Welcome to Class #53/12/14Please turn in

HW #4:• Extra practice booklet

– Topic #1 “Arithmetic Operations with Numbers”

#1 – 32 ONLY

• Textbook: P. 6 #4, P. 16 #21, 22, 23, 25

P. 17 #30

Warm-up: Sample Test #2:Do #1 – 9, 10 – 24, 32 – 34 only

Work on this on your own or in pairs.

This is practice for Test #2 next week.

Tonight’s positive quote

3

Often people attempt to live their lives backwards; they try to have more things, or more money, in order to do more of what they want, so they will be happier.  The way it actually works is the reverse.  You must first be who you really are, then do what you need to do, in order to have what you want.  ~Margaret Young

1. Warm-up (turn in HW#4)

2. Prime factored form

3. More practice with integers

4. Go over HW & Quiz #1

5. Exponents

6. Order of Operations

7. Absolute value of a number

8. OOP chains fun!

Agenda 10/1/14

How to write a number in prime factored form

Factors, Prime Numbers &

Composite Numbers

Definition

• Product – An answer to a multiplication problem.

7 x 8 = 56

Product

Definition

• Factor – a number that is multiplied by another to give a product.

7 x 8 = 56

Factors

Definition

• Factor – a number that divides evenly into another number.

56 ÷ 8 = 7

Factors

More practice with

integers

Example: 7 is prime because the only numbers that will divide into it evenly are 1 and 7.

Definition• Prime Number – a number

that has only two factors, itself and 1.

Examples of Prime Numbers

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37…

Example: The number 8. The factors of 8 are 1, 2, 4, 8.

Definition

• Composite number – a number that has more than two factors.

Examples of Composite Numbers

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, …

One is special because . . .

One is not prime.(because it doesnot have exactly

two differentfactors).

One is not Composite.(because it doesnot have morethan 2 factors).

Definition• Prime Factorization – A way to

write a composite number as the product of its prime factors.

2 x 2 x 3 = 12or

22 x 3 = 12

How to do a Prime Factorization

48Step 1 – Write down any composite number.

- - Factor Tree Method - -

Step 2 – Start dividing bythe prime #s (start with 2). If the composite number is divisible by 2, write it down and find the next factor.

If not, check if the factor is evenly divisible by 3, 5, 7, 9, etc.

2 x 24

How to do a Prime Factorization

48Step 3 – Check the factors. If they are prime, you are done.If they are not, proceed to Step 4.

- - Factor Tree Method - -

Step 4 – Continue dividing. If one of the factors is divisible by 2, write it down and find the next factor.If not, check if the factor is evenly divisible by 3, 5, 7, 9, etc.

2 x 24

2 x 2 x 12

How to do a Prime Factorization

48Step 5 – Check the factors. If they are prime, proceed to Step 6.If they are not, repeat Step 4.

- - Factor Tree Method - -

2 x 24

2 x 2 x 12

2 x 2 x 2 x 6

How to do a Prime Factorization

48Step 5 – Check the factors. If they are prime, proceed to Step 6.If they are not, repeat Step 4.

- - Factor Tree Method - -

Step 6 – Write the Prime Factorization in Exponential Form.

2 x 24

2 x 2 x 12

2 x 2 x 2 x 6

2 x 2 x 2 x 2 x 3

24 x 3 = 48

Find the Prime Factorization

273 x 9

33 = 273 x 3 x 3Prime Factorization

Prime Factorization in Exponential Form

Find the Prime Factorization

182 x 9

2 x 32 = 182 x 3 x 3 Prime Factorization

Prime Factorization in Exponential Form

Rules for Multiplication & Division

• If the signs are the same, the product or quotient will be positive

• If the signs are the different, the product or quotient will be negative.

5 2 10 5 2 10and

20 2 40 20 2 10and

Simplify.

1)

2)

3)

4)

5)

6)

7)

8)

102

36( 9)

27 ( 3)

24 ( 3)

6 4 2( ) ( )

24 8 ( )

100 4( )

5 4 2( )

Simplify the following. Be careful!

1) -6(7) =

2) 6(-7) =

3) 6 - 7 =

4) (-6) - 7 =

5) (-9) - 5 =

6) -9(-5) =

7) (9) - 5 =

8) 9(-5) =

-42

-42

-1

-13

-14

45

4

-45

Exponents or Powers

Objective - To simplify expressions involving exponents.

34= 3 3 3 3 = 81

Exponent or power

Base

Read, “Three to the fourth power.”

Rewrite each power as repeated multiplicationand evaluate (find the value).

1)

2)

3)

4)

25

42

310

212

5 5 25

2 2 2 2 16

10 10 10 100012 12 144

Power Verbal Phrase Meaning27 “Seven to the 2nd power” 7 7

“Seven squared”

35 “Five to the 3rd power” 5 5 5 “Five cubed”

49 “Nine to the 4th power” 9 9 9 9

52 “Two to the 5th power” 2 2 2 2 2

Power Meaning2( 7) ( 7) ( 7)

35 1 5 5 5

4( 9) ( 9) ( 9) ( 9) ( 9)

52 1 2 2 2 2 2

Simplify the following.

1)

2)

3)

4)

5)

6)

7)

8)

9)

10)

34

( 3)4

34

( ) 4 3

( ) 2 4

(7 2)2

7 22

6( 3)2

62

112

-81

81

-64

-64

16

25

3

54

-36

12

ORDER OF OPERATIONS

Order of Operations

• Parentheses (inside to outside)

• Exponents

• Multiply & Divide from left to right

• Add & Subtract from left to right

PEMDAS

Order of Operations

Parenthesis

Exponents

6 + 5(6)6 + 30 = 36

2 + 3 252 + 75 = 77

Multiply / DivideLEFT TO RIGHT 8 4 = 32

Add / SubtractLEFT TO RIGHT 10 - 3 + 8

7 + 8 = 15

1) 6 + 5(8 - 2)

2 3 52 2)

3) 16 2 4

4) 10 3 2 4

Simplify the following.1)

2)

3)

4)

( )4 3 6 2 10

24 2 18 5 1 [ ( )]

8 36 4 5

8 5 4

10 6

(4 + 18)2 - 10(22)2 - 10

44 - 10 = 34

24 - 2[18 6]

24 - 2[3]

24 - 6 = 18

8 - 9 + 5-1 + 5

4

8 + 204284

= 7

The order of operations (Text p. 49)

| ABSOLUTE VALUE |

What do you know about the

absolute value of a number?

Talk to your shoulder partner!

Problem 9-45 Absolute Value Operation

a.Study the relationship between the # entered in parentheses and the results shown. Write a statement describing this operation.

b.Why would you ever need an absolute value?

Absolute value (p. 389)- A numbers distance from zero on the number line. It is represented by two vertical bars

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

3

5

10

12

7

23

0

54.

16

3

5

10

12

-7

-23

0

5.4

-16

10

33 2 2 9 ? 4

Order of Operation Chains

OOP Chains!

•Work in pairs for this activity.•Each person needs this worksheet and one envelope.

OOP Chains Worksheet

• Each problem has 3 correct pieces to get from the original problem to the simplified form.

• However, each problem also has a whammy (one incorrect piece) that is there to throw you off course!

• You need to correctly find the OOP Chains and correctly identify all the whammies!

Solution:

HW #5•Extra practice booklet topic # 3 “Order of Operations” # 1 – 15 (show all work)

•Worksheet p. 24 “Why did the ant run across the cracker box?”

•Worksheet p. 62 “Can you build this?”