Unit 1 Seminar Welcome to MM150! To resize your pods: Place your mouse here. Left mouse click and hold. Drag to the right to enlarge the pod. To maximize chat, minimize roster by clicking here

MM150 Unit 1 Seminar Agenda Welcome and Syllabus Review A Review of Sets of Numbers Sections 1.1 - 1.6

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

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.

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

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.

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.

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

Getting the Most out of MML Monday, August 27 at 10:00 PM ET To attend, click the link http://khe2.acrobat.com/kumcalgebra 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.

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

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

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

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

Factor Tree 72 2 36 2 18 2 9 3 3 72 = 2 * 2 * 2 * 3 * 3 72 = 23 * 32

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

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

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

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

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 -7 + 9 = 2 Think: 9 – 7 = 2. Then take sign of larger, 2. 19

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)

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

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

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

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

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

Multiplying Fractions and Mixed Numbers ½ * 3/4 = 1 * 3 2 4 = 3 8 3 ½ * 1 ¼ = 7 * 5 2 4 = 35 8

Dividing Fractions ÷ 2 7 * 7 2 6

Dividing Mixed Numbers 9 ½ ÷ 4 3/5 = 19 ÷ 23 2 5 = 19 * 5 2 23 = 95 46

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.

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

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

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

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

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

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

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

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 = 25 93 = 1 = 1 55 914 9 (14-3) 911 37

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; 230 = 1; 1000 = 1 Anything to the first power is itself. a1=a 81 = 8; (-1/2)1 = -1/2; 251 = 25 38

A negative exponent moves the term to the other side of the fraction bar. a-1 = 1/a and 1/a-1 = a 6(-3) = 72 19(-4) = 1 7(-2) 63 194

Scientific Notation 3.1 x 104 9.2346 x 10-5 1.89 x 100 40

Converting from Scientific Notation to Decimal Notation 9.2346 x 10-5 = 0.000092346 Another way to look at it: 9.2346 x 10-5 = 9.2346 x 1/100,000 = 9.2346/100,000 = 0.000092346 41

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

Converting from Decimal Notation to Scientific Notation Convert 45,678 to scientific notation 4.5678 x 104 Convert 0.0000082 to scientific notation 8.2 x 10-6 43