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

e-mail: mbruce@kaplan.edu AIM: mbruceku Office Hours: by appointment Mary Bruce e-mail: mbruce@kaplan.edu AIM: mbruceku Office Hours: by appointment 3

Seminar Choices Wednesday, 10:00 PM - 11:00 PM ET with me  (Mary Bruce) (Weeks 1, 2, 4, 6, 8, 9) Wednesday, 10:00 PM – 11:00 PM ET with Lisa James (Weeks 1, 3, 5, 7) Thursday, 9:00 PM - 10:00 PM ET with Terry Clark (Weeks 1, 3, 5, 7) Monday, 8:00 PM – 9:00 PM ET with Lisa James (Weeks 2, 4, 6, 8) The seminars are optional. They do not count towards your grade but are strongly recommended.

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 each for a total of 540 Final Project Unit 9 for 145 points

Earning Full Credit on the Discussion Board Original Post Interaction Up to 20 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 (Writing Center can help you with APA citation rules). 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 Videos Ask the Instructor Key is to START EARLY!

Symbols Multiplication * (shift + 8) or () or [] Square root sqrt[16] = 4 Division / Exponents 3^2 (3 squared) 9

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

Factors of a Natural Number A factor is a number that goes evenly into another number To find the factors of a number, start with 1 and find pairs of factors until a factor repeats. Example: Find all the factors of 12 1*12, 2*6, 3*4, 4*3 (factors repeat) All factors of 12 are: 1, 2, 3, 4, 6, 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. 13

GCF (Greatest Common Factor) 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. But the greatest common factor is: The GCF is 4. 14

*Another way of finding a GCF is to break a number down into a product of prime numbers. What is a prime number? 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. 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 17

Steps to Finding the Least Common Multiple (LCM) There are two steps: Write down the PRIME FACTORS with the greatest exponent (factors don’t have to be in common). Determine the product of the prime factors. 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 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 -7 + 9 = 2 Think: 9 – 7 = 2. Then take sign of larger, 2. 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)

Subtraction of Integers Example 3: -12 – (-14) (negative twelve minus negative fourteen) = -12 + 14 (double negative means +) = 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 23

Fractions and Decimals Fractions and decimals that terminate or repeat are types of rational numbers. We can always change from a fraction to a decimal or vice versa: Example: Change 7/8 to a decimal. Example: Change 65/99 to a decimal.

Simplifying Fractions 15/45 Divide both the numerator and denominator by 15 (GCF). 25

Mixed Numbers 2 7/8 Write the mixed number 2 7/8 as an improper fraction. 2 7/8 = (2*8 + 7) / 8 = 23/8 26

Converting an Improper Fraction to a Mixed Number 58/4 14 2/4 14 1/2 14 4 / 58 4 18 16 2 27

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

Adding/Subtracting Mixed Numbers Example: 8 2/3 – 6 ¾ Change to improper fractions Get a common denominator Subtract and simplify

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 square 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

Simplifying Radicals To simplify a square root, try to find the highest perfect square that goes into the radicand √32 = √16 * √2 = 4√2 √50 = √25 * √2 = 5√2

Adding and Subtracting Radical Terms Radicals are “things”… Example: 2√5 + 4√5 = 6√5 (can combine because the terms have the same radicand) 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 35

Exponents 672 34 -73 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

Scientific Notation 3.1 x 104 9.2346 x 10-5 1.89 x 100 37

Converting from Scientific Notation to Decimal Notation 38

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 39