1. Welcome to MM212! Unit 1 Seminar: To resize your pods: Place your mouse here. Left mouse click and hold. Drag to the right to enlarge the pod. To maximize chat, minimize roster by clicking here

2. Highlights from the Syllabus Contact information: –Kaplan email: ahalverson@kaplan.eduahalverson@kaplan.edu –AIM Instant Messenger Name: ahalversonoffice –Office hours: Monday, 9:00pm – 10:00pm (ET) Sunday, 9:00pm – 10:00pm (ET) Or by Appointment

3. Seminar Policies Show up on time Participate often in a respectful manner Stay on topic, and stay until the end.

4. Seminar Policies Show up on time Participate often in a respectful manner Stay on topic, and stay until the end. I will often post chunks of information all at once, but then I will pause and ask whether there are any questions. This gives you time to catch up on reading, and it gives me time to read your comments and questions. I highly recommend keeping some paper and a pencil handy for trying problems along the way.

5. Seminar Policies If I specifically want you to answer a question or solve a problem for me, I will begin the line with EVERYONE: followed by the question.

6. Seminar Policies If I specifically want you to answer a question or solve a problem for me, I will begin the line with EVERYONE: followed by the question. I grade you on whether you respond to these questions.

7. Seminar Policies If I specifically want you to answer a question or solve a problem for me, I will begin the line with EVERYONE: followed by the question. I grade you on whether you respond to these questions. If you have a particular comment/question for me, start the line with ANDREW: so I know to read it and respond to it.

8. Seminar Policies (Grading) I grade you on your responses to the questions I pose that begin with EVERYONE: Leaving early or arriving late will also receive a deduction.

9. Seminar (Option #2) Sometimes you may not be able to come to the seminar, and that’s okay In those events, you will complete the Seminar Option #2 assignment. Under the “Seminar” week under the Unit tab, there will be a quiz containing six problems The questions are multiple choice, and each correct answer will be worth 1 point Option 2 is due by Tuesday at 11:59 pm ET of the Unit

10. Questions? EVERYONE: Any questions on the seminar?

11. Discussion Forum Discussion Questions provide a forum for students to ask questions and answer important questions about the course material.

12. Discussion Forum Discussion Questions provide a forum for students to ask questions and answer important questions about the course material. The Discussion Questions also allow students to receive feedback from the instructor and other students in the class.

13. Discussion Forum Discussion Questions provide a forum for students to ask questions and answer important questions about the course material. The Discussion Questions also allow students to receive feedback from the instructor and other students in the class. A Discussion Question grade will be posted to the grade sheet for each Unit.

14. Discussion Forum (Grading) The discussion grade is worth 30 points each week

15. Discussion Forum (Grading) The discussion grade is worth 10 points each week There are two discussion questions each week

16. Discussion Forum (Grading) The discussion grade is worth 10 points each week There are two discussion questions each week To receive full credit, you must do the following:

17. Discussion Forum (Grading) The discussion grade is worth 10 points each week There are two discussion questions each week To receive full credit, you must do the following: –(1) fully answer each discussion question

18. Discussion Forum (Grading) The discussion grade is worth 10 points each week There are two discussion questions each week To receive full credit, you must do the following: –(1) fully answer each discussion question –(2) in each discussion forum provide at least two responses to posts provided by me or your classmates

19. Discussion Forum (Grading) The discussion grade is worth 10 points each week There are one discussion question each week To receive full credit, you must do the following: –(1) fully answer the discussion question –(2) in each discussion forum provide two “substantive” responses to posts provided by me or your classmates

20. Discussion Forum (TIPS) To receive full credit, here are some tips for you:

21. Discussion Forum (TIPS) To receive full credit, here are some tips for you: –(1) feel free to respond to any question I ask (even if it’s not specifically directed to you. Any question is far game for you to answer )

22. Discussion Forum (TIPS) To receive full credit, here are some tips for you: –(1) feel free to respond to any question I ask (even if it’s not specifically directed to you. Any question is far game for you to answer ) –(2) Show your work to every problem

23. Discussion Forum (TIPS) To receive full credit, here are some tips for you: –(1) feel free to respond to any question I ask (even if it’s not specifically directed to you. Any question is far game for you to answer ) –(2) Show your work to every problem –(3) Say more than “I agree” or “Good job” in your responses. These are usually not considered substantive,and so they will receive no credit. Asking questions of each other and responding to the questions I pose will usually help to avoid this

24. Discussion Forum One more note……Perfection is not required All that I ask is that you make your best effort.

25. Discussion Forum One more note……Perfection is not required All that I ask is that you make your best effort. If you make an error, I or your classmates will provide constructive criticism and also provide tips for improvement

26. Discussion Forum One more note……Perfection is not required All that I ask is that you make your best effort. If you make an error, I or your classmates will provide constructive criticism and also provide tips for improvement The discussion forum is your place to do a problem and receive feedback before you submit the graded assignments.

27. Discussion Forum Lastly, I also use the forum to cover material we are not able to cover in the seminar.

28. Discussion Forum Lastly, I also use the forum to cover material we are not able to cover in the seminar. Participating a lot in the discussion forum can help you learn the material and receive feedback from me on how to do the problems.

29. Discussion Forum and Seminar (TIPS) Each week the Discussion and Seminar grades account for 36 points (for a total of 324 points)

30. Discussion Forum and Seminar (TIPS) Each week the Discussion and Seminar grades account for 36 points (for a total of 324 points) This will account for 32% of your overall grade.

31. Discussion Forum and Seminar (TIPS) TIP: I strongly encourage you to participate fully participate in both the discussion forum and seminar.

32. Discussion Forum and Seminar (TIPS) TIP: I strongly encourage you to participate fully participate in both the discussion forum and seminar. Doing these will give your grade a good boost by 32%.

33. Discussion Forum and Seminar (TIPS) TIP: I strongly encourage you to participate fully participate in both the discussion forum and seminar. Doing these will give your grade a good boost by 32%. But also, not doing these assignments can drag your grade down by 32%.

34. EVERYONE: Any questions on the discussion forum or seminar?

35. MML Graded Practice The graded assignments will be done using the MyMathLab (MML) resource. To access it, you will click on “MML Graded Practice” under the Unit tab

36. MML Graded Practice There is no time limit on how long you take to complete this assignment. The assignment may be submitted more than one time –This means you can continue doing the assignments until you make a 100%. –Don’t let this opportunity pass you by! It must be completed during the unit assigned.

37. MML Resources The MML resource is a supplement to your textbook, but it is an excellent resource to receive additional help. Let’s review some of the features of MML…

38. MML Resources Help Me Solve – This feature is as it sounds…. It helps you to walk you through the steps to solve a problem. When using this feature, I would recommend taking notes on what the program says and how it solves the problem. You can use those notes as you work additional and similar problems

39. MML Resources View An Example – when you click this button, you will see a similar problem to the one you are working on. The difference from the “Help Me Solve” feature is that the MML program will walk solve the problem for you, as if an instructor was at the blackboard showing you

40. MML Resources Ask My Instructor – when you click this button, an email will be sent to me to ask for my assistance on solving a problem. When you use this feature, I would like you to attempt the problem and show me your work in solving the problem. Seeing your work allows me to see how you are approaching the problem. Plus, it allows me to see what areas you are strong in, and what areas you need assistance with When you do the “Graded Practice”, I would discourage you from using this feature, because I am not fully able to discuss or provide the solution. I encourage you to use this feature on other practice problems you do in MML.

41. Enter Answers in MML Please be sure to do the tutorial “How do I enter answers?” This will show you how to enter your answers in MML. To access this tutorial, click on “MML Resources” under the Course Home tab.

42. MML Features One feature to note is that for each problem you work, there will be a reference to the Chapter and Section that the problem comes from.  Plus, it will refer you to a similar exercise out of the textbook. For example, in the picture above, the question comes from Chapter 1, Section 3, and refers to problem 15 from that homework set When you have a question on a problem, I would like you to refer to the referenced problem out of the textbook. You can use our assistance to aid with the graded problem

43. Let’s get started!!!

44. Unit 1: Sets of Numbers NATURAL NUMBERS: also called COUNTING NUMBERS are whole numbers used for counting.

45. Unit 1: Sets of Numbers NATURAL NUMBERS: also called COUNTING NUMBERS are whole numbers used for counting. The set starts with 1 and increases in increments of. The set would look like this: {1, 2, 3, 4, 5, 6, …}.

46. Unit 1: Sets of Numbers NATURAL NUMBERS: also called COUNTING NUMBERS are whole numbers used for counting. T The set starts with 1 and increases in increments of. The set would look like this: {1, 2, 3, 4, 5, 6, …}. The “…” at the end means that this set follows this pattern. For example, 7 would be the next number in the set

47. Unit 1: Sets of Numbers NATURAL NUMBERS: also called COUNTING NUMBERS are whole numbers used for counting. T The set starts with 1 and increases in increments of. The set would look like this: {1, 2, 3, 4, 5, 6, …}. The “…” at the end means that this set follows this pattern. For example, 7 would be the next number in the set EVERYONE: Would 0 be a Natural Number?

48. Unit 1: Sets of Numbers NATURAL NUMBERS: also called COUNTING NUMBERS are whole numbers used for counting. T The set starts with 1 and increases in increments of. The set would look like this: {1, 2, 3, 4, 5, 6, …}. The “…” at the end means that this set follows this pattern. For example, 7 would be the next number in the set EVERYONE: Would 0 be a Natural Number? –Answer: No  The set starts with 1 and you cannot increase to get to 0

49. Whole Numbers WHOLE NUMBERS: include all of the natural numbers plus the number 0. The set looks like this: {0, 1, 2, 3, 4, …}.

50. Whole Numbers WHOLE NUMBERS: include all of the natural numbers plus the number 0. The set looks like this: {0, 1, 2, 3, 4, …}. EVERYONE: Would 5 be a Whole Number?

51. Whole Numbers WHOLE NUMBERS: include all of the natural numbers plus the number 0. The set looks like this: {0, 1, 2, 3, 4, …}. EVERYONE: Would 5 be a Whole Number? –Answer: Yes! The Whole Numbers include the set of Natural Numbers. Since 5 is a Natural Number, then 5 would also be a Whole Number

52. Whole Numbers WHOLE NUMBERS: include all of the natural numbers plus the number 0. The set looks like this: {0, 1, 2, 3, 4, …}. EVERYONE: Would 5 be a Whole Number? –Answer: Yes! The Whole Numbers include the set of Natural Numbers. Since 5 is a Natural Number, then 5 would also be a Whole Number EVERYONE: Would -5 be a Whole Number?

53. Whole Numbers WHOLE NUMBERS: include all of the natural numbers plus the number 0. The set looks like this: {0, 1, 2, 3, 4, …}. EVERYONE: Would 5 be a Whole Number? –Answer: Yes! The Whole Numbers include the set of Natural Numbers. Since 5 is a Natural Number, then 5 would also be a Whole Number EVERYONE: Would -5 be a Whole Number? –Answer: No  Since -5 is a not Natural Number, then -5 would not be a Whole Number

54. Integers INTEGERS: are the positive and negative whole numbers. Fractions and decimals do not fall into this category. The set is {…, -2, -1, 0, 1, 2, …}.

55. Integers INTEGERS: are the positive and negative whole numbers. Fractions and decimals do not fall into this category. The set is {…, -2, -1, 0, 1, 2, …}. EVERYONE: Would 5 be an Integer?

56. Integers INTEGERS: are the positive and negative whole numbers. Fractions and decimals do not fall into this category. The set is {…, -2, -1, 0, 1, 2, …}. EVERYONE: Would 5 be an Integer? –Answer: Yes! The Integers include the set of positive Whole Numbers. Since 5 is a Whole Number, then 5 would also be a Integer

57. Integers INTEGERS: are the positive and negative whole numbers. Fractions and decimals do not fall into this category. The set is {…, -2, -1, 0, 1, 2, …}. EVERYONE: Would 5 be an Integer? –Answer: Yes! The Integers include the set of positive Whole Numbers. Since 5 is a Whole Number, then 5 would also be a Integer EVERYONE: Would -5 be an Integer?

58. Integers INTEGERS: are the positive and negative whole numbers. Fractions and decimals do not fall into this category. The set is {…, -2, -1, 0, 1, 2, …}. EVERYONE: Would 5 be an Integer? –Answer: Yes! The Integers include the set of positive Whole Numbers. Since 5 is a Whole Number, then 5 would also be a Integer EVERYONE: Would -5 be an Integer? –Answer: Yes -5 is the negative version of the Whole Number 5, and so that would make it an Integer

59. Rational Numbers RATIONAL NUMBERS: are numbers that can be expressed in the form of a ratio

60. Rational Numbers RATIONAL NUMBERS: are numbers that can be expressed in the form of a ratio –Tip: Any number that can be written as a fraction will be a rational number

61. Rational Numbers RATIONAL NUMBERS: are numbers that can be expressed in the form of a ratio –Tip: Any number that can be written as a fraction will be a rational number EVERYONE: Would -1/2 be a Rational Number?

62. Rational Numbers RATIONAL NUMBERS: are numbers that can be expressed in the form of a ratio –Tip: Any number that can be written as a fraction will be a rational number EVERYONE: Would -1/2 be a Rational Number? –Answer: Yes Since -1/2 is a fraction, then it would be a rational number. It doesn’t matter that it’s also negative.

63. Rational Numbers RATIONAL NUMBERS: are numbers that can be expressed in the form of a ratio –Tip: Any number that can be written as a fraction will be a rational number EVERYONE: Would -1/2 be a Rational Number? –Answer: Yes Since -1/2 is a fraction, then it would be a rational number. It doesn’t matter that it’s also negative. EVERYONE: Would 5 be a Rational Number?

64. Rational Numbers RATIONAL NUMBERS: are numbers that can be expressed in the form of a ratio –Tip: Any number that can be written as a fraction will be a rational number EVERYONE: Would -1/2 be a Rational Number? –Answer: Yes Since -1/2 is a fraction, then it would be a rational number. It doesn’t matter that it’s also negative. EVERYONE: Would 5 be a Rational Number? –Answer: Yes! Recall that 5 can be written as the fraction 5/1. That means that it is a fraction, and thus, it is a rational number

65. Irrational Numbers IRRATIONAL NUMBERS: when these are in decimal form, these two conditions must be true: –the decimal number is NON-REPEATING (does not repeat) –the decimal number is NON-TERMINATING (does not stop) NOTE: If your number is a rational number, then it will NOT be an irrational number Examples of irrational numbers include: √2, Π

66. Real Numbers REAL NUMBERS include all rational and irrational numbers, which includes all the sets described thus far TIP: every number will be a Real Number

67. Unit 1: Addition of Real Numbers The ADDITIVE INVERSE of a term is its OPPOSITE

68. Unit 1: Addition of Real Numbers The ADDITIVE INVERSE of a term is its OPPOSITE –For example, the additive inverse of 5 is -5. –The additive inverse of -10x is 10x. – In other words, the same thing with the opposite sign.

69. Unit 1: Addition of Real Numbers The ADDITIVE INVERSE of a term is its OPPOSITE –For example, the additive inverse of 5 is -5. The additive inverse of -10x is 10x. In other words, the same thing with the opposite sign. EVERYONE: What’s the additive inverse of -3?

70. Unit 1: Addition of Real Numbers The ADDITIVE INVERSE of a term is its OPPOSITE –For example, the additive inverse of 5 is -5. The additive inverse of -10x is 10x. In other words, the same thing with the opposite sign. EVERYONE: What’s the additive inverse of -3? Answer: The opposite of a negative is a positive. Thus, the additive inverse of -3 would be 3

71. Unit 1: Addition of Real Numbers The next idea is that of the absolute value

72. Unit 1: Addition of Real Numbers The next idea is that of the absolute value ABSOLUTE VALUE describes a distance, the distance from zero on the number line. I think of this as moving a game piece. (Note: this number is never a negative number)

73. Unit 1: Addition of Real Numbers The next idea is that of the absolute value ABSOLUTE VALUE describes a distance, the distance from zero on the number line. I think of this as moving a game piece. (Note: this number is never a negative number) If you’re looking for the absolute value of 5: | 5 |, then start your game piece on positive 5, move your piece one spot at a time until you reach zero, and count up how many jumps you made. | 5 | = 5 since the number 5 is 5 jumps away from zero.

74. Absolute Value EVERYONE: What’s the |7| = ?

75. Absolute Value EVERYONE: What’s the |7| = ? Answer: |7| = 7 EVERYONE: What’s the |-25| = ?

76. Absolute Value EVERYONE: What’s the |7| = ? Answer: |7| = 7 EVERYONE: What’s the |-25| = ? Answer: |-25| = 25 NOTE: The absolute value makes everything positive

77. Absolute Value EVERYONE: Questions so far?

78. Unit 1: Addition of Real Numbers SAME SIGN RULE: if you are adding two terms of the same sign – both positive or both negative – then ADD the values and KEEP the sign.

79. Unit 1: Addition of Real Numbers SAME SIGN RULE: if you are adding two terms of the same sign – both positive or both negative – then ADD the values and KEEP the sign. Example: 5 + 7 = 12

80. Unit 1: Addition of Real Numbers SAME SIGN RULE: if you are adding two terms of the same sign – both positive or both negative – then ADD the values and KEEP the sign. Example: 5 + 7 = 12 Example: -5 + (-7) = -12

81. Addition of Numbers DIFFERENT SIGNS RULE: if you are adding two terms that have different signs – one term is positive and the other is negative – then SUBTRACT the smaller from the larger, and TAKE THE SIGN OF THE LARGER

82. Addition of Numbers DIFFERENT SIGNS RULE: if you are adding two terms that have different signs – one term is positive and the other is negative – then SUBTRACT the smaller from the larger, and TAKE THE SIGN OF THE LARGER Example: 4 + (-3) = 1

83. Addition of Numbers DIFFERENT SIGNS RULE: if you are adding two terms that have different signs – one term is positive and the other is negative – then SUBTRACT the smaller from the larger, and TAKE THE SIGN OF THE LARGER Example: 4 + (-3) = 1 Example: (-6) + 1 = -5

84. Addition of Numbers EVERYONE: Add: -40 + (-32)

85. Addition of Numbers EVERYONE: Add: -40 + (-32) Answer: -72 EVERYONE: Add: -14 + 8

86. Addition of Numbers EVERYONE: Add: -40 + (-32) Answer: -72 EVERYONE: Add: -14 + 8 Answer: -6

87. Questions? EVERYONE: Questions?

88. Unit 1: Subtraction of Real Numbers Since we know how to add numbers together, we are going to change the subtraction problem into an addition problem. This will allow us to use our sign rules You may do this if you follow this process: 1.Keep the first number as it is 2.Change the minus (subtraction) to a plus (addition) 3.Replace the second number with its additive inverse (opposite) Example: We can change 3 – 4 into addition by writing: 3 + (-4). Then we apply our rules for adding different signs to get: 3 – 4 = -1

89. Subtraction of Numbers EVERYONE: Subtract: 6 – 2

90. Subtraction of Numbers EVERYONE: Subtract: 6 – 2 –Answer: 6 – 2 = 4 EVERYONE: Subtract 3 – 5

91. Subtraction of Numbers EVERYONE: Subtract: 6 – 2 –Answer: 6 – 2 = 4 EVERYONE: Subtract 3 – 5 –Answer: For this we would do the following: 3 – 5 = 3 + (-5) = -2 Done! Thus, the answer is -2

92. EVERYONE: Questions?

93. Unit 1: Multiplication and Division of Real Numbers SIGN RULES Alright – the sign rules. Luckily, the signs rules for multiplication and division are the same. Below are the rules, assuming only two numbers are involved.

94. Unit 1: Multiplication and Division of Real Numbers SIGN RULES Alright – the sign rules. Luckily, the signs rules for multiplication and division are the same. Below are the rules, assuming only two numbers are involved. Positive * Positive = Positive Positive / Positive = Positive

95. Unit 1: Multiplication and Division of Real Numbers SIGN RULES Alright – the sign rules. Luckily, the signs rules for multiplication and division are the same. Below are the rules, assuming only two numbers are involved. Positive * Positive = Positive Positive / Positive = Positive Positive * Negative = Negative Positive / Negative = Negative

96. Unit 1: Multiplication and Division of Real Numbers SIGN RULES Alright – the sign rules. Luckily, the signs rules for multiplication and division are the same. Below are the rules, assuming only two numbers are involved. Positive * Positive = Positive Positive / Positive = Positive Positive * Negative = Negative Positive / Negative = Negative Negative * Positive = Negative Negative / Positive = Negative

97. Unit 1: Multiplication and Division of Real Numbers SIGN RULES Alright – the sign rules. Luckily, the signs rules for multiplication and division are the same. Below are the rules, assuming only two numbers are involved. Positive * Positive = Positive Positive / Positive = Positive Positive * Negative = Negative Positive / Negative = Negative Negative * Positive = Negative Negative / Positive = Negative Negative * Negative = Positive Negative / Negative = Positive

98. Multiplication EVERYONE: Multiply (4)(6)

99. Multiplication EVERYONE: Multiply (4)(6) Answer: 24 EVERYONE: Multiply (-2)(-3)

100. Multiplication EVERYONE: Multiply (4)(6) Answer: 24 EVERYONE: Multiply (-2)(-3) Answer 6 EVERYONE: Divide (20)/(-5)

101. Multiplication EVERYONE: Multiply (4)(6) Answer: 24 EVERYONE: Multiply (-2)(-3) Answer 6 EVERYONE: Divide (20)/(-5) Answer: -4

102. EVERYONE: Questions?

103. Unit 1: Multiplication and Division of Real Numbers ZERO IN MULTIPLICATION AND DIVISION There are 2 cases

104. Unit 1: Multiplication and Division of Real Numbers ZERO IN MULTIPLICATION AND DIVISION There are 2 cases 1.0 in the numerator (dividend) only, then the answer will be 0

105. Unit 1: Multiplication and Division of Real Numbers ZERO IN MULTIPLICATION AND DIVISION There are 2 cases 1.0 in the numerator (dividend) only, then the answer will be 0 2.0 in the denominator (divisor) only, then the answer will be UNDEFINED

106. Questions? EVERYONE: Questions on multiplying or dividing?

107. Exponents Exponents is a shorthand way of writing multiplication. Suppose you had: (2)(2)(2)(2). The way to write this with exponents is: 2 4 The little number is called a superscript, and it tells you how many times to multiply the base times itself. Example: 4 3 = 4*4 *4 = 16 Example: (-3) 2 = (-3)(-3) = 9

108. Exponents Exponents is a shorthand way of writing multiplication.

109. Exponents Exponents is a shorthand way of writing multiplication. Suppose you had: (2)(2)(2)(2). The way to write this with exponents is: 2 4

110. Exponents Exponents is a shorthand way of writing multiplication. Suppose you had: (2)(2)(2)(2). The way to write this with exponents is: 2 4 The little number is called a superscript, and it tells you how many times to multiply the base times itself.

111. Exponents Exponents is a shorthand way of writing multiplication. Suppose you had: (2)(2)(2)(2). The way to write this with exponents is: 2 4 The little number is called a superscript, and it tells you how many times to multiply the base times itself. Example: 4 3 = 4*4 *4 = 64

112. Exponents Exponents is a shorthand way of writing multiplication. Suppose you had: (2)(2)(2)(2). The way to write this with exponents is: 2 4 The little number is called a superscript, and it tells you how many times to multiply the base times itself. Example: 4 3 = 4*4 *4 = 16 Example: (-3) 2 = (-3)(-3) = 9

113. Order of Operations The order of operations are a set of rules you follow in order to simplify a mathematical expression. The order is as follows: Parentheses Exponents Multiply/Divide Add/Subtract I will use PEMDAS for short Let me explain what each mean and how they will be simplified

114. Parentheses PARENTHESES: refers to all grouping symbols. Grouping symbols are one of the following: –parentheses ( ) braces { } –brackets [ ] absolute value | | Do what operations you can inside until there is only a single number left inside (no operations to do). Then get rid of the parentheses. –Treat absolute value as a parentheses –If have an absolute value, simplify until you get a single number inside. Then take the absolute value of the number

115. Exponents EXPONENTS/RADICALS: for exponents, expand and evaluate (write as a long multiplication problems then multiply). For radicals (square roots, cube roots, etc.), calculate these in the same step as you would work on exponents.

116. Multiply and Divide MULTIPLICATION and DIVISION: perform these as they occur from left to right. Do not first do all multiplication and then come back for division. The projects and quizzes will test you on this. Be sure to do your multiplication and division from left to right

117. Add and Subtract ADDITION and SUBTRACTION: by now, this is all you have left to do. Perform these as they occur from left to right. Do not first do all addition and then come back for subtraction. The projects and quizzes will test you on this. Be sure to do your addition and subtraction from left to right

118. PEMDAS examples The best way to see how PEMDAS works is to see it in some examples. Here’s our first one… Example: Apply PEMDAS to the following 2(3 – 5 + 6) + 5

119. PEMDAS examples The best way to see how PEMDAS works is to see it in some examples. Here’s our first one… Example: Apply PEMDAS to the following 2(3 – 5 + 6) + 5 = 2(-2 + 6) + 5 [do 3 – 5 in the parentheses]

120. PEMDAS examples The best way to see how PEMDAS works is to see it in some examples. Here’s our first one… Example: Apply PEMDAS to the following 2(3 – 5 + 6) + 5 = 2(-2 + 6) + 5 [do 3 – 5 in the parentheses] = 2(4) + 5 [do -2 + 6 in the parentheses]

121. PEMDAS examples The best way to see how PEMDAS works is to see it in some examples. Here’s our first one… Example: Apply PEMDAS to the following 2(3 – 5 + 6) + 5 = 2(-2 + 6) + 5 [do 3 – 5 in the parentheses] = 2(4) + 5 [do -2 + 6 in the parentheses] = 8 + 5 [multiply 2(4) to get 8]

122. PEMDAS examples The best way to see how PEMDAS works is to see it in some examples. Here’s our first one… Example: Apply PEMDAS to the following 2(3 – 5 + 6) + 5 = 2(-2 + 6) + 5 [do 3 – 5 in the parentheses] = 2(4) + 5 [do -2 + 6 in the parentheses] = 8 + 5 [multiply 2(4) to get 8] = 13 [add 8 + 5 to get 13] Done!

123. PEMDAS example Here’s another example:11 – 3(4) 2 ÷ (-6)

124. PEMDAS example Here’s another example:11 – 3(4) 2 ÷ (-6) 11 – 3(4) 2 ÷ (-6) = 11 – 3(16) ÷ (-6)[do exponent: 4 2 to get 16]

125. PEMDAS example Here’s another example:11 – 3(4) 2 ÷ (-6) 11 – 3(4) 2 ÷ (-6) = 11 – 3(16) ÷ (-6)[do exponent: 4 2 to get 16] = 11 – 48 ÷ (-6) [multiply 3*16 to get 48]

126. PEMDAS example Here’s another example:11 – 3(4) 2 ÷ (-6) 11 – 3(4) 2 ÷ (-6) = 11 – 3(16) ÷ (-6)[do exponent: 4 2 to get 16] = 11 – 48 ÷ (-6) [multiply 3*16 to get 48] = 11 – (-8) [divide 48/(-6) to get -8]

127. PEMDAS example Here’s another example:11 – 3(4) 2 ÷ (-6) 11 – 3(4) 2 ÷ (-6) = 11 – 3(16) ÷ (-6)[do exponent: 4 2 to get 16] = 11 – 48 ÷ (-6) [multiply 3*16 to get 48] = 11 – (-8) [divide 48/(-6) to get -8] = 11 + 8 [two negatives next to each other makes a “+” sign]

128. PEMDAS example Here’s another example:11 – 3(4) 2 ÷ (-6) 11 – 3(4) 2 ÷ (-6) = 11 – 3(16) ÷ (-6)[do exponent: 4 2 to get 16] = 11 – 48 ÷ (-6) [multiply 3*16 to get 48] = 11 – (-8) [divide 48/(-6) to get -8] = 11 + 8 [two negatives next to each other makes a “+” sign] = 19 [add 11 + 8 to get the 19] Done!

129. EVERYONE: Simplify: -2(2 – 5) ÷ (-1) + 7

130. Answer: -2(2 – 5) ÷ (-1) + 7 = -2(-3) ÷ (-1) + 7 [Subtract in the parentheses] = 6 ÷ (-1) + 7 [Multiply/divide; left to right] = -6 + 7 = 1 [Finish with Addition] Done!