Integer Operations and Absolute Value Lesson 2

Integer Operations and Integer Operations and Absolute ValueAbsolute Value

Lesson 2Lesson 2

WarmupComplete the multiplication table.

0 1 2 3 4 5-1-2-3-4-5-6 6

Number Line

•Integers are positive & negative numbers.

•Is 0 positive or negative?

Neither!

Ordering Integers.

0 1 2 3 4 5-1-2-3-4-5-6 6

least greatest

Put the following numbers in order from least to greatest.Ex. 5, -2, -4, 3, 0, -1

-4…-2…-1…0…3…5

On your own…Order from least to greatest1. 10, 8, -5, 0, -2.5, -4, 92. -6.2, -7, 5.4, 12, 1

Order from greatest to least.1. 5, -3, 4, -4, 2, -22. 10, 8, -5, 0, -2.5, -4, 9

-5, -4, -2.5, 0, 8, 9, 10

10, 9, 8, 0, -2.5, -4, -5

-7, -6.2, 1, 5.4, 12

5, 4, 2, -2, -3, -4

They look like equations but are separated with these symbols.

reater than

ess than

reater than or equal to

ess than or equal to

Use <, >, = to complete the

problem.

5 4

>Hold up 1 for > and 2 for <.

Use <, >, = to complete the

problem.

-2 -3

>Hold up 1 for > and 2 for <.

Use <, >, = to complete the

problem.

0 -1

>Hold up 1 for > and 2 for <.

True or False?-6 < -2

0 42-6 -4 -2 6

True

Hold up 1 for true and 2 for false.

True or False?-5 < 7

0 42-6 -4 -2 6

True

Hold up 1 for true and 2 for false.

True or False?6 < 0

0 42-6 -4 -2 6

False

Hold up 1 for true and 2 for false.

True or False?-6 > 5

0 42-6 -4 -2 6

False

Hold up 1 for true and 2 for false.

Absolute Value: The number of units a number is from zero on the number line. (Always Positive)

0 42-6 -4 -2 6

|-4| = 4

Abso ute Va ue

Is written using these brackets.

Not to be confused with (parenthesis)

Absolute Value

|6| = 6 and |-6| = 6

Greater than or less than

Using the number line to determine which sign would make this true.

|-4| |2|0 1 2 3 4 5-1-2-3-4-5-6 6

>

-|5| |-2|<

5- 2

Greater than or less than

On your own…1.|-3| ___ |-2|

2.|-8| ___ |-4|

3.|-1| ___ |1|

4.-|-4| ___ |-8|

5.-|-3| ___ -|-2|

6.-|-4| ___ |0|

>

>

=

<

<

<

|5| + |-2|

5 2+

7

|5| - |-2|

5 2-

3

Integer Addition

Adding Two Positive Integers Add the absolute values and keep the sign. The sum is positive.

Adding Two Negative Integers Add the absolute values and keep the sign. The sum is negative.

Adding a Positive Integer and a Negative Integer

Add the absolute values and keep the sign from the greater absolute value. The sum is the same sign as the number with the greatest absolute value.

Adding Integer Video Adding Integers Interactive

Integer Subtraction

Subtraction is like adding the opposite.

Rewrite subtraction as addition, changing the subtraction sign and write the additive inverse of the subtrahend (second value in problem).

8 – 5 = 8 + (-5) =

4 – (-3) = 4 + (___) =

-6 – 2 = ___ + (___) =

-3 – (-4) = ____ + (____) =

Subtracting Integer Video

Subtracting Integer Interactive (counters)Subtracting Integer Interactive (number line)

Addition/Subtraction

1) 13 + (-8) =

3) 17 – (-3) =

4) 5 + (-10) + (-11) =

5) -3 – 5 + (-7) – (-4) =

2) (-3) + (-12) =

+

+

-

-

-

5

15

16

20

11

813

13 8

105

11

5 21

34

5

4 15

7

- -+Multiplying and Dividing

Integers VideoMultiplying and Dividing Integers Game

What rules can we create based on the last 6

problems?

Integer Multiplication

Multiplying Two Positive Integers

The product is positive.

Multiplying Two Negative Integers

The product is positive.

Multiplying a Positive Integer and a Negative Integer

The product is negative.

- -

+Ex. 1) (-5)(3)

XX

= -15

- -

+Ex. 2) (-12)(-3)= 36

- -

+Ex. 3) (9)(-9)= -81

- -

+Ex. 1) (-7)(3)

= -21

- -

+Ex. 2) (-9)(-8) = 72

- -

+Ex. 3) (5)(-6)= -30

Multiplying Three or More Integers

Count the number of negative signs.

If there is an odd number, the product is negative.

If it is an even number of negative signs, your answer is positive.

25243

Multiplying Three or More Integers

Example 5: Find the producta. 2( -3)(4)b. 3(-2)(-5)c. (-3)(-4)(-2)(-1)d. (-1)(-1)(-1)(-1)(-1) o

Integer Division

Dividing Two Positive Integers The quotient is positive.

Dividing Two Negative Integers The quotient is positive.

Dividing a Positive Integer and a Negative Integer

The quotient is negative.

- -

+X

X

- -

+

- -

+

= -32

= 6

= -97

63)4

848

)3

3216

)2

84)1

= -24

Multiply/Divide

1) 4(-5) =

3) (-5)(-3)(2) =

4) –(-2)(-4)(6) =

5) (-3)(-2)(3)

2) (-3)(-8) =

-

+

-

+

+

20

24

48

30

189

=9

= 2

You Try