1. KU 122 Unit #7 Seminar Kirsten Muller, M. A., M. Ed. Slide 7- 1 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

2. What’s going on this week? Please remember to complete the following activities: o Reading o Practice Problems o Seminar o Discussion—Pay close attention to the feedback to your classmates! o Project All assignments are due Tuesday, November 3, 2009, by 11:59 PM EST. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

3. Introduction to Real Numbers and Algebraic Expressions 7.1Introduction to Algebra 7.2The Real Numbers 7.3Addition of Real Numbers 7.4Subtraction of Real Numbers 7.5Multiplication of Real Numbers 7.6Division of Real Numbers 7.7Properties of Real Numbers 7.8Simplifying Expressions; Order of Operations 7

4. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Algebraic Expressions An algebraic expression consists of variables, constants, numerals, and operation signs. x + 38 19 – y When we replace a variable with a number, we say that we are substituting for the variable. This process is called evaluating the expression.

5. Slide 7- 5 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Translating to Algebraic Expressions per of decreased byincreased by ratio of twice less than more than divided into times minus plus quotient product difference sum divided bymultiplied bysubtracted from added to DivisionMultiplicationSubtractionAddition

6. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Translate each phrase to an algebraic expression. PhraseAlgebraic Expression Eight more than some number One-fourth of a number Two more than four times some number Eight less than some number Five less than the product of two numbers Twenty-five percent of some number Seven less than three times some number x + 8, or 8 + x 4x + 2, or 2 + 4x n – 8 ab – 5 0.25n 3w – 7

7. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Natural Numbers The set of natural numbers = {1, 2, 3, …}. These are the numbers used for counting. Whole Numbers The set of whole numbers = {0, 1, 2, 3, …}. This is the set of natural numbers with 0 included.

8. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Integers The set of integers = {…,  5,  4,  3,  2,  1, 0, 1, 2, 3, 4, 5, …}.

9. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Absolute Value The absolute value of a number is its distance from zero on a number line. We use the symbol |x| to represent the absolute value of a number x.  5 units from 0 

10. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Find the absolute value of each number. a. |  5|b. |36| c. |0|d. |  52|

11. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Subtraction a  b The difference a  b is the number c for which a = b + c.

12. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Subtract. 1.  15  (  25)2.  13  40

13. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Objective Multiply real numbers.

14. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Multiply. 1. (7)(  9)2. 40(  1)3.  3  7

15. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley The Product of Two Negative Numbers To multiply two negative numbers, multiply their absolute values. The answer is positive.

16. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example C Multiply. 1.  9  3(  4) 2.  6  (  3)  (  4)  (  7)

17. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley The product of an even number of negative numbers is positive. The product of an odd number of negative numbers is negative.

18. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Simplify:

19. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Multiply. 1. 8(a – b) 2. (b – 7)c 3. –5(x – 3y + 2z)

20. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Factor. a.6x – 12 b. 8x + 32y – 8

21. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Factor. Try to write just the answer, if you can. a. 7x – 7y b. 14z – 12x – 20

22. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley A term is a number, a variable, a product of numbers and/or variables, or a quotient of two numbers and/or variables. Terms are separated by addition signs. If there are subtraction signs, we can find an equivalent expression that uses addition signs.

23. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Like Terms Terms in which the variable factors are exactly the same, such as 9x and –5x, are called like, or similar terms. Like TermsUnlike Terms 7x and 8x8y and 9y 2  3xy and 9xy5a 2 b and 4ab 2 The process of collecting like terms is based on the distributive laws.

24. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Combine like terms. Try to write just the answer. 1. 8x + 2x 2. 3x – 6x 3. 3a + 5b + 2 + a – 8 – 5b

25. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Remove parentheses and simplify. (8x + 5y – 3)  (4x – 2y  6)

26. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Remove parentheses and simplify. (3a + 4b – 8) – 3(–6a – 7b + 14)

27. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Simplify. 5(3 + 4) – {8 – [5 – (9 + 6)]}

28. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Simplify. [6(x + 3) – 4x] – [4(y + 3) – 8(y – 4)]

29. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Simplify. 1. 2.

30. Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Example Simplify:

31. Project Review a. - 5 + 5 = b. 4 + (-3) = c. - 6 ∙ 7 = d. - 6 (-7) = e. 76 + (-15) + (-18) + (- 6) = Translate each phrase: a. Seven more than a number b. Three multiplied by a number c. Three times a number plus seven Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

32. Questions?? Email me: kmuller@kaplan.edu Address me in “Course Questions.” Office Hours: Tuesday 7:00-9:00 PM EST Cell phone: 816-591-2070 Have a great week! Slide 7- 32 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley