Chapter 2

Chapter 2

Integers

+ - * ÷

Integers

Integers- Negative and Positive whole numbers. INCLUDES 0

Write some integers on your paper:

…-4, -3, -2, -1, 0, 1, 2, 3, 4…

Ordering integers

Order the following from least to greatest:

1) -7, 2, -1, 0, -2

-7, -2, -1, 0, 2

2) 9, -4, 12, -11, -1

-11, -4, -1, 9, 12

3) 0, -99, 44, -60, 16

-99, -60, 0, 16, 44

Absolute Value

Absolute Value- The distance between the number and zero on a number line.

The absolute value of n looks like: │n│

Find the absolute value of the following:

│6│ │-8│ │15│

Opposite

Opposite of a number- same distance from 0. On different sides of 0. Opposite numbers have the same AV.

Find the opposite:

-6

14

-27

Evaluate:

-│8│

-│-5│

(-6)

-(- 4)

Do Now 9/30

Write the opposite and Absolute Value:

1) 18

2) -45

3) -16

Evaluate:

4) -(-2)

5) - │-18│

Adding Integers – Number Line

Use your number line to add integers:Positive numbers right, Negative numbers left

1) 3 + (-4)

2) -5 + 2

1) Start at zero

2) Move 3 units to the right

3) Move 4 units to the left

1) Start at zero

2) Move 5 units to the left

3) Move 2 units to the right

Adding Integers – Number Line

Use your number line to add integers:Positive numbers right, Negative numbers left

3) -6 + -1

4) -4 + 2

1) Start at zero

2) Move 6 units to the left

3) Move 1 unit to the left

1) Start at zero

2) Move 4 units left

3) Move 2 units right

Do Now 10/1/09

Add using a number line:1) 7 + (-10)

2) -2 + ( -3)

3) -8 + 5

4) 5 + 3

Adding Integers- Walking on a number line

1) -2 + 42) 7 + (-8)3) -6 + -34) 5 + (-4) 5) -8 + 36) -2 + (-7)7) 12 + (-8)8) -16 + 9

9) 9 + (-11)10) -6 + 1411) 17 + (-7)12) -14 + - 613) 7 + (-4) 14) -8 + 815) -12 + (-7)16) 15 + (-8)

17) 19 + (-11)18) -16 + 319) 7 + (-7)20) -16 + - 221) 15 + (-8) 22) -8 + 323) -12 + (-2)24) 19 + (-7)

What are the Adding Integer RULES?!

Write a rule for:

(+) + (+)

(-) + (- )

( - ) + (+) / (+) + (- )

Adding Integers - Integer song:

Integer Operations Song

(Row Row Row Your Boat)Same sign - add and keepDifferent sign - subtractKeep the sign of the bigger numberThen you’ll be exact.

Adding Integers – Using the Song

1) -3 + -4

2) -8 + -5

7) 33 + -15

8) -29 + -64

3) -20 + -30

4) 7 + -8

9) -47 + -20

10) -8 + 75

5) -6 +1 +-3

6) 4 + -7 + -11

11) 7 + -13 + 6

12) -19 + 48 + -5

Do Now 10/5

Add:

1) -35 + 42

2) -64 + -37

3) 73 + -19

4) -128 + -84

Adding Integers – Zero Pairs

zero pairs- is a pair of numbers whose sum is zero.

1) 4 + -7

2) 3 + -2

3) -6 + 5

4) -3 + - 4

Subtracting Integers – Add Opposite

Subtract Integers- Add the opposite of the second number.

1) 11 – 12

2) -5 – 3

3) -7 – (-6)

4) 8 – (-2)

Do Now 10/7/09

Subtract – Add the opposites1) -6 – 9

2) 72 – 114

3) -18 – (-88)

4) 25 – (-93)

Subtracting Integers –Song

Subtract – no, don’t do!Just change the second signNow add the numbers like you didAnd then you will be fine

Subtracting Integers – Using the song

1) -3 – (-4)

2) -8 – (-5)

7) 33 – (-15)

8) -29 - 64

3) 20 – (-30)

4) 7 – (-8)

9) -47 – (-20)

10) -8 - 75

5) -6 - 1 - 3

6) 4 - (-7) – (-11)

11) 7 – (-13) - 6

12) -19 - 48 – (-5)

Do Now- 10/8/09

Subtract:1) -8 – (-3)

2) - 74 – 19

3) -56 – (-32)

4) 43 – 93

Adding and Subtracting Integers

Be careful, you have to decide which rule to follow (adding or subtracting)

1) -54 + 84

2) - 35 – 32

3) 49 – 9

4) 23 + -84

5) -34 - 63

6) - 5 – 28

7) 19 – 57

8) 38 + -45

9) -79 + -11

10) -42 – 34

Do Now 10/14/09

Add or subtract:1) 14 + -12

2) 48 – 59

3) -71 + - 34

4) -84 - 49

Multiplying and Dividing Integers-

Multiply and Divide numbers as you normally do.

-If both signs are positive or negative the answer is positive

-If one sign is positive and one sign is negative the answer is negative

Multiply and Divide

1) -12 ÷ 3

2) -14 * -7

3) -35 ÷ -5

4) 6 * -5

5) 49 ÷ -7

6) -30 ÷ -10

7) -7 * 3

8) -9 * -2

Do Now 10/15

1) 20 * (-3)

2) 16 ÷ (-8)

3) -40 ÷ (-20)

4) -8 * 5

Multiplying and Dividing with Zeros

Zero – 0Multiplying-

0 * -32 = 0

Dividing- 0 ÷ -4 = 0 =

-4

-4 ÷ 0= -4 =0

0

undefined = u

Multiplying and Dividing Integers- Song

Multiply or Divide - what do I do now?Same sign- positive –

Different sign- negativeI got it now KERPOW!!

Multiplying and Dividing Integers- Song

1) -10 ÷ 5

2) -2 * -7 * 5

3) -90 ÷ -5

4) 6 * -3 * -3

5) 49 ÷ -7

6) -110÷ -10

7) -7 * -4 * -2

8) -9 * -12

Do Now 10/16

Add/subtract/Multiply and Divide1. 5 + -3

2. -3 * 7

3. -28 ÷ -2

4. 14 – (-8)

Peer Grading of projects

1. Tell what Grade you should get and why on back of rubric.

2. Show each other all the rules on your project. (check that each person included all parts of the rules)

3. Show each other all the real life examples on your project. (check that there are atleast 3 and that they are different ideas).

Do Now: Identify the following properties of Math (use your text if you forgot):

1- Identity Property-Sum of a number and zero = the numberProduct of a number and 1 = the number

a + 0 = ab * 1 = b

2- Commutative Property-Can add or multiply numbers in any order

a+b = b +a cd= dc

3-Associative Property-Changing the grouping will not affect the sum or product

a + (b+c) = (a + b) + c abc= cba

Distributive Property-You can multiply a number and a sum by multiplying the number by each part of the sum and then adding these products. The same applies to subtraction.

A(B + C) = AB + AC

D(E – F) = DE – DF

Ex1: -5 (x + 10)

-5x + -5(10)

= -5x + -50 or

= -5x – 50

Ex2: 2 (x - 7)

2x - 2(7)

= 2x - 14

Ex3: 3 [x – 20 + (-5)]

3 (x) – 3 (20) + 3 (-5)

3x – 60 + (-15)

3x + (-60) + (-15)

3x + (-75)

Simplify using Distributive Property

1) -2 (5 + 12)

2) -4(-7 – 10)

3) 2(w – 8)

4) -8(z + 25)

Tell Which property each displays:Do Now 10/28

1) 3(2x + 1)= 6x +3

2) (2 + 4) + y = 2 + (4 + y)

3) 4x = x*4

4) 6(2*15)= (6*2)15

Like Terms- Identical variable parts raised to the same power

For example: 2m and 14m

3x4 and 12x4

12xy2z and xy2z

3 and 62

Write 3 more examples on your page:

Simplify the expression by combining like terms:

1. c + 8c

2. 3m + -4m

3. 15y2 + 9y + 11y2

4. -5x -7t +2x -9t

Like Terms-

1. 5x – 2x

2. 2a + 3a

3. 7p – 3p + 25

4. 10k + 21+ -8k

5. 13z + 7 - 5z

Simplify the expressions:

1. 9w (w + -4)

2. 8(1 +4d) – 3d

3. 9p – ( 7p + 2)

4. 11(2g - 4) +12 -18g

Solve Equations Involving Distribution

3(x – 9) = -39

z + 4(6 – z) = 21

8 = -7(y + 1) + 2y