1. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 1 Real Numbers and Introduction to Algebra

2. 22 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: 1. -3 + 15 5 8 2. 3(-4) 2 – 80 2. 6[5 + 2(3 - 8) - 3] 4. -12 + 3×8 4 5. (-2)(0)(-3) -6 Simplify each expression.

3. 33 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: 1. -3 + 15 5 8 2. 3(-4) 2 – 80 2. 6[5 + 2(3 - 8) - 3] 4. -12 + 3×8 4 5. (-2)(0)(-3) -6 Simplify each expression. 51 40

4. 44 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: 1. -3 + 15 5 8 2. 3(-4) 2 – 80 2. 6[5 + 2(3 - 8) - 3] 4. -12 + 3×8 4 5. (-2)(0)(-3) -6 Simplify each expression. 51 40 -32

5. 55 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: 1. -3 + 15 5 8 2. 3(-4) 2 – 80 2. 6[5 + 2(3 - 8) - 3] 4. -12 + 3×8 4 5. (-2)(0)(-3) -6 Simplify each expression. 51 40 -32 -48

6. 66 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: 1. -3 + 15 5 8 2. 3(-4) 2 – 80 2. 6[5 + 2(3 - 8) - 3] 4. -12 + 3×8 4 5. (-2)(0)(-3) -6 Simplify each expression. 51 40 -32 -48 3

7. 77 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Bellwork: 1. -3 + 15 5 8 2. 3(-4) 2 – 80 2. 6[5 + 2(3 - 8) - 3] 4. -12 + 3×8 4 5. (-2)(0)(-3) -6 Simplify each expression. 51 40 -32 -48 3 0

8. Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 1.6 / 1.7 Multiplying and Dividing Real Numbers

9. 99 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Objectives:  Multiply and divide real numbers  Solve problems with multiplication and division  Evaluate algebraic expressions  Find reciprocals

10. 10 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 1. The product of two numbers with the same sign is a positive number. 2. The product of two numbers with different signs is a negative number. Multiplying Real Numbers

11. 11 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Multiply. a. 4(–2) = –8 b. ‒ 7( ‒ 5) = 35 c. 9( ‒ 6.2) = ‒ 55.8 d. Example 1

12. 12 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Multiply. a. 4(–2) = –8 b. ‒ 7( ‒ 5) = 35 c. 9( ‒ 6.2) = ‒ 55.8 d. Example 1

13. 13 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Multiply. a. 4(–2) = –8 b. ‒ 7( ‒ 5) = 35 c. 9( ‒ 6.2) = ‒ 55.8 d. Example 1

14. 14 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Multiply. a. 4(–2) = –8 b. ‒ 7( ‒ 5) = 35 c. 9( ‒ 6.2) = ‒ 55.8 d. Example 1

15. 15 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Multiply. a. 4(–2) = –8 b. ‒ 7( ‒ 5) = 35 c. 9( ‒ 6.2) = ‒ 55.8 d. Example 1

16. 16 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Multiply. a. 4(–2) = –8 b. ‒ 7( ‒ 5) = 35 c. 9( ‒ 6.2) = ‒ 55.8 d. Example 1

17. 17 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. If b is a real number, then b · 0 = 0 and 0 ·b = 0. Products Involving Zero

18. 18 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. If b is a real number, then b · 0 = 0 and 0 ·b = 0. Example: 9(0)( ‒ 5) = 0 Products Involving Zero

19. 19 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Evaluate. a. (–2) 4 = (–2)(–2)(–2)(–2) = 16 b. ‒ 7 2 = ‒ (7 ·7) = ‒ 49 Example 2

20. 20 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Evaluate. a. (–2) 4 = (–2)(–2)(–2)(–2) = 16 b. ‒ 7 2 = ‒ (7 ·7) = ‒ 49 Example 2

21. 21 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Evaluate. a. (–2) 4 = (–2)(–2)(–2)(–2) = 16 b. ‒ 7 2 = ‒ (7 ·7) = ‒ 49 Example 2

22. 22 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Evaluate. a. (–2) 4 = (–2)(–2)(–2)(–2) = 16 b. ‒ 7 2 = ‒ (7 ·7) = ‒ 49 Example 2

23. 23 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Evaluate. a. (–2) 4 = (–2)(–2)(–2)(–2) = 16 b. ‒ 7 2 = ‒ (7 ·7) = ‒ 49 Example 2

24. 24 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Reciprocal or Multiplicative Inverse Two numbers whose product is 1 are called reciprocals or multiplicative inverses of each other. Quotients Involving Zero The number 0 does not have a reciprocal. Finding Reciprocals

25. 25 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Reciprocal or Multiplicative Inverse Two numbers whose product is 1 are called reciprocals or multiplicative inverses of each other. Quotients Involving Zero The number 0 does not have a reciprocal. Finding Reciprocals “flip the fraction”

26. 26 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Reciprocal or Multiplicative Inverse Two numbers whose product is 1 are called reciprocals or multiplicative inverses of each other. Quotients Involving Zero The number 0 does not have a reciprocal. Finding Reciprocals “flip the fraction” cannot divide by zero!

27. 27 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Find the reciprocal. a. 55 The reciprocal is b. Example 3

28. 28 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Find the reciprocal. a. 55 The reciprocal is b. Example 3

29. 29 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Find the reciprocal. a. 55 The reciprocal is b. Example 3

30. 30 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Find the reciprocal. a. 55 The reciprocal is b. Example 3

31. 31 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Find the reciprocal. a. 55 The reciprocal is b. Example 3

32. 32 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Dividing Real Numbers 1. The quotient of two numbers with the same sign is a positive number. 2. The quotient of two numbers with different signs is a negative number.

33. 33 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Divide. a. b. c. Example 4

34. 34 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Divide. a. b. c. Example 4

35. 35 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Divide. a. b. c. Example 4

36. 36 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Divide. a. b. c. Example 4

37. 37 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. If a and b are real numbers, and b  0, then Division Involving Zero If a is a nonzero number, then

38. 38 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. If a and b are real numbers, and b  0, then Division Involving Zero If a is a nonzero number, then cannot divide by zero!

39. 39 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. If a and b are real numbers, and b  0, then Division Involving Zero If a is a nonzero number, then Negative sign in numerator or out front cannot divide by zero!

40. 40 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Use order of operations to evaluate each expression. a. b. Example 5

41. 41 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Use order of operations to evaluate each expression. a. b. Example 5

42. 42 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Use order of operations to evaluate each expression. a. b. Example 5

43. 43 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Use order of operations to evaluate each expression. a. b. Example 5

44. 44 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Use order of operations to evaluate each expression. a. b. Example 5

45. 45 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Use order of operations to evaluate each expression. a. b. Example 5

46. 46 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Use order of operations to evaluate each expression. a. b. Example 5

47. 47 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Determine whether ‒ 8 is a solution of Example 6

48. 48 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Determine whether ‒ 8 is a solution of Example 6 Plug it in!

49. 49 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Determine whether ‒ 8 is a solution of Example 6 Plug it in!

50. 50 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Determine whether ‒ 8 is a solution of Example 6 Plug it in!

51. 51 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Determine whether ‒ 8 is a solution of Example 6 Plug it in! Simplify.

52. 52 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Determine whether ‒ 8 is a solution of Example 6 Plug it in! Simplify.

53. 53 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Determine whether ‒ 8 is a solution of Example 6 Plug it in! Simplify.

54. 54 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Determine whether ‒ 8 is a solution of Example 6 Since we have a true statement, ‒ 8 is a solution of the equation. Plug it in! Simplify.

55. 55 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Exit Pass I q is a negative number, r is a positive number, and t is a positive number, determine whether each expression simplifies to positive, negative, or undeterminable. 1. q × r × t 2. t + r 3. q 2 × r × t 4. t (q + r) 5. q + t 6. r (q − t)

56. 56 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Exit Pass I q is a negative number, r is a positive number, and t is a positive number, determine whether each expression simplifies to positive, negative, or undeterminable. 1. q × r × t 2. t + r 3. q 2 × r × t 4. t (q + r) 5. q + t 6. r (q − t) negative

57. 57 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Exit Pass I q is a negative number, r is a positive number, and t is a positive number, determine whether each expression simplifies to positive, negative, or undeterminable. 1. q × r × t 2. t + r 3. q 2 × r × t 4. t (q + r) 5. q + t 6. r (q − t) negative positive

58. 58 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Exit Pass I q is a negative number, r is a positive number, and t is a positive number, determine whether each expression simplifies to positive, negative, or undeterminable. 1. q × r × t 2. t + r 3. q 2 × r × t 4. t (q + r) 5. q + t 6. r (q − t) negative positive

59. 59 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Exit Pass I q is a negative number, r is a positive number, and t is a positive number, determine whether each expression simplifies to positive, negative, or undeterminable. 1. q × r × t 2. t + r 3. q 2 × r × t 4. t (q + r) 5. q + t 6. r (q − t) negative positive undeterminable

60. 60 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Exit Pass I q is a negative number, r is a positive number, and t is a positive number, determine whether each expression simplifies to positive, negative, or undeterminable. 1. q × r × t 2. t + r 3. q 2 × r × t 4. t (q + r) 5. q + t 6. r (q − t) negative positive undeterminable

61. 61 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Exit Pass I q is a negative number, r is a positive number, and t is a positive number, determine whether each expression simplifies to positive, negative, or undeterminable. 1. q × r × t 2. t + r 3. q 2 × r × t 4. t (q + r) 5. q + t 6. r (q − t) negative positive undeterminable positive