1. Unit 1 Seminar Welcome to MM150! To resize your pods:
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2. MM150 Unit 1 Seminar Agenda Welcome and Syllabus Review
A Review of Sets of Numbers
Sections

3. Lea Rosenberry e-mail: LRosenberry@kaplan.edu
Google Chat:
Office Hours: By Appointment 3

4. Seminars – Three Choices
Wednesday
8-9 PM ET
Shelly Pruitt
Thursday
10-11 PM ET
Lea Rosenberry
Saturday
11 AM to Noon ET
Unit 1 ü
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
Unit 9
If none of these options work, you can watch an archive if you wish.
Seminar is ungraded.

5. Grading Criteria Threaded Discussion MML Graded Practice Final Project
Units 1-9 at 35 points each for a total of 315
MML Graded Practice
Units 1-9 at 60 points for a total of 540
Final Project
Unit 9 for 145 points

6. Earning Full Credit on the Discussion Board
Original Post
Interaction
Up to 25 Points
Up to 10 Points
Original, thoughtful analysis of the discussion question, and/or
All applicable posting instructions followed, and/or
Example (if required) is given in an orderly, step by step process with appropriate explanation, and/or
Formatting is correct with no strange characters or other formatting issues, and/or
All parts of the discussion question are answered.
Responses to classmates’ posts are thoughtful and advance the discussion, and
Substantive responses to 2 or more classmates are given.

7. More About Discussions
Rules about plagiarism apply.
If you use an outside source, please reference it and use proper citation procedures.
Discussion Boards can only be completed up to 2 weeks late.

8. MML Graded Practice
Problems can be done over and over again until you get a perfect score.
Help is available.
Show me an Example
Help Me Solve This
Ask the Instructor

9. Getting the Most out of MML
Monday, August 27 at 10:00 PM ET
To attend, click the link
Learn how to get the most out of MyMathLab (MML), including navigating in MML, entering answers, getting 100% on MML Graded Practice assignments, and using MML resources.

10. Sets of Numbers Natural Numbers: {1, 2, 3, 4, …}
Whole Numbers: {0, 1, 2,3, …}
Integers: {…-3, -2, -1, 0, 1, 2, 3, …}
Rational Numbers: ½, 0.5, -6,
Irrational Numbers: , √[2], √[3]
Real Numbers: all rational and irrational numbers

11. Example: Find all factors of 12
An easy way to approach this task is to think of pairs of factors you could use, then make the final list from them.
1*12 AND 2*6 AND 3*4
Make sure you have every factor pair listed!
Therefore, the factors of 12 (in numerical order) are 1, 2, 3, 4, 6, and 12. 11

12. EVERYONE: Find all factors of 56.
1 * 56
2 * 28
4 * 14
7 * 8
Therefore, the factors of 56 (in numerical order) are 1, 2, 4, 7, 8, 14, 28, and 56. 12

13. Example: Determine the GCF of 12 and 56.
We have already created these lists, so I will just put them under each other here:
12: 1, 2, 3, 4, 6, 12
56: 1, 2, 4, 7, 8, 14, 28, 56
Now, just plain old COMMON FACTORS of 12 and 56 include 1, 2, and 4.
The GCF is 4. 13

14. Factor Tree 72
3 3
72 = 2 * 2 * 2 * 3 * 3
72 = 23 * 32

15. Steps to Finding GCF There are two steps:
Write down only the COMMON PRIME FACTORS (the big numbers; save the exponents for the next step).
(For only the common prime factors) given the choice of powers, use the LOWEST POWER for each prime factor. 15

16. GCF Example Using Prime Factorization
Find GCF (72, 150).
72 = 23 * 32
150 = 2 * 3 * 52
GCF(72, 150) = 2? * 3?
GCF(72, 150) = 2 * 3 = 6 16

17. Steps to Finding the Least Common Multiple
There are two steps:
Write down the PRIME FACTORS with the greatest exponent.
Determine the product of the prime factors. 17

18. LCM example using Prime Factorization
72 = 23 * 32
150 = 2 * 3 * 52
LCM(72, 150) = 2? * 3? * 5?
LCM(72, 150) = 23 * 32 * 52 = 1800 18

19. Addition of Integers Same sign 4 + 6 = 10 12 + 3 = 15 -3 + (-8) = -11
-2 + (-5) = -7
Opposite sign
3 + (-4) = -1 Think: 4 – 3 = 1. Then take sign of larger, -1
= Think: 9 – 7 = 2. Then take sign of larger, 2. 19

20. Subtraction of Integers
Example 1:
4 – 9 (positive four minus positive nine)
= 4 + (-9) (positive four plus negative nine)
= -5 (by the different signs rule of addition)
Example 2:
-3 – 7 (negative three minus positive seven)
= -3 + (-7) (negative three plus negative seven)
= -10 (by the same sign rule of addition)

21. Subtraction of Integers
Example 3:
-12 – (-14) (negative twelve minus negative
fourteen)
= (negative twelve plus positive
= 2 (by the different signs rule of addition)

22. Multiplication and Division of Integers
Two positives = positive
Two negatives = positive
One of each sign = negative
Examples:
(3)(-2) = -6
-9/ (-3) = 3 22

23. Simplifying Fractions
15/45
Divide both the numerator and denominator by 15.
15/45 = (15 / 15) / (45 / 15) = 1/3 23

24. Mixed Numbers 2 7/8 Write 2 7/8 as an improper fraction.
2 7/8 = 2 + 7/8
2/1 + 7/8
16/8 + 7/8
23/8
2 7/8 = (2*8 + 7) / 8 = 23/8 24

25. Converting an Improper Fraction to a Mixed Number
58/4
14 2/4
14 1/2 14
4 / 58 4 18 16 2 25

26. Multiplying Fractions and Mixed Numbers
½ * 3/4
= 1 * 3
= 3 8
3 ½ * 1 ¼
= 7 * 5
= 35 8

27. Dividing Fractions
÷ 2 7
* 7 2 6

28. Dividing Mixed Numbers
9 ½ ÷ 4 3/5
= 19 ÷ 23
= * 5
= 95 46

29. Radical Expressions
The radical symbol looks like this: √x and the x that is located within or under the radical is called the radicand.
An expression that contains a radical is called a radical expression. The following is the cube root of a: 2√a and this is also a radical expression. The small 2 in front of the radical is known as the index and it indicates that this is a square root. When no index is present, then the radical is understood to be a square root with an index of 2.

30. Here are the perfect squares: (the right side of the equal sign)
112 = 121
122 = 144
132 = 169
142 = 196
152 = 225
162 = 256
172 = 289
182 = 324
192 = 361
02 = 0
12 = 1
22 = 4
32 = 9
42 = 16
52 = 25
62 = 36
72 = 49
82 = 64
92 = 81
102 = 100

31. √32
√50
= √(16 * 2)
= √16 * √2
= 4 √2
= √(25 * 2)
= √25 * √2
= 5 √2

32. Adding and Subtracting Radical Terms
Radicals are “things”…
Example:
2√5 + 4√5 = 6√5
2 apples + 4 apples = 6 apples
2√3 + 4√5 = 2√3 + 4√5 (can’t combine)
2 oranges + 4 apples = 2 oranges + 4 apples 32

33. Simplify: 8 sqrt[11] + 2 sqrt[11]

34. Multiplying Radicals sqrt[25] * sqrt[4] sqrt[100] 10
NOTE: sqrt[25] = 4 and sqrt[4] = 2
5 * 2
Either way you get the same answer 34

35. Dividing Radicals sqrt[36/9] sqrt[36]/sqrt[9] 6/3 2 NOTE: 36/9 = 4
2 Either way you end up with same answer

36. Exponents
672 34
-73 59
So, if you’re presented with 2*2*2*2*2*2*2, you can rewrite this as 2^7 or 27.
Beware of this situation:
-24 vs. (-2)4
-24 = -(2)(2)(2)(2) = -16
(-2)4 = (-2)(-2)(-2)(-2) = 16 36

37. PRODUCT RULE OF EXPONENTS.
(ax) * (ay) = a(x + y) (KEEP THE BASE and ADD THE EXPONENTS.)
23 * 22 = 2 (3 + 2) = 25
57 * 58 = 5 (7+8) = 515
QUOTIENT RULE OF EXPONENTS.
(ax) / (ay) = a(x - y) (KEEP THE BASE & SBTRCT THE EXPONENTS)
57 = 5 (7-5) = 52 = = = 1
(14-3) 37

38. POWER RULE OF EXPONENTS.
(ax)y = axy (Keep The Base and MULTIPLY THE EXPONENTS.)
(22)3 = 2 (2*3) = 26 = 64
(811)4 = 8 (11*4) = 844
Anything to the zero power is 1.
a0=1, a ≠ 0
40 = 1; (-10)0 = 1; = 1; = 1
Anything to the first power is itself.
a1=a
81 = 8; (-1/2)1 = -1/2; = 25 38

39. A negative exponent moves the term to the other side of the fraction bar.
a-1 = 1/a and /a-1 = a
6(-3) = (-4) = 1
7(-2)

40. Scientific Notation
3.1 x 104
x 10-5
1.89 x 100 40

41. Converting from Scientific Notation to Decimal Notation
x =
Another way to look at it:
x 10-5
= x 1/100,000 = /100,000 = 41

42. Converting from Scientific Notation to Decimal Notation
1.89 * 103
1,890
Another way to look at it
1.89 * 1,000 42

43. Converting from Decimal Notation to Scientific Notation
Convert 45,678 to scientific notation
x 104
Convert to scientific notation
8.2 x 10-6 43