2. Chapter 1 Review College Algebra

3. Remember the phrase “Please Excuse My Dear Aunt Sally” or PEMDAS. ORDER OF OPERATIONS 1. Parentheses - ( ) or [ ] 2. Exponents or Powers 3. Multiply and Divide (from left to right) 4. Add and Subtract (from left to right)

4. Evaluate 7 + 4 3. Is your answer 33 or 19? You can get 2 different answers depending on which operation you did first. We want everyone to get the same answer so we must follow the order of operations.

5. Once again, evaluate 7 + 4  3 and use the order of operations. = 7 + 12(Multiply.) = 19 (Add.)

6. Example #1 14 ÷ 7 2 - 3 = 2 2 - 3 (Divide l/r.) = 4 - 3 (Multiply.) = 1(Subtract.)

7. Example #2 3(3 + 7) 2 ÷ 5 = 3(10) 2 ÷ 5(parentheses) = 3(100) ÷ 5(exponents) = 300 ÷ 5(multiplication) = 60(division)

8. Example #3 20 - 3 6 + 10 2 + (6 + 1) 4 = 20 - 3 6 + 10 2 + (7) 4(parentheses) = 20 - 3 6 + 100 + (7) 4(exponents) = 20 - 18 + 100 + (7) 4 (Multiply l/r.) = 20 - 18 + 100 + 28 (Multiply l/r.) = 2 + 100 + 28 (Subtract l/r.) = 102 + 28 (Add l/r.) = 130(Add.)

9. Which of the following represents 11 2 + 18 - 3 3 · 5 in simplified form? 1. -3,236 2. 4 3. 107 4. 16,996 Answer Now

10. Simplify 16 - 2(10 - 3) Answer Now 1. 2 2. -7 3. 12 4. 98

11. Simplify 24 – 6 · 4 ÷ 2 Answer Now 1. 72 2. 36 3. 12 4. 0

12. 1.substitute the given numbers for each variable. 2.use order of operations to solve. Evaluating a Variable Expression To evaluate a variable expression:

13. Example # 4 n + (13 - n)  5 for n = 8 = 8 + (13 - 8)  5 (Substitute.) = 8 + 5  5 (parentheses) = 8 + 1 (Divide l/r.) = 9 (Add l/r.)

14. Example # 5 8y - 3x 2 + 2n for x = 5, y = 2, n =3 = 8  2 - 3  5 2 + 2  3 (Substitute.) = 8  2 - 3  25 + 2  3 (exponents) = 16 - 3  25 + 2  3 (Multiply l/r.) = 16 - 75 + 2  3 (Multiply l/r.) = 16 - 75 + 6 (Multiply l/r.) = -59 + 6 (Subtract l/r.) = -53 (Add l/r.)

15. What is the value of -10 – 4x if x = -13? Answer Now 1. -62 2. -42 3. 42 4. 52

16. What is the value of 5k 3 if k = -4? Answer Now 1. -8000 2. -320 3. -60 4. 320

17. What is the value of if n = -8, m = 4, and t = 2 ? Answer Now 1. 10 2. -10 3. -6 4. 6

19. An expression is NOT an equation because it DOES NOT have an equal sign. There are 2 types of expressions. 5 + 84 Numerical 3x 3x + 10 Algebraic Notice there are no equal signs in these expressions so they are not equations !

20. A numerical expression contains only numbers and symbols and NO LETTERS. 5 times 3 plus 8 (53) + 8

21. An algebraic expression contains only numbers, symbols, and variables. It is sometimes referred to as a variable expression. The product of 3 and x 3x The sum of m and 8 m + 8 The difference of r and 2 r - 2

22. What is a variable? A variable represents an unknown value. 1) 4 + x 2) 10 – ? 3) 5y 4) 20 A variable can be any letter of the alphabet since it represents an unknown.

23. Word Phrases for multiplication are: The product of 5 and a number c Seven times a number t 6 multiplied by a number d 5 c or 5c 7 t or 7t 6 d or 6d

24. The Placement rule for multiplication is: The product of 5 and a number c Seven times a number t 6 multiplied by a number d 5 c or 5c 7 t or 7t 6 d or 6d Always write the variable AFTER the number.

25. Evaluate means to find the value of an algebraic expression by substituting numbers in for variables. m = 2 6 + m ? 6 + 2 8

26. Evaluate means to find the value of an algebraic expression by substituting numbers in for variables. r = 3 7 + r ? 7 + 3 10

27. Evaluate the variable expression when n = 6. 1)2) Evaluate just means solve by substitution.

28. Evaluate the variable expression when n = 6. Evaluate just means solve by substitution. 3) 4)

29. Evaluate the algebraic expression when n = 8. 1)2)

30. Evaluate the expression if a = 3 and b = 4. 1)2)

31. Evaluate the expression if a = 3 and b = 4. 3)4)

32. Evaluate the expression if x = 5 and y = 3. 1) 2)

33. #2 Show the substitution. Show your work down. Circle your answer. Show your work one step at a time down. No equal signs! Evaluate means solve. Evaluate i f x = 3 and y = 4

34. Combining Like Terms  In algebra we often get very long expressions, which we need to make simpler. Simpler expressions are easier to solve!  To simplify an expression we collect like terms. Like terms include letters that are the same and numbers.

35. Let ’ s try one…  Step One: Write the expression. 4x + 5x -2 - 2x + 7  Collect all the terms together which are alike. Remember that each term comes with an operation (+,- ) which goes before it. 4x, 5x, and -2x -2 and 7  Simplify the variable terms. 4x+5x-2x = 9x-2x = 7x  Simplify the constant (number) terms. -2+7 = 5  You have a simplified expression by writing all of the results from simplifying. 7x + 5

36. Another example…  10x – 4y + 3x 2 + 2x – 2y 3x 2 10x, 2x -4y – 2y  3x 2 + 12x – 6y Remember you cannot combine terms with the same variable but different exponents.

37. Now you try… Simplify the following:  5x + 3y - 6x + 4y + 3z  3b - 3a - 5c + 4b  4ab – 2a 2 b + 5 – ab + ab 2 + 2a 2 b + 4  5xy – 2yx + 7y + 3x – 4xy + 2x A A A A

38. You Try #1  Simplify the following: 1. 5x + 3y - 6x + 4y + 3z 5x, -6x 3y, 4y 3z -x + 7y + 3z

39. You Try #2  Simplify the following: 2. 3b - 3a - 5c + 4b 3b, 4b -3a -5c -3a + 7b – 5c

40. You Try #3  Simplify the following: 3. 4ab – 2a 2 b + 5 – ab + ab 2 + 2a 2 b + 4 4ab, -ab -2a 2 b, 2a 2 b 5, 4 ab 2 3ab + ab 2 + 9

41. You Try #4  Simplify the following: 4. 5xy – 2yx + 7y + 3x – 4xy + 2x 5xy, -2yx, -4xy 7y 3x, 2x -xy + 7y + 5x

42. by Mr. Fitzgerald

43. Five Properties 1.Distributive 2.Commutative 1.“order doesn’t matter” 3.Associative 1.“grouping doesn’t matter” 4.Identity properties of one and zero 5.Inverse “opposite”

45. (2 + 1) + 4 = 2 + (1 + 4) Associative Property of Addition 1.

46. 3 + 7 = 7 + 3 Commutative Property of Addition 2.

47. 8 + 0 = 8 Identity Property of Addition 3.

48. 6 4 = 4 6 Commutative Property of Multiplication 5.

49. 17 + (-17) = 0 Inverse Property of Addition 6.

50. 2(5) = 5(2) Commutative Property of Multiplication 7.

51. 3(2 + 5) = 32 + 35 Distributive Property 9.

52. 6(78) = (67)8 Associative Property of Multiplication 10.

53. 5 1 = 5 Identity Property of Multiplication 11.

55. (6 – 3)4 = 64 – 34 Distributive Property 13.

56. 1(-9) = -9 Identity Property of Multiplication 14.

57. 3 + (-3) = 0 Inverse Property of Addition 15.

58. 1 + [-9 + 3] = [1 + (-9)] + 3 Associative Property of Addition 16.

59. -3(6) = 6(-3) Commutative Property of Multiplication 17.

60. -8 + 0 = -8 Identity Property of Addition 18.

61. 37 – 34 = 3(7 – 4) Distributive Property 19.

62. 6 + [(3 + (-2)] = (6 + 3) + (- 2) Associative Property of Addition 20.

63. 7 + (-5) = -5 + 7 Commutative Property of Addition 21.

64. (5 + 4)9 = 45 + 36 Distributive Property 22.

65. -3(5 4) = (-3 5)4 Associative Property of Multiplication 23.

66. -8(4) = 4(-8) Commutative Property of Multiplication 24.

68. 5 1 / 7 + 0 = 5 1 / 7 Identity Property of Addition 25.

69. 3 / 4 – 6 / 7 = – 6 / 7 + 3 / 4 Commutative Property of Addition 26.

70. 1 2 / 5 1 = 1 2 / 5 Identity Property of Multiplication 27.

71. -8 2 / 5 + 0 = -8 2 / 5 Identity Property of Addition 29.

72. [(- 2 / 3 )(5)]9 = - 2 / 3 [(5)(9)] Associative Property of Multiplication 30.

74. 6(3 – 2n) = 18 – 12n Distributive Property 31.

75. 2x + 3 = 3 + 2x Commutative Property of Addition 32.

76. ab = ba Commutative Property of Multiplication 33.

77. a + 0 = a Identity Property of Addition 34.

78. a(bc) = (ab)c Associative Property of Multiplication 35.

79. a1 = a Identity Property of Multiplication 36.

80. a +b = b + a Commutative Property of Addition 37.

81. a(b + c) = ab + ac Distributive Property 38.

82. a + (b + c) = (a +b) + c Associative Property of Addition 39.

83. a + (-a) = 0 Inverse Property of Addition 40.