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Please CLOSE YOUR LAPTOPS, and turn off and put away your cell phones,

Please CLOSE YOUR LAPTOPS, and turn off and put away your cell phones, and get out your note-taking materials. Sections 1.2, 1.8, 2.1 Number Sets and Properties of Real Numbers. Today’s lecture will be followed by a 20-minute quiz (Weekly Quiz 1). Sets of numbers:

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Please CLOSE YOUR LAPTOPS, and turn off and put away your cell phones,

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  1. Please CLOSE YOUR LAPTOPS, and turn off and put away your cell phones, and get out your note-taking materials.

  2. Sections 1.2, 1.8, 2.1 Number Sets and Properties of Real Numbers Today’s lecture will be followed by a 20-minute quiz (Weekly Quiz 1).

  3. Sets of numbers: • Natural (counting) numbers: N = {1, 2, 3, 4, 5, 6 . . .} • Whole numbers: W = {0, 1, 2, 3, 4 . . .} • Integers: Z = {. . . -3, -2, -1, 0, 1, 2, 3 . . .}

  4. More sets of numbers: • Rational numbers: the set (Q) of all numbers that can be expressed as a quotient of integers, with denominator  0 • Irrational numbers: the set (I) of all numbers that can NOT be expressed as a quotient of integers • Real numbers: the set (R) of all rational and irrational numbers combined The information on sets is easy to forget come quiz or test time, so make sure you have it written down in your notes!

  5. Page 11 in your online textbook (same in hardcopy version) provides a helpful diagram of all these number sets and their relationships to each other. Underneath this diagram on page 11 are some example problems (EXAMPLE 5) that will be useful in preparing to do the homework problems.

  6. Make sure you know how to open and use the online textbook. Depending on which browser you are using, you may have some trouble getting the online textbook to open the first time you try to use it. Come to the open lab if you need any help with this.

  7. You can highlight material in your online textbook, pin notes to any page, watch short videos of examples, quickly search for any word or concept anywhere in the book, and access many other useful learning tools. Learn how to use this resource!

  8. Sample problems with real numbers and subsets: What would be the answer if this question used the number -18 instead of 0?

  9. Which of the following statements are true? T T F T T F F T • A number can be negative and rational. • All irrational numbers are real. • All positive numbers are natural numbers. • All natural numbers are positive. • 27 is a rational number. • is an irrational number. • -7 is a whole number. • -5/3 is both rational and real.

  10. Properties of Real Numbers: • Commutative property • of addition: a + b = b + a • of multiplication: a· b = b· a • Associative property • of addition: (a + b) + c = a + (b + c) • of multiplication: (a· b) · c = a· (b· c) • Distributive property of multiplication over addition • a(b + c) = ab + ac

  11. Sample problem from today’s homework:

  12. Sample problem from today’s homework:

  13. Sample problems from today’s homework:

  14. Simplifying Algebraic Expressions: The terms of an expression are the addends of the expression (parts separated by + or – signs). Like terms contain the same variables raised to the same powers. To combine like terms, add or subtract their numerical coefficients, then multiply the result by the common variable factors. (Thecoefficientis the number in front of a term.)

  15. 6x2 + 7x2 19xy – 30xy 13xy2 – 7x2y 13x2 -11xy Can’t be combined (since the terms are not like terms) Examples of Combining Terms Terms Before Combining After Combining Terms

  16. Warning: It’s a bad idea to get too addicted to the “help me solve this” function, because you won’t have this to help you on quizzes and tests!!

  17. Sample problems from today’s homework:

  18. The assignment on this material (HW 4) is due at the start of the next class session. From now on, you may use a scientific calculator on homework, and on all quizzes and tests after today’s quiz. Graphing calculators and calculator apps won’t be allowed on tests and quizzes, so don’t rely on them to do your homework problems. Lab hours: Mondays through Thursdays 8:00 a.m. to 7:30 p.m.

  19. No calculators or notes can be used on this quiz. • Write your name, date, section info and on the worksheet handout and use this sheet for any scratch work you do for this quiz. • You may start the quiz when the password is written on the whiteboard. You will have 20 minutes to finish this eight-question quiz. • Remember to turn in your answer sheet to the TA when the quiz time is up. • If you finish the quiz early, you are free to leave class, or you can go back to the lab to work on Please open your laptops, log in to the MyMathLab course web site, and open Weekly Quiz 1.

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