Transcript Document
MM150 – 30 Seminar 1 • Professor: Jack Refling • 7 PM Eastern Time on Wednesday • Topics • Course Policies • Real Numbers and their Properties Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar 1 Available Resources • • • • • • (MML) MyMathLab – “Ask my Instructor” Kaplan Math Center – live tutors & seminars Discussion Boards – ask for help Seminar discussions Internet resources Online Textbook (Use “Ungraded Tutorials/Multimedia Textbook”) • Study Buddy (exchange e-mails) Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar 2 My General Philosophy • So that we get off on the right foot … let me tell you what I believe regarding math and your taking this class. The reason you enrolled in this class is because it is a requirement in order to graduate with your degree. • That requirement is not going to change or disappear. Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar Put "?" in front of Questions so it is easier to see them. 3 My General Philosophy (continued) • I do not care if you have never been good at math. I do not care if you do not like math. I do not care if you stopped taking math in 3rd grade. None of that matters to me! Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar Put "?" in front of Questions so it is easier to see them. 4 My General Philosophy (continued) • What does matter to me is this … #1. You give me a chance to help you #2. You maintain a POSITIVE ATTITUDE so you give yourself a chance to be successful #3. We work TOGETHER as a TEAM so we will ALL be successful. #4. NO ONE QUITS OR DISAPPEARS! Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar Put "?" in front of Questions so it is easier to see them. 5 Syllabus Discussion • Weekly Assignments – Discussion Board – One posts and two responses – MML weekly assignment • Final Project – Examples in units 6, 7, 8 and 9 – Project of your own definition Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar 6 Expectations • What I expect of you – Assignments completed on time – Initial post to DB by end of day Saturday – Questions • What you should expect from me – Grades posted on time – Individual feedback – Responses to any questions you have Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar 7 Factors The natural numbers that are multiplied together to equal another natural number are called factors of the product. Example: The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. Divisors If a and b are natural numbers and the quotient of b divided by a has a remainder of 0, then we say that a is a divisor of b or a divides b. Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar 8 Prime and Composite Numbers A prime number is a natural number greater than 1 that has exactly two factors (or divisors), itself and 1. A composite number is a natural number that is divisible by a number other than itself and 1. The number 1 is neither prime nor composite, it is called a unit. Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar 9 Greatest Common Divisor Page 6 The greatest common divisor (GCD), also called the greatest common factor (GCF), of a set of natural numbers is the largest natural number that divides (without remainder) every number in that set. Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar 10 Example (GCD) Find the GCD of 63 and 105. 63 = 3 * 3 * 7 = 32 * 7 105 = 3 * 5 * 7 Smallest exponent of each factor: 3 and 7 So, the GCD is 3 * 7 = 21. Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar 11 Page 7 Least Common Multiple The least common multiple (LCM) of a set of natural numbers is the smallest natural number that is divisible (without remainder) by each element of the set. Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar 12 Example (LCM) Find the LCM of 63 and 105. 63 = 3 * 3 * 7 = 32 * 7 105 = 3 * 5 * 7 Greatest exponent of each factor: 32, 5 and 7 So, the LCM is 32 * 5 * 7 = 315. Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar 13 Example of GCD and LCM Find the GCD and LCM of 48 and 54. Prime factorizations of each: 48 = 2 • 2 • 2 • 2 • 3 = 24 • 3 54 = 2 • 3 • 3 • 3 = 2 • 33 GCD = 2 • 3 = 6 LCM = 24 • 33 = 432 Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar 14 Radicals 2, 17, 53 are all irrational numbers. The symbol is called the radical sign. The number or expression inside the radical sign is called the radicand. Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar 15 Principal Square Root Page 40 The principal square root of a number n, written n is the positive number that when multiplied by itself, gives n. For example, 16 = 4 since 4 4 = 16 49 = 7 since 7 7 = 49 Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar 16 Perfect Square Any number that is the square of a natural number is said to be a perfect square. The numbers 1, 4, 9, 16, 25, 36, and 49 are the first few perfect squares. Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar 17 Product Rule for Radicals a b a b, a 0, b 0 Simplify: a) 40 40 4 10 4 10 2 10 2 10 b) 125 125 25 5 25 5 5 5 5 5 Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar 18 Page 41 Addition and Subtraction of Irrational Numbers To add or subtract two or more square roots with the same radicand, add or subtract their coefficients. The answer is the sum or difference of the coefficients multiplied by the common radical. Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar 19 Example: Adding or Subtracting Irrational Numbers Simplify: 4 7 3 7 Simplify: 8 5 125 4 7 3 7 8 5 125 (4 3) 7 8 5 25 5 7 7 8 5 5 5 (8 5) 5 3 5 Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar 20 Exponents Page 54 When a number is written with an exponent, there are two parts to the expression: an, where a is called the base and n is called the exponent. The exponent tells how many times the base should be multiplied by itself, for real numbers. 45 4 4 4 4 4 Can't Type? press F11 Can’t Hear? Check: Speakers, Volume or Re-Enter Seminar 21