1. MM150 SEMINAR UNIT 1 with MK McGee
Welcome to our first seminar.
**You will need a pen or pencil and some paper**
You can get a calculator, too.
MM150 SEMINAR UNIT with MK McGee                                                

2. WELCOME TO MM150 SEMINAR 1
--No textbook? Call KC-ASSIST ( ) and your advisor. --
--Office Hours by appointment – me!
-- SEMINAR: Not required or graded, but strongly encouraged
-- Reading each week(video lectures, too)
--MyMathLab(MML) 20 homework problems each week (60 points)
Kaplan help desk:
Due each week on Tuesday by 11:59 PM (Locks out)
--Discussion Board: Three mathematical postings EACH week (35 points) You need to work a math problem
-- Week 1: Introduce yourself
-- Final Project: Due at end of Week 9 (145 points)

3. Prime Factorization (Section 1.1) Find the Prime Factorization of 36
Neither 9 nor 4 are prime , so we keep factoring
These are all prime numbers
The prime factorization of 36 is:
= 3·3·2·2 Do a quick check. Is 3· 3 · 2· 2 = 36?

4. What is the Prime Factorization of 48?

5. Greatest Common Divisor GCD (Section 1.1)
To find the GCD of numbers, first find the Prime Factorization of each number, then take the smallest exponent of factors common to ALL of the numbers.
Find the GCD of 36 and 42
3² · 2² · 2 · 3
The common factors are 3 and 2 and we want to take the
smallest exponent of each one, so the GCD is:
3 · 2 = 6

6. What is the GCD of 24 and 48?
1) What is the Prime Factorization of 24?
2) What is the Prime Factorization of 48?
3) What are the common factors?
4) What are the smallest exponents of each common factor?
5) What is the GCD of 24 and 48?

7. Least Common Multiple LCM (Section 1.1)
To find the LCM of numbers, first find the Prime Factorization of each number, then take the largest exponent of all the factors.
Find the LCM of 36 and 42
3² · 2² · 2 · 3
Then take the largest exponents of each factor.
The LCM is:
3² · 2² · 7 = 9 · 4 · 7 = 252

8. What is the LCM of 12 and 18? What is the Prime Factorization of 12?
3) What is the highest exponent of each factor?
4) What is the LCM of 12 and 18?

9. Signs (Section 1.2) Multiplying Real Numbers:
Positive x Positive = Positive
3 x 4 = 12
Negative x Negative = Positive
(-3) x (-5) = 15
Negative x Positive = Negative
(-3) x 2 = -6
Positive x Negative = Negative
3 x (-2) = -6
Dividing Real Numbers:
Positive ÷ Positive = Positive
18 ÷ 3 = 6
Negative ÷ Negative = Positive
(-18) ÷ (-3) = 6
Negative ÷ Positive = Negative
(-18) ÷ 3 = -6
Positive ÷ Negative = Negative
18 ÷ (-3) = -6

10. A summary of working with signs for Multiplication and Division:
5 × (-7) =
(-3) × 4 =
(-3) × (-5) =
20 ÷ (-4) =
(-14) ÷ 2 =
(-12) ÷ (-3) =

11. Addition and Subtraction of Integers(Section 1.2)
Evaluate:
a) =
b) 4 – (– 3) =
c) –4 + 3 =
d) –4 – 3 =
d) –4 – (–3) = –7 + 3 =

13. A mountain climber is 2,152 feet above sea level and a deep sea diver is 42 feet below sea level. What is the vertical height difference between the two?
The mountain climber is at a height of 2,152 feet
The deep sea diver is BELOW sea level at a height of -42 feet
The difference of their heights is 2,152 - (-42)
or 2,
= 2,194 feet

14. TRY THIS ONE:
Suppose the temperature in Alaska is -14°F and the temperature in Nevada is 102°F. How many degrees warmer is Nevada than Alaska?

15. RATIONAL NUMBERS (SECTION 1.3)
Rational numbers are the set of numbers of the form
p/q
where p and q are integers and q does not equal 0.
For example: 2/3, -4/5, 1 5/7, 0 , 8/5 are rational numbers.
Numbers like 2/3 and -4/5 are called fractions.
--the number above the fraction line is called the
NUMERATOR
-- the number below the fraction line is called the
DENOMINATOR

16. The method to figure this is:
A common application for using rational numbers is in cooking. What if you need to change the serving size of a recipe?
For example: A recipe will make 24 cookies. You only want to make 18 cookies. How much of each ingredient would you need for this recipe?
½ cup butter
2 cups flour
1 cup sugar
½ teaspoon vanilla
**************************************************
The method to figure this is:
(Desired Serving Size ÷ Recipe Serving size) · Ingredient

17. 3/4 · 1/2 = 3/8 cup of butter 3/4 · 2 = 3/4 · 2/1 = 6/4 = 3/2
(Desired Serving Size ÷ Recipe Serving size) · Ingredient
= 18 ÷ 24
= 3/4
We now need to multiply each of our ingredients by 3/4
½ cup butter
3/4 · 1/2
= 3/8 cup of butter
2 cups flour
3/4 · 2
= 3/4 · 2/1
= 6/4
= 3/2
= 1 ½ cups flour

18. 4.234682…is an irrational number are also irrational numbers
Irrational Numbers (Section 1.4)
AN IRRATIONAL NUMBER IS A REAL NUMBER WHOSE DECIMAL REPRESENTATION IS A NONTERMINATING, NONREPEATING DECIMAL NUMBER.
…is an irrational number
are also irrational numbers

19. Radicals are all irrational numbers. The symbol
is called the radical sign. The number or expression inside the radical sign is called the radicand.

20. Principal Square Root
The principal (or positive) square root of a number n, written
is the positive number that when multiplied by itself, gives n.
For example:

21. Product Rule for Radicals
Simplify:

22. Product Rule for Radicals
Simplify: