the number line.
So…
• The symbol for absolute value of a
number, n, is | |
• Opposites have the same absolute value.
• **Remember, drop the bars, drop the
sign—that’s your answer every time!!!!
4
Unless…
• The negative sign is OUTSIDE
of the absolute value bars.
= -4
Example:
Find |-4| =
4
Find
|2|=
You Try:
2
4.) Find |-5| +|-3| =
1.) Find |-1| =
1
2.) Find |7|=
7
3.) Find |-9|=
9
8
5.) Find |7| - |-4|=
3
6.) Find |-1| + |-1|=
2
Comparing and Ordering
Integers
You can use a NUMBER LINE to compare integers.
As you move left on a number
line the numbers become
LESS.
Comparing and Ordering
Integers
As you move to the RIGHT on a
number line the numbers
become GREATER.
Example: Compare -6 -4
You Try:
1.) Compare 5
-3
2.) Compare -12
3.) Compare 2
4.) Compare -20
9
4
-1
Example: Ordering Integers
Order the scores on
the scoreboard from
least to greatest:
You can use a number
line to help you.
In order from least to
greatest these scores
are: -400, -200,
100, 300.
Tigers
Bulldogs
Lions
Spartans
-200
300
-400
100
You Try:
1. Order these scores from least to greatest:
-25, 100, -50, and 75
-50, -25, 75, 100
2. In golf, a negative score is called “under par.”
List the golf scores -1, +2, -3, and +4 from least
to greatest.
-3, -1, 2, 4
Time to practice!
Let’s go!!