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Lesson 6.1 Notes: Comparing and Ordering Integers
Warm-Up:
We will be studying positive and negative numbers in this chapter. Answer these questions to see
what you know.
1) If the temperature outside was negative, what would that tell you about the weather?
2) If the temperature outside was positive, what would that tell you about the weather?
3) If your bank account had a positive amount in it, what would that mean?
4) If your bank account had a negative amount in it, what would that mean?
5) List any words that you can think of that might tell you if a number was positive or negative:
Positive Words
Negative Words
Stop___________________________________________
VOCABULARY:
Integers
Negative integers
Positive integers
Opposite
Absolute Value
Increase
Decrease
Deposit
Withdrawal
Integers and Their Opposites
Zero
Negative integer Positive integer
Two numbers are opposites if they are the same distance from zero on a number line but are on
opposite sides of zero.
Examples:
EXAMPLE 1 : Writing integers to represent real life situations
Temperatures The temperature increased 12 degrees between 7 A.M. and 7 P.M.
The temperature decreased 14 degrees between 7 P.M. and 7 A.M. You can use integers to represent
the increase and decrease in the temperature:
12 degree increase: ____________
14 degree decrease: ____________
NOW YOU TRY IT!
1) Write the opposite of each of the following integers:
-17
_____
41
_____
3
_____
-215
_____
2) Write each of the following as an integer:
a) A decrease of 20 degrees
_____
b) A deposit of $5 to your account
_____
c) A withdrawal of $2 to your account
_____
d) An increase of 3 degrees to the temperature _____
EXAMPLE 2: Comparing Integers Using a Number Line
As you move RIGHT on the number line, numbers get LARGER or INCREASES.
As you move LEFT on the number line, numbers get SMALLER or DECREASES.
Let’s draw an example of this:
a) Compare –1 and –4:
Step 1: Graph -1 and -4 on the number line
Draw a number line; number the intervals; put a point on the numbers you are graphing.
Step 2: See which number is to the right and which is to the left.
Answer: -1 ______-4
b) Compare –19 and -9:
Answer:
-19 ______-9
NOW YOU TRY IT! Graph and then complete the statement using < or >
3)
3 _____ –5
4) –7 ____ 2
5) –36_____ –20
EXAMPLE 3: Ordering Integers Using a Number Line
Golf: The scores below are based on par for a 36 hole golf course.
Golfer
Score
Patrick
-3
Steven
-6
Joe
-2
Dan
1
Charles
2
Brad
-4
Vincent
-5
Randy
3
Graph each integer (score) on the number line (be sure to label it first!).
1. List the integers (scores) in order from least to greatest.
2. Which golfer has the highest score?
3. Which golfer has the lowest score?
4. Which golfer is in the lead? (hint: the goal in golf is to have a low score)
EXAMPLE 4 - Finding Absolute Value
Animals 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?
Solution
Seagull: | 107 | =
The absolute value
of a number n is
written as | n |.
Try:
1. | –6 |
2. | 5 |
3. |-105|
Shark: | –112 | =