Integers and Absolute Value

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This is where numbers becomemagical. You will learn new rulesthat govern how we evaluatenumbers !!!

Mastery of integer rules is required for successful completion of this class.Concentrate…….Ask Questions….MEMORIZE integer rules and operations !!

Naming the numbers we know … What are Integers?

• Counting Numbers are used to count. They are also called natural numbers. {1, 2, 3, …..}

This set is found inside the set of . . . .

Whole numbers {0, 1, 2, 3, …}

This set of whole numbers is found inside the set of . . .

Integers. Integers are WHOLE NUMBERS AND THEIR OPPOSITES.

{ . . . -4, -3, -2, -1, 0 , 1, 2, 3, …}

THE BIGGER “BARRELS” WILL COME LATER!!

VocabularyIntegers:Whole numbers and their oppositesOpposites:Numbers the same distance from 0 on a number line,

on opposite sides of 0Absolute value:Distance from 0 on a number line – a statement of

distance, NEVER negative….Zero Pair: An integer and its opposite

Important! The literal definition of a negative sign is “the opposite of.”

Add this to your notes!!!!!!!!!!!!!

Learn to represent, graph, and order integers

We have two main objectives in this lesson. Each objective has multiple parts.

Learn to find opposites and absolute value of integers…..this will add another grouping symbol

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Learn to represent, graph, and order integers

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Representing an integer means to give a situation that can be described with a positive or negative value.

For example, walking up 5 steps would be a +5. Walking back down those steps would be a -5.

Depositing $75 in the bank would be +75. Spending$30 of the money would be -30.

Describing Integer Values:

Earning $50.00_________

Having a $30 debt ________

7 o below 0 _______

300 ft. below sea level ________

Hiking to an altitude of 4000’ _______ 30 sec. before liftoff _____

Completing a 40 yd. pass _________

Sacking the quarterback 15 yds. behind the line of scrimmage _____

+50

-30

-7

-300

+4000

-30

+40

-15

You can graph positive and negative numbers on a number line. This means to make a dot on the value.You can graph positive and negative numbers on a number line. This means to make a dot on the value.

On a number line, opposites are the same distance from 0 but on different sides of 0.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.Integers are the set of all whole numbers and their opposites.

–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

Opposites

Positive IntegersNegative Integers

0 is neither negative nor positive.

Graph each integer on the number line. Then use a to indicate the opposite. You notes say to use a square…..it doesn’t matter.

4, -3, 0, -1, 2

–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

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Turn your notes over.

X

|–3| = 3 |3| = 3

The absolute value of an integer is its distance from 0 on a number line. The symbol for absolute value is | |.

The absolute value of an integer is its distance from 0 on a number line. The symbol for absolute value is | |.

–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

3 units 3 units

Opposites are the same distance from 0. This means they have the same absolute value. Opposites create a ZERO PAIR.

Opposites are the same distance from 0. This means they have the same absolute value. Opposites create a ZERO PAIR.

• Absolute values are never negative.

• Opposite integers have the same absolute value.

• |0| = 0

Read |3| as “the absolute value of 3.”

Read |–3| as “the absolute value of negative 3.”

Reading in Math

Comparing Integers

• Any + is greater than any –

• Any + is greater than 0

• 0 is greater than any –

• The farther an integer is to the right on a number line, the greater its value

-2 ____ -4

8 ____ -9

-12 ____ -9

0 _____ -6

|-5| _____4

* - |-9| _____ | -1|

-2 ____ -4

8 ____ -9

-12 ____ -9

0 _____ -6

|-5| _____4

* - |-9| _____ | -1|

≤ , ≥ , =≤ , ≥ , =

≥

≥

≤

≥

≥ 5 _____ 4

-9 ____ 1≤

The “opposite” of |9| is -9

Lesson Quiz

Name a positive or negative number to represent each situation.

1. A profit of $250

2. 18 degrees below 0

3. 40 sec. before launch?

4. What is the opposite of 4?

5. What is the opposite of -9?

6. |-8| =

–18

+250

-40

-4

+9

8 37. |-3| =

Learn to represent, graph, and order integers?

Did we…………

Learn to find opposites and absolute value of integers…..this will add another grouping symbol?

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