Math 090Beginning Algebra

Mr. Kennicutt

Course Info

• Class:– Friday

4:00 PM – 9:30 PM– Saturday

8:00 AM – 1:30 PM

• Office Hours:– Friday 2 – 4 PM in SO 230

• My MATH LAB code– kennicut08342 (501)– kennicut10698 (502)

• Your Grade

• NO CELLPHONES!

Topic Percent of Grade

Tests 45 %

Final Exam 20 %

Homework 15 %

Quizzes 10 %

Attendance 5 %

Contact Info

Mr. Kennicutt

Email: jrk9@buffalo.edu

Phone: 303-578-8471

Your Book

• Pre-Algebra– Academic Year

Fall/Spring 2010-2011

• ISBN:9780558741198 • Custom Made for CCD

• My Math Lab• Advantages– Homework online– Help solving problems– Easy to Track– Green

Homework

• Turn in homework on the day of the test• Show Work!• No Calculators• Circle Correct Answers• 25 Lab hours (more to come)• First Homework Assignment Due:

June 17th Late Homework accepted but 10 % off

Tentative Course Schedule

Attendance

• I do take attendance• 2 or more absences and I can fail / withdraw

you

• Please notify me by email or phone (text) if you are going to miss class.

Accommodations

• Director of the Center for Persons with Disabilities (CPD)– Room 134, South

Classroom Building1st Floor

– CPD phone number: (303) 556-3300.

• If you think you need to meet with the CPD, please call and schedule an appointment

Satisfactory Progress

FREE Class

• Pass class with grade of C or better• Must retake class the following semester• Must have not missed more than 1 class• Must have completed 25 hours of Math Lab

Hours• All Exams and Final, Completed 75 % of HW

Homework

• Bring in back sheet of syllabus– Secret Name

• My Math Lab

• Website• In Class Work• Check out MML

1.1

Fractions

Definitions

Natural numbers: 1, 2, 3, 4,…,

, ,NumeratorFraction BarDenominator

Ex. The improper fraction can be written , a mixed number.

1

2

2

3

15

7

12

5

22

5

Whole numbers: 0, 1, 2, 3, 4,…,

Fractions:

Proper fraction: has a value of less then 1; the numerator is smaller than denominator.Improper fraction: has a value of 1 or greater then 1; the numerator is larger than or equal to the denominator.Mixed number: is a combination of a whole number and a fraction.

Fraction Bar: Represents Division.1 ÷ 2; 2 / 3; 15 ÷ 7

Learn the Definition of Factor

• In the statement 2 × 9 = 18, the numbers 2 and 9 are called factors.

• All the factors of 18 are: 1, 2, 3, 6, 9, 18

Prime vs. Composite

• Prime: – A natural number greater than 1 is prime if its

products include only 1 and itself.• Ex. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37,…

• Composite:– A natural number greater than 1 that is not prime

is called a composite number.• Ex. 4, 6, 8, 9, 10, 12,…

Prime Factorization

• Write each number as the product of prime factors…

3524

A fraction is in lowest terms, when the numerator and denominator have no common factors other than 1.

• Writing a Fraction in Lowest Terms:• Step 1: Write the numerator and the denominator as the

product of prime factors.• Step 2: Divide the numerator and denominator by the

greatest common factor, the product of all factors common to both.

• Basic Principle of Fractions:– If the numerator and denominator are multiplied or divided by

the same nonzero number, the fraction remains unchanged.

Write in lowest terms.12

20

You Trywrite the answers in your notebook, do not answer out loud.

• Write each fraction in lowest terms

• Prime or Composite, if composite do prime factorization.– 31– 64– 33– 2

€

10

15

15

45

You are driving down the road in your car on a wild, stormy night, when you pass by a bus stop and you see three people waiting for the bus

• An old lady who looks as if she is about to die.• An old friend who once saved your life.• The perfect partner you have been dreaming about.

Knowing that there can only be one passenger in your car, whom would you choose?

The old lady of course!

After helping the old lady into the car, you can give your keys to your friend, and wait with your perfect partner

for the bus lady of course!

Multiply and Divide FractionsMultiplying Fractions:

If and are fractions, then · = .a

b

a

b

c

d

c

d

a c

b d

To multiply two fractions, multiply their numerators and then multiply their denominators.

Dividing Fractions:

If and are fractions, then ÷ = .a

b

a

bc

d

c

da d

b c

To divide two fractions, is to multiply its reciprocal; the fraction flipped upside down.

€

7

9⋅12

14=

7 ⋅12

9 ⋅14=

7 ⋅3⋅2 ⋅23⋅3⋅2 ⋅7

=2

3

€

9

10÷

3

5=

9

10⋅5

3=

9 ⋅510 ⋅3

=3⋅3⋅52 ⋅5 ⋅3

=3

2=1

1

2€

31

3⋅1

3

4=

10

3⋅

7

4=

10 ⋅73⋅4

=2 ⋅5 ⋅73⋅2 ⋅2

=35

6= 5

5

6

You Try

€

3

8⋅

4

9

3

4÷

5

8

12

3÷ 4

1

2

Add and Subtract FractionsAdding Fractions:If and are fractions, then + = .a

b

c

b

a

b

c

b

a c

b

Subtracting Fractions:

If and are fractions, then .a

bc

b

a c a c

b b b

Examples

€

3

7+

2

7=

3+ 2

7=

5

7

€

2

10+

3

10=

2 + 3

10=

5

10=

5

2 ⋅5=

1

2

€

8

12−

3

12=

8 − 3

12=

5

12

€

15

8−

3

8=

15 − 3

8=

12

8=

2 ⋅2 ⋅32 ⋅2 ⋅2

=3

2=1

1

2

Different DenominatorIf the fractions do not share a common denominator. The

least common denominator (LCD) must first be found as follows:

Step 1: Factor each denominator.

Step 2: For the LCD, use every factor that appears in any factored form. If a factor is repeated, use the largest number of repeats in the LCD.

€

3

4=

?

32

Example7 2

30 45

21 4

90

25

90 5

3 3

5

2 5

5

18

5 14 2

6 3 29 14

6

43

6

17

6

3 2

3 2

7 2

30 45

29 7

6 23

2

3 1

10 4

6 5

20

1

20

2 5

2

3 1

0 51 4

You Try

€

1

9+

5

9

4

15+

5

9

7

18−

4

15