Transcript Integers & Absolute Value

Integers &
Absolute Value
Integers & Absolute Value
Objectives:
To be able to identify, compare, and order positive
and negative integers.
To be able to determine the absolute value of
numbers and expressions.
Why learn this: To use positive and negative
numbers to measure temperature, height (as in
above and below sea level), money, and more.
We use absolute value to determine the distance
from a point, without regard to the direction we
are moving from that point.
Integers & Absolute Value
Vocabulary:
 Integer - all positive whole numbers, their
opposites, and zero
 Opposites - two numbers that are the same
distance from zero on the number line, but in
opposite directions. Ex. 2, -2
 Number Line -
 Absolute Value - a number’s distance from zero
on the number line (always a positive value).
WHERE DO WE
SEE INTEGERS IN
OUR DAILY LIVES
Money!
Temperature!
Elevations (height or depth of places in the world)
Years
Time
Recipes/Cooking
Integers are EVERYWHERE!
Integers less than zero
are negative integers
Integers greater than zero
are positive integers
-6 -5 -4 -3 -2 -1 0 1 2
negatives are
written with
a (-) sign
zero is neither
negative nor
positive
3 4 5 6
positives CAN
be written
with a (+) sign
5
4
3
2
1
0
-1
-2
-3
-4
-5
positives
are written
with + sign
Integers greater than zero
are positive integers
zero is neither
negative nor
positive
negatives
written with
a - sign
Integers less than zero
are negative integers
Writing Integers in Real-Life Situations
Write an integer to describe each situation
Example 1: an increase of 6 inches
+6
Example 2: owe your parents $15
- 15
Example 3: a loss of 7 pounds
-7
Example 4: earned 5 dollars interest
+5
Example 5: a temperature of 9 degrees below zero
-9
Graphing integers on a Number Line
Graph each integer on the number line
Example 1: Graph - 4 on the number line
Example 2: Graph - 8 on the number line
Example 3: Graph + 10 on the number line
Example 4: Graph + 2 on the number line
-10
-8 -6 -4
-2
0
2
4
6
8
10
Graphing integers on a Number Line
Graph each integer on the number line
Example 1: Graph - 4 on the number line
Example 2: Graph - 8 on the number line
Example 3: Graph + 10 on the number line
Example 4: Graph + 2 on the number line
-10
-8 -6 -4
-2
0
2
4
6
8
10
Extension
The number shows the
amounts of money Erica,
Jerry, Bob, and Ray
have in their wallets or
owe one of their parents.
Ray
Erica
Jerry
Who has the most money?
Who has the least money?
Who owes four dollars?
Bob
10
8
6
4
2
0
-2
-4
-6
-8
-10
Quick Practice
Write the opposite of each number.
a) 2
b) 4
c) -3
d) -11
a) -2
b) -4
c) 3
d) 11
Graphing integers on a Number Line
When graphing integers on a number line, make sure to:
• Use at least 3 numbers
• Use one number that is less then the number (to the
left) and one number that is greater (to the right)
• Put a dot to indicate which integer you are graphing
Example: Graph -3 on a number line:
-4
-3
-2
Comparing Integers
Comparing Integers
Replace the □ with <, >, or = to make the sentence true.
Example 1: - 9 □ 8
-9<8
Example 2: 83 □ 84
83 < 84
Example 3: 5 □ - 5
5>-5
Example 4: - 6 □ - 4
-6<-4
Example 5: - 7 □ - 7
-7=-7
Ordering Integers
Order each set of integers from least to greatest.
Example 1: - 162, - 10, - 81, 59 →
- 162, - 81, - 10, 59
Example 2: 9, - 8, 4, - 9 →
- 9, - 8, 4, 9
Example 3: 2, 6, - 2, 0 →
- 2, 0, 2, 6
Example 4: 7, 5, - 1, - 5 →
- 5, - 1, 5, 7
Quick Practice
Which number in the pair is farther away
from zero.
a) 4, -5
a)
-5
b) 2, 5
b) 5
c) -1, -3
c) -3
d) -12, 11
d) -12
Integers & Absolute Value
What is absolute value?
The distance of some number from zero on the
number line
Absolute Value is ALWAYS positive!
What does absolute value look like?
7 units
-8 -7 -6 -5 -4 -3 -2 -1 0 1
7 units
2 3 4 5 6 7 8
Integers & Absolute Value
What is absolute value?
The distance of some number from zero on the
number line (ALWAYS Positive)
What does absolute value look like?
the absolute
value of 7
|7|=
7
the absolute
value of – 7
|–7 |=
7
Integers & Absolute Value
Absolute Value
Evaluate the expression.
Example 1: | 3 |
3
Example 2: | - 68 |
68
Example 3: | 6 | + | - 9 |
6 + 9
= 15
Example 4: | - 8 | - | - 9 |
8 – 9
= -1
Quick Practice
Find each absolute value.
a) l-21l
a) 21
b)l14l
b)14
c) l-1l
c) 1
d)l21l
d)21
Integers & Absolute Value
Extension
Evaluate 6 + | n | if n = - 16.
6 + | n | = 6 + | - 16 |
= 6 + 16
= 22
Integers & Absolute Value
Absolute Value in real life!
An eyeglass prescription is given as a positive or
negative number. A prescription for a person who is
farsighted is positive. A prescription for a person
who is nearsighted is negative. The greater absolute
value, the stronger the prescription. Which
prescription is stronger, -3 or 2?
Step 1: Think about the problem. What information
was given and what am I trying to figure out?
Integers & Absolute Value
Absolute Value in real life!
An eyeglass prescription is given as a positive or
negative number. A prescription for a person who is
farsighted (can’t see near) is positive. A prescription
for a person who is nearsighted is negative. The
greater absolute value, the stronger the prescription.
Which prescription is stronger, -3 or 2?
Step 2: Determine the answer
What is the absolute value of each prescription?
| -3 |
|2|
3
2
Which prescription is greater?
-3!
Absolute Value in real life!
A seagull is flying at an altitude of 107 feet and a
shark is swimming at a depth of 112 feet relative to
sea level. Which animal is farther from sea level?
107 feet
Sea level (0 feet)
-112 feet
l-4l
>
l-3l
l12l
= l-12l
l-20l
>
l10l
l-14l
<
l-15l
l-7l >
6
-5
< l-4l
-15
<
5
19
= l-19l