Foundations of Real World Math
Purpose of Course showclose
“Why is math important? Why do I have to learn math?” These are typical questions that you have most likely asked at one time or another in your education. While you may learn things in math class that you will not use again, the study of mathematics is still an important one for human development. Math is widelyused in daily activities (e.g. shopping, cooking, etc.) and in most careers (e.g. medicine, teaching, engineering, construction, business, statistics in psychology, etc.). Math is also considered a “universal language.” One of the fundamental reasons why you learn math is to help you tackle problems, both mathematical and nonmathematical, with clear, concise, and logical steps. In this course, you will study important fundamental math concepts.
This course begins your journey into the “Real World Math” series. These courses are intended not just to help you learn basic algebra and geometry topics, but also to show you how these topics are used in everyday life. In this course, you will cover some of the most basic math applications, like decimals, percents, and even the dreaded “fword”–fractions. You will not only learn the theory behind these topics, but also how to apply these concepts to your life. You will learn some basic mathematical properties, such as the reflexive property, associative property, and others. The best part is that you most likely already know them, even if you did not know the proper mathematical names.
Let’s start with fractions. Have fractions ever been bothersome to you? Do you think that there is no purpose for them? In this course, you will learn that fractions are all around us in the forms of measurement, ratios, and proportions–and we think you might change your tune on the subject. You will see how to solve those sometimes troubling fraction problems, like the ones that use 1 ? and 3 ?, which don’t divide as evenly as you’d like. In case you’re not yet familiar with fractions, let’s offer a common every day example: a recipe for making chocolate chip cookies. You see a recipe that calls for 2 ? cups of flour, ¾ cup of sugar, and ½ teaspoon of vanilla, and you need to make 2 ½ the recipe amount. Each of these measurements involves fractions. If you want to make the right amount of cookies, you have to determine how much you need of each ingredient.
This course will also introduce you to decimals and percentages, which are widely used in money, finances, and measurement. Decimals are all around you, including when you download applications for your smart phone. Say, for example, you’ve just purchased the newest Angry Birds application for $0.99. The number 0.99 is a decimal. If you want to spend no more than $10.00, then you will have to determine how many other applications you can download without going over budget. In this course, you will learn how to solve complex decimal problems, such as 13.4561 – 21.03 and 301.21 * 140.31.
You will also learn to write ratios and solve proportions in the course. You are probably already very familiar with ratios, even if you’re not aware of it. A recipe that calls for “2 parts milk to 1 part flour,” or a speed limit sign that reads “55 miles per hour,” or a newspaper ad listing apples at a cost of $2.99 per pound — these are all examples of ratios. Ratios and proportions are particularly useful when doing an everyday activity like planning a party: “If I need two hams for nine guests, how many hams will I need for thirty guests?” Learning how to set up and solve problems like this is a very useful mathematical concept that is applicable to real life situations.
Finally, have you wondered how graph and charts are created with certain data? Data can be visually represented in various forms (bar graphs, circle graphs, etc.) to convey information to a reader. In this course, you will see data in common forms and will have to interpret data (for example, reading a chart of the most downloaded songs from iTunes or interpreting football statistics for your fantasy league). The final unit of the course pertains to charts and graphs and includes the interpretation and creation of various charts and graphs.
Course Information showclose
Course Designer: Eric Clark
Primary Resources: This course is composed of a range of different free, online materials. However, the course makes primary use of the following materials:
 Salman Khan’s Khan Academy Mathematics Videos
 College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} edition (Note: there is a detailed Solutions Manual for the odd problems within the textbook)
 Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics
 Subunit 1.4 Assessment
 Subsubunit 2.3.4 Assessment
 Subsubunit 2.4.2 Assessment
 Subsubunit 2.5.2 Assessment
 Subsubunit 3.2.1.5 Assessment
 Subsubunit 3.2.2.4 Assessment
 Subsubunit 3.2.6 Assessment
 Subsubunit 4.2.4 Assessment
 Subsubunit 5.2.2 Assessment
 Subsubunit 6.1.2.2 Assessment
 Subsubunit 6.3.2 Assessment
 Subunit 7.2 Assessment
 Subunit 7.3 Assessment
 Subunit 7.4 Assessment
 Subunit 7.5 Assessment
 Subunit 7.7 Assessment
 The Final Exam
In order to pass this course, you will need to earn a 70% or higher on the Final Exam. Your score on the exam will be tabulated as soon as you complete it. If you do not pass the exam, you may take it again.
Time Commitment: This course should take you a total of approximately 140.5 hours to complete. Each unit includes a “time advisory” that lists the amount of time you are expected to spend on each subunit. It may be useful to take a look at these time advisories and determine how much time you have over the next few weeks to complete each unit and to then set goals for yourself. For example, Unit 1 should take approximately 9.75 hours to complete. Perhaps you can sit down with your calendar and decide to complete subunit 1.1 (a total of 4 hours) on Monday night; subunit 1.2 (a total of 3.5 hours) on Tuesday night; subunits 1.3 and 1.4 (a total of 2.25 hours) on Wednesday night; etc.
Tips/Suggestions: Please make sure to take comprehensive notes as you work through each resource. Complete all practice problems, because this will allow you to fully understand each concept. These notes will serve as a useful review as you study for your Final Exam.
This course features a number of Khan Academy™ videos. Khan Academy™ has a library of over 3,000 videos covering a range of topics (math, physics, chemistry, finance, history and more), plus over 300 practice exercises. All Khan Academy™ materials are available for free at www.khanacademy.org.

Learning Outcomes showclose
Upon successful completion of this course, the student will be able to:
 Apply properties of operations as strategies to add and subtract. (1.OA.B.3)
 Apply properties of operations as strategies to multiply and divide. (3.OA.B.5)
 Explain how negative numbers are used together to describe quantities having an opposite direction. (6.NS.C.5)
 Solve realworld and mathematical problems involving the four operations(including fractions and decimals). (4.MD.A.2)
 Find the greatest common factor and least common multiple of whole numbers. (6.NS.B.4)
 Recognize a fraction as part of a whole. (3.NF.A.1)
 Explain equivalence of fractions. (3.NF.A.3)
 Use equivalent fractions as a strategy to add and subtract fractions with like and unlike denominators. (5.NF.A.1)
 Solve word problems involving addition and subtraction of fractions referring to the same whole and having like and unlike denominators. (5.NF.A.2)
 Determine how to solve multiplication and division of fractions problems. (5.NF.B.3, 5.NF.B.4a)
 Solve real world problems involving multiplication and division of fractions. (5.NF.B.6, 5.NF.B.7)
 Use decimal notation for fractions. (4.NF.C.6)
 Read, write, and compare decimals. (5.NBT.A.3)
 Perform operations with multidigit whole numbers and withdecimals to hundredths. (5.NBT.B.7)
 Solve multistep reallife and mathematical problems posed with decimals. (7.EE.B.3)
 Use ratio concepts to solve problems. (6.RP.A.1)
 Analyze proportional relationships, and use them to solve realworld and mathematical problems. (7.RP.A.2)
 Convert between percent, decimal, and fraction notation. (6.RP.A.3d, 7.NS.A.2d)
 Use proportional relationships to solve multistep percent problems. (7.RP.A.3)
 Represent and interpret data in various graphs. (3.MD.B.3)
Course Requirements showclose
√ Have access to a computer.
√ Have continuous broadband Internet access.
√ Have the ability/permission to install plugins or software (e.g. Adobe Reader or Flash).
√ Have the ability to download and save files and documents to a computer.
√ Have the ability to open Microsoft files and documents (.doc, .ppt, .xls, etc.).
√ Have competency in the English language.
√ Have read the Saylor Student Handbook.
Unit Outline show close
Expand All Resources Collapse All Resources

Unit 1: Number Properties
Just as in life, there are certain things in math that make you shrug and say, “Well, duh. I knew that; it’s common sense.” This unit will discuss some of the basic algebraic properties which you already know, but may not necessarily know the names of, because they are what some math teachers refer to as the “common sense” properties.
Unit 1 Time Advisory show close
The really neat thing about these properties is that you can see their uses in everyday, nonmathematical ways. For example, if you drive to work, you “commute.” Whether you are driving to work from home, or to home from work, you are making the same trip. (Ignoring those times you take a back road because you do not want to spend two hours sitting on the interstate, of course!) In math, the commutative property tells us when we can move numbers around and still get the same answer. Another example is the associative property. The people you hang out with are also known as your “associates.” If you are hanging out with two friends, but one of them is in a different room, you still have the same group of friends. The same applies to certain mathematical situations. If you are grouping numbers, depending upon the situation, the grouping is not going to change anything.
Unit 1 Learning Outcomes show close
 1.1 Laws and Properties of Addition

1.1.1 Commutative Law of Addition
 Lecture: Khan Academy’s “Commutative Law of Addition”
Link: Khan Academy’s “Commutative Law of Addition” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video to learn about the Commutative Law of Addition (also known as the Commutative Property of Addition). Watch the presentation carefully two or three times until you are able to explain how changing the order of the addition of two numbers obtains the same result.
Watching this lecture and pausing to take notes should take less than 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “The Commutative Property of Addition”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “The Commutative Property of Addition” (PDF)
Instructions: Please click on the link above and study the “Associative Property of Addition” on pages 15 and 16 of the textbook, stopping at “Grouping Symbols.” The material may also be located through the bookmark on the left side (1 The Whole Numbers, 1.2 Adding and Subtracting Whole Numbers, “The Commutative Property of Addition”), which will take you directly to the reading. This reading provides an example of the property and the formal definition of the Commutative Property of Addition.
Reading these sections should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Commutative Law of Addition”

1.1.2 Associative Law of Addition
 Lecture: Khan Academy’s “Associative Law of Addition”
Link: Khan Academy’s “Associative Law of Addition” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video to learn about the Associative Law of Addition (also known as the Associative Property of Addition). Watch the presentation carefully two or three times until you are able to explain how to associate the addition of three numbers to obtain the same result.
Watching this lecture and pausing to take notes should take less than 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “The Associative Property of Addition”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “The Associative Property of Addition” (PDF)
Instructions: Please click on the link above and study the “Associative Property of Addition” on page 17 of the textbook, stopping at “The Additive Identity.” The material may also be located through the bookmark on the left side (1 The Whole Numbers, 1.2 Adding and Subtracting Whole Numbers, “The Associative Property of Addition”), which will take you directly to the reading. This reading provides an example of the property and the formal definition of the Associative Property of Addition.
Reading this section should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Associative Law of Addition”

1.1.3 Identity Property of Addition
 Lecture: Khan Academy’s “Identity Property of 0”
Link: Khan Academy’s “Identity Property of 0” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to explain how adding zero to any number is the original number.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics' PreAlgebra Textbook, 2nd Edition: “The Additive Identity”
Link: College of the Redwoods: Department of Mathematics' PreAlgebra Textbook, 2^{nd} Edition: “The Additive Identity” (PDF)
Instructions: Please click on the link above and study “The Additive Identity” located on pages 17 and 18 of the textbook, stopping at “Adding Larger Whole Numbers.” The material can also be located through the bookmark on the left side (1 The Whole Numbers, 1.2 Adding and Subtracting Whole Numbers, “The Additive Identity”), which will take you directly to the reading. This reading provides an example of the property and the formal definition of the Additive Identity Property.
Reading this section should take less than 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Identity Property of 0”

1.1.4 Property Recognition Activity
 Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “1.2 Adding and Subtracting Whole Numbers Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “1.2 Adding and Subtracting Whole Numbers Exercises” (PDF)
Instructions: Please click on the link above; complete the oddnumbered exercises for 11–27 on page 25 and the oddnumbered exercises for 67–79 on page 27 of the textbook. These exercises can also be located through the bookmark on the left side (1 The Whole Numbers, 1.2 Adding and Subtracting Whole Numbers, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to recognize addition laws and properties and apply the concepts. The solutions to these problems are located in the “Answers” section on page 30 of the textbook. The solutions page can also be located through the bookmark on the left side (1 The Whole Numbers, 1.2 Adding and Subtracting Whole Numbers, “Answers”).
Completing this activity should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Applications  Geometry”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Applications  Geometry” (PDF)
Instructions: Please click on the link above and study the section titled “Applications – Geometry” on pages 21 and 22 of the textbook. The material can also be located through the bookmark on the left side (1 The Whole Numbers, 1.2 Adding and Subtracting Whole Numbers, “Applications  Geometry”), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems beside Example 5 on page 21 and Examples 6 and 7 on page 22. This reading provides applications to the properties and laws of addition.
Reading this section and completing the exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “1.2 Adding and Subtracting Whole Numbers Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “1.2 Adding and Subtracting Whole Numbers Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 51–65 on pages 26 and 27 of the textbook. These exercises can also be located through the bookmark on the left side (1 The Whole Numbers, 1.2 Adding and Subtracting Whole Numbers, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to apply addition laws and properties. The solutions to these problems are located in the “Answers” section on page 30 of the textbook. The solutions page can also be located through the bookmark on the left side (1 The Whole Numbers, 1.2 Adding and Subtracting Whole Numbers, “Answers”).
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “1.2 Adding and Subtracting Whole Numbers Exercises”

1.1.5 Inverse Property of Addition
 Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “The Additive Inverse”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “The Additive Inverse” (PDF)
Instructions: Please click on the link above and study the “Additive Inverse” located on page 120 of the textbook, including Example 8. The material can also be located through the bookmark on the left side (2 The Integers, 2.2 Adding Integers, “Properties of Addition of Integers”), which will take you directly to the reading. After you study and read this section, complete the “You Try It” problem next to Exercise 8. This reading provides an example of the property and the formal definition of the Additive Inverse Property.
Reading this section should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: Khan Academy’s “Inverse Property of Addition”
Link: Khan Academy’s “Inverse Property of Addition” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to explain how the Inverse Property of Addition results in zero.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “The Additive Inverse”
 1.2 Laws and Properties of Multiplication

1.2.1 Commutative Law of Multiplication
 Lecture: Khan Academy’s “Commutative Law of Multiplication”
Link: Khan Academy’s “Commutative Law of Multiplication” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to explain how changing the order of the multiplication of two numbers obtains the same result.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “The Commutative Property of Multiplication”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “The Commutative Property of Multiplication” (PDF)
Instructions: Please click on the link above; study the introduction to “Multiplication and Division of Whole Numbers” on page 33 and continue through “The Commutative Property of Multiplication” on page 34. The material can also be located through the bookmark on the left side (1 The Whole Numbers, 1.3 Multiplication and Division of Whole Numbers), which will take you directly to the reading. This reading provides an example of the property and the formal definition of the Commutative Property of Multiplication.
Reading this section should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Commutative Law of Multiplication”

1.2.2 Associative Law of Multiplication
 Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “The Associative Property of Multiplication”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “The Associative Property of Multiplication” (PDF)
Instructions: Please click on the link above and study “The Associative Property of Multiplication” on page 35 of the textbook. The material can also be located through the bookmark on the left side (1 The Whole Numbers, 1.3 Multiplication and Division of Whole Numbers, “The Associative Property of Multiplication), which will take you directly to the reading. This reading provides an example of the property and the formal definition of the Associative Property of Multiplication.
Reading this section should take less than 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: Khan Academy’s “Associative Law of Multiplication”
Link: Khan Academy’s “Associative Law of Multiplication” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to explain how to associate the multiplication of three numbers to obtain the same result.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “The Associative Property of Multiplication”

1.2.3 Identity Property of Multiplication
 Lecture: Khan Academy’s “Identity Property of 1”
Link: Khan Academy’s “Identity Property of 1” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to explain how multiplying any number by one results in the original number.
Watching this lecture and pausing to take notes should take less than 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “The Multiplicative Identity”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “The Multiplicative Identity” (PDF)
Instructions: Please click on the link above and study “The Multiplicative Identity” on page 34 of the textbook. The material can also be located through the bookmark on the left side (1 The Whole Numbers, 1.3 Multiplication and Division of Whole Numbers, “The Multiplicative Identity”), which will take you directly to the reading. This reading provides an example of the property and the formal definition of the Multiplicative Property.
Reading this section should take less than 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Identity Property of 1”

1.2.4 Property Recognition Activity
 Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “1.3 Multiplication and Division of Whole Numbers Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “1.3 Multiplication and Division of Whole Numbers Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 5–27 on page 44 of the textbook. These exercises can also be located through the bookmark on the left side (1 The Whole Numbers, 1.3 Multiplication and Division of Whole Numbers, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to recognize addition laws and properties and apply these concepts. The solutions to these problems are located in the “Answers” section on page 49 of the textbook. The solutions page can also be located through the bookmark on the left side (1 The Whole Numbers, 1.3 Multiplication and Division of Whole Numbers, “Answers”).
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Application  Area”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Application  Area” (PDF)
Instructions: Please click on the link above and study the section titled “Application –Area” through Example 4 on pages 42 and 43 of the textbook. The material can also be located through the bookmark on the left side (1 The Whole Numbers, 1.3 Multiplication and Division of Whole Numbers, “Applications  Area”), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems beside Example 4 on page 43. This reading provides applications to the properties and laws of multiplication.
Reading this section should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “1.3 Multiplication and Division of Whole Numbers Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “1.3 Multiplication and Division of Whole Numbers Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 49–59 on pages 45 and 46 of the textbook. These exercises can also be located through the bookmark on the left side (1 The Whole Numbers, 1.3 Multiplication and Division of Whole Numbers, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to find the area of rectangles as well apply multiplication such as if a math tutor was paid $20 per hour and worked 20 hours, how much would the tutor get paid? The solutions to these problems are located in the “Answers” section on page 50 of the textbook. The solutions page can also be located through the bookmark on the left side (1 The Whole Numbers, 1.3 Multiplication and Division of Whole Numbers, “Answers”).
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “1.3 Multiplication and Division of Whole Numbers Exercises”

1.2.5 Inverse Property of Multiplication
 Lecture: Khan Academy’s “Inverse Property of Multiplication”
Link: Khan Academy’s “Inverse Property of Multiplication” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to explain how the inverse property of multiplication results in one.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “The Multiplicative Inverse Property”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “The Multiplicative Inverse Property” (PDF)
Instructions: Please click on the link above and study “The Multiplicative Inverse Property” through Example 1 on pages 266 and 267 of the textbook. The material can also be located through the bookmark on the left side (4 Fractions, 4.3 Reciprocals, “The Multiplicative Inverse Property”), which will take you directly to the material. After you read and study this section, attempt the “You Try It” problem beside Example 1. Check your answer on page 267. This reading provides an example of the property and the formal definition of the Multiplicative Inverse Property.
Reading this section should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Inverse Property of Multiplication”

1.2.6 Multiplication by Zero
 Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Multiplication by Zero”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Multiplication by Zero” (PDF)
Instructions: Please click on the link above and study the section titled “Multiplication by Zero” on pages 34 and 35 of the textbook. You may stop when you reach the section titled “The Associative Property of Multiplication.” The material can also be located through the bookmark on the left side (1 Whole Numbers, 1.3 Multiplication and Division of Whole Numbers, “Multiplication by Zero”), which will take you directly to the reading. This reading provides an example of the property and the formal definition of the Multiplication by Zero.
Reading this section should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Multiplication by Zero”

1.3 Dividing by Zero Is Undefined
 Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Division by Zero Is Undefined”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Division by Zero Is Undefined” (PDF)
Instructions: Please click on the link above and study the section titled “Division by Zero Is Undefined” on page 40 of the textbook, stopping at “Dividing Larger Whole Numbers.” The material can also be located through the bookmark on the left side (1 The Whole Numbers, 1.3 Multiplication and Division of Whole Numbers, “Division by Zero is Undefined”), which will take you directly to the reading. This reading provides an example of the property and the formal definition of why division by zero is undefined.
Reading this section should take less than 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “1.3 Multiplication and Division of Whole Numbers Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “1.3 Multiplication and Division of Whole Numbers Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 69–75 on page 46 of the textbook. The exercises can also be located through the bookmark on the left side (1 The Whole Numbers, 1.3 Multiplication and Division of Whole Numbers, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to apply multiplication laws and properties. The solutions to these problems are located in the “Answers” section on page 50 of the textbook. The solutions page can also be located through the bookmark on the left side (1 The Whole Numbers, 1.3 Multiplication and Division of Whole Numbers, “Answers”).
Completing this activity should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: Khan Academy’s “Why Dividing by Zero Is Undefined”
Link: Khan Academy’s “Why Dividing by Zero Is Undefined” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to explain why dividing by zero is undefined.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Division by Zero Is Undefined”

1.4 Distributive Property
 Lecture: Khan Academy’s “The Distributive Property” and “The Distributive Property 2”
Link: Khan Academy’s “The Distributive Property” (YouTube) and “The Distributive Property 2” (YouTube)
Instructions: Please click on the links above and take notes as you watch these videos. Watch the first presentation carefully two or three times until you are able to explain how the distributive property applies with an addition expression. Watch the second presentation carefully two or three times until you are able to explain how the distributive property applies with a subtraction expression.
Watching these lectures and pausing to take notes should take approximately 30 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Mental ArithmeticUsing the Distributive Property”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Mental ArithmeticUsing the Distributive Property” (HTML or PDF)
Instructions: Please click on the link above and read “The Distributive Property” section through “Sample Set A.” Then, complete “Practice Set A,” exercises 17. The solutions to the problems are revealed below each problem. These problems will allow you to practice using the distributive property to simplify algebraic expressions.
Reading this section and completing these exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: The Saylor Foundation’s “Number Properties Assessment”
Link: The Saylor Foundation’s “Number Properties Assessment” (HTML)
Instructions: Please click on the link above and complete the “Number Properties Assessment” multiplechoice assignment. These assignments incorporate concepts from the Associative, Commutative, Identity, Inverse, and Distributive Properties. You may want to review these concepts associated with the questions by revisiting the Khan videos in this unit.
Completing this assessment should take approximately 30 minutes.
Note: You must be logged into your Saylor Foundation School account in order to access this assessment. If you do not yet have an account, you will be able to create one, free of charge, after clicking the link.
 Lecture: Khan Academy’s “The Distributive Property” and “The Distributive Property 2”

Unit 2: Order of Operations
In life, we often have procedures that everybody uses to avoid problems. When driving a car, for example: if you want to change lanes, you have to first look to make sure the lane is clear, activate your turn signal, check the lane again, move into the lane, and deactivate your turn signal. You do not move into the lane, activate your signal, make sure the lane is clear, and deactivate your signal. That can, and eventually will, cause a serious accident. In order to avoid costly errors, mathematicians had to agree on the series of steps that are needed to simplify expressions involving the four basic operations, grouping symbols, and exponents. This series of steps is known as the “order of operations” and is more commonly known as either PEMDAS or “Please Excuse My Dear Aunt Sally, she Left to Right.” This tells us in which order to simplify the expression. (Tip: it is multiply OR divide and add OR subtract– whichever you see first.)
Unit 2 Time Advisory show close
Mathematicians also needed a way to quickly write out a repeated multiplication problem, like 2 x 2 x 2 x 2 x 2, so they invented the use of exponents. This unit will introduce you to the process of working with basic exponents. As you go higher, you will learn more about exponents.
Another topic you will learn about in this unit is the concept of “greatest common factor.” Mathematically, the greatest common factor (GCF) is the largest number you can divide two or more numbers by. In real life, it also makes appearances, both mathematical and nonmathematical. A detective trying to make connections between an arrested criminal and a suspected accomplice is going to be less interested in the facts that they have both eaten at McDonald’s and both like strawberry milkshakes than in the fact that the suspected accomplice has been the criminal’s best friend for twenty years. That fact is far greater to the investigation.
The last topic you will cover is related to greatest common factor but is different. It is known as “least common multiple.” Here, you are trying to determine the smallest number that two numbers can both divide into. Again, it appears in life. Let’s say your favorite radio station is running a promotion: every fifth caller receives free concert tickets, and every twelfth caller receives a free gas card. How long will it take before they have a caller who receives both prizes on the same phone call? This is an example of using the least common multiple. (In case you are wondering, it would be the 60^{th} caller who won both prizes.)
Unit 2 Learning Outcomes show close

2.1 Greatest Common Divisor/Factor
 Lecture: Khan Academy’s “Greatest Common Divisor”
Link: Khan Academy’s “Greatest Common Divisor” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to explain how to solve problems finding the greatest common divisor/factor.
Watching this lecture and pausing to take notes should take approximately 30 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “The Greatest Common Factor”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “The Greatest Common Factor” (HTML or PDF)
Instructions: Please click on the link above and read the entire section on “The Greatest Common Factor (GCF)” through “Sample Set A.” Look closely at the section titled “A Method for Determining the Greatest Common Factor.” Then, complete “Practice Set A,” exercises 1–4 and the evennumbered problems for 6–20. The solutions to the problems are shown below each problem. These problems will allow you to practice finding the greatest common factor between numbers.
Reading this section and completing this activity should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assignment: Khan Academy's "Greatest Common Divisor"
Link: Khan Academy’s “Greatest Common Divisor” (HTML)
Instructions: Please click on the link above and complete the “Greatest Common Divisor” assignment. This assignment incorporates concepts from the greatest common divisor. It may help to review the concepts associated with the questions by revisiting the Khan videos in Unit 2. For this assignment, you will compute your answer and type it into the answer box. You may then click on “Check Answer” to see if you were correct or if you need to try again.
Completing this assignment should take approximately 45 minutes.
Terms of Use: This exercise is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Greatest Common Divisor”

2.2 Least Common Multiple
 Lecture: Khan Academy’s “Least Common Multiple”
Link: Khan Academy’s “Least Common Multiple” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to explain how to solve problems finding the least common multiple.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “The Least Common Multiple”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “The Least Common Multiple” (HTML or PDF)
Instructions: Please click on the link above and read the “Least Common Multiple” section. Start with the “Multiples” section, and then complete “Practice Set A,” exercises 1–3. Continue with the “Common Multiples” section, and then complete “Practice Set B,” exercises 6–8. Finish by reading “The Least Common Multiple (LCM)” section, and then complete “Practice Set C,” exercises 11–13. Then, complete the evennumbered problems for 16–44. The solutions to the problems can be revealed by the “Show Solution” link under each problem. These problems will allow you to practice finding the least common multiple between numbers.
Reading this section and completing this activity should take approximately 2 hours.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assignment: Khan Academy’s “Least Common Multiple”
Link: Khan Academy’s “Least Common Multiple” (HTML)
Instructions: Please click on the link above and complete the “Least Common Multiple” assignment. This assignment incorporates concepts from the least common multiple. It may help to review the concepts associated with the questions by revisiting the Khan videos in Unit 2. For this assignment, you will compute your answer and type it into the answer box. You may then click on “Check Answer” to see if you were correct or if you need to try again.
Completing this assignment should take approximately 45 minutes.
Terms of Use: This exercise is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Assignment: Khan Academy’s “LCM and GCF Word Problems”
Link: Khan Academy’s “LCM and GCF Word Problems” (YouTube)
Instructions: Click on the link above and watch this video, which consists of two least common multiple and greatest common factor word problems. Pause the video after each problem has been given, and try to work out the answer on your own before coming back to the video to check your answer. It may help to review the concepts associated with the questions by revisiting the Khan videos in Unit 2.
Completing this assignment should take approximately 1 hour.
Terms of Use: This exercise is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Least Common Multiple”
 2.3 Negative Numbers

2.3.1 Negative Numbers Introduction
 Lecture: Khan Academy’s “Negative Numbers Introduction”
Link: Khan Academy’s “Negative Numbers Introduction” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to understand how negative numbers work.
Watching this lecture and pausing to take notes should take approximately 45 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Negative Numbers Introduction”

2.3.2 Adding Negative Numbers
 Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2ndEdition: “Adding Integers with Like Signs”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd}Edition: “Adding Integers with Like Signs” (PDF)
Instructions: Please click on the link above and study the section titled “Adding Integers with Like Signs” on pages 115–117 of the textbook. You may stop when you reach the section titled “Adding Integers with Unlike Signs” on page 117. The material can also be located through the bookmark on the left side (2 The Integers, 2.2 Adding Integers, “Adding Integers with Like Signs”), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems beside Examples 1 and 2 on page 115 and Example 3 on page 116. This material provides examples of adding two positive and two negative integers.
Reading this section and completing the exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: Khan Academy’s “Adding Negative Numbers”
Link: Khan Academy’s “Adding Negative Numbers” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to explain how to add negative numbers.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2ndEdition: “Adding Integers with Like Signs”

2.3.3 Adding Integers with Different Signs
 Lecture: Khan Academy’s “Adding Integers with Different Signs”
Link: Khan Academy’s “Adding Integers with Different Signs” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to explain how to add integers with different signs.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Adding Integers with Unlike Signs”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Adding Integers with Unlike Signs” (PDF)
Instructions: Please click on the link above and study the section titled “Adding Integers with Unlike Signs” on pages 117–119 of the textbook. You may stop when you reach the section titled “Properties of Addition of Integers” on page 119. The material can also be located through the bookmark on the left side (2 The Integers, 2.2 Adding Integers, “Adding Integers with Like Signs”), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems beside Example 4 on page 117 and Example 5 on page 118. This material provides examples of adding one positive and one negative integer.
Reading this section and completing the exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “2.2 Adding Integers Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “2.2 Adding Integers Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 13–35 and 65–83 on pages 124 and 125 of the textbook. The exercises can also be located through the bookmark on the left side (2 The Integers, 2.2 Adding Integers, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to recognize addition properties as well as determine the profit and loss for a company. The solutions to these problems are located in the “Answers” section on page 126 of the textbook. The solutions page can also be located through the bookmark on the left side (2 The Integers, 2.2 Adding Integers, “Answers”).
Completing this activity should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Adding Integers with Different Signs”

2.3.4 Adding/Subtracting Negative Numbers
 Lecture: Khan Academy’s “Adding/Subtracting Negative Numbers”
Link: Khan Academy’s “Adding/Subtracting Negative Numbers” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to explain how to subtract integers.
Watching this lecture and pausing to take notes should take approximately 45 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “2.3 Subtracting Integers”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “2.3 Subtracting Integers” (PDF)
Instructions: Please click on the link above and study the section titled “Subtracting Integers” on pages 128 through 132. The material can also be located through the bookmark on the left side (2 The Integers, 2.3 Subtracting Integers, “Subtracting Integers”), which will take you directly to the reading. After reading and studying the “Subtracting Integers” section, complete the “You Try It” problems beside Example 1 on page 129 and Example 4 on page 131. This material provides examples of subtracting integers.
Reading this section and completing the exercises should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “2.3 Subtracting Integers Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “2.3 Subtracting Integers Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 1–23 and 51–59 on pages 133 and 134 of the textbook. The exercises can also be located through the bookmark on the left side (2 The Integers, 2.3 Subtracting Integers, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to recognize subtraction and properties and apply the concepts when dealing with a temperature change and comparing highest and lowest points. The solutions to these problems are located in the “Answers” section on page 135 of the textbook. The solutions page can also be located through the bookmark on the left side (2 The Integers, 2.3 Subtracting Integers, “Answers”).
Completing this activity should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assignment: Khan Academy’s “Adding Negative Numbers”
Link: Khan Academy’s “Adding Negative Numbers” (HTML)
Instructions: Please click on the link above and complete the “Adding Negative Numbers” assessment. This quiz incorporates concepts from negative numbers introduction, adding negative numbers, adding integers with different signs, and adding/subtracting negative numbers. It may help to review the concepts associated with the questions by revisiting the Khan videos in Unit 2. For this quiz, you will compute your answer and type it into the answer box. You may then click on “Check Answer” to see if you were correct or if you need to try again.
Completing this activity should take approximately 30 minutes.
Terms of Use: This exercise is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Assignment: Khan Academy’s “Negative Number Word Problems”
Link: Khan Academy’s “Negative Number Word Problems” (HTML)
Instructions: Please click on the link above and complete the “Negative Number Word Problems” assignment. This assignment incorporates concepts from negative numbers introduction, adding negative numbers, adding integers with different signs, and adding/subtracting negative numbers. It may help to review the concepts associated with the questions by revisiting the Khan videos in Unit 2. For this assignment, you will compute your answer and type it into the answer box. You may then click on “Check Answer” to see if you were correct or if you need to try again.
Completing this assignment should take approximately 45 minutes.
Terms of Use: This exercise is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Adding/Subtracting Negative Numbers”

2.3.5 Multiplying Positive and Negative Numbers
 Lecture: Khan Academy’s “Multiplying Positive and Negative Numbers”
Link: Khan Academy’s “Multiplying Positive and Negative Numbers” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to explain how to multiply integers with different signs.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “2.4 Multiplication and Division of Integers”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “2.4 Multiplication and Division of Integers” (PDF)
Instructions: Please click on the link above and study the sections titled “Multiplication and Division of Integers” on pages 137 and 138 as well as “Multiplying by Minus One” and “The Product of Two Integers” on pages 140–142 of the textbook. The material can also be located through the bookmark on the left side (2 The Integers, 2.4 “Multiplication and Division of Integers”) and (2 The Integers, 2.4 Multiplication and Division of Integers, “Multiplying by Minus One”), which will take you directly to the readings. After reading and studying these sections, complete the “You Try It” problems beside Examples 1 and 2 on pages 141 and 142. This material provides examples of multiplication of integers and rules associated with each problem.
Reading this section and completing the exercises should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “2.4 Multiplication and Division of IntegersExercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “2.4 Multiplication and Division of IntegersExercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 17–47 as well as problem 85 on pages 145 through 147 of the textbook. These exercises can also be located through the bookmark on the left side (2 The Integers, 2.4 Multiplication and Division of Integers, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to recognize multiplication properties and apply these concepts. The solutions to these problems are located in the “Answers” section on page 147 of the textbook. The solutions page can also be located through the bookmark on the left side (2 The Integers, 2.4 Multiplication and Division of Integers, “Answers”).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Multiplying Positive and Negative Numbers”

2.3.6 Dividing Positive and Negative Numbers
 Lecture: Khan Academy’s “Dividing Positive and Negative Numbers”
Link: Khan Academy’s “Dividing Positive and Negative Numbers” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to explain how to divide integers with different signs.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “2.4 Multiplication and Division of Integers”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “2.4 Multiplication and Division of Integers” (PDF)
Instructions: Please click on the link above and study the section titled “Division of Integers” on pages 143 and 144 of the textbook. The material can also be located through the bookmark on the left side (2 The Integers, 2.4 Multiplication and Division of Integers, “Division of Integers”), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems beside Example 4 on page 144. This reading provides examples of division of integers and rules associated with each problem.
Reading this section and completing the exercises should take approximately 20 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “2.4 Multiplication and Division of Integers Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “2.4 Multiplication and Division of Integers Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 61–83 on page 146 of the textbook. These exercises can also be located through the bookmark on the left side (2 The Integers, 2.4 Multiplication and Division of Integers, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to recognize division properties and apply these concepts. The solutions to these problems are located in the “Answers” section on page 147 of the textbook. The solutions page can also be located through the bookmark on the left side (2 The Integers, 2.4 Multiplication and Division of Integers, “Answers”).
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assignment: Khan Academy’s “Multiplying and Dividing Negative Numbers”
Link: Khan Academy’s “Multiplying and Dividing Negative Numbers” (HTML)
Instructions: Please click on the link above and complete the “Multiplying and Dividing Negative Numbers” assignment. This assignment incorporates concepts from multiplying and dividing negative numbers. It may help to review the concepts associated with the questions by revisiting the Khan videos in Unit 2. For this assignment, you will compute your answer and type it into the answer box. You may then click on “Check Answer” to see if you were correct or if you need to try again.
Completing this assignment should take approximately 30 minutes.
Terms of Use: This exercise is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Dividing Positive and Negative Numbers”
 2.4 Exponent Basics

2.4.1 Understanding Exponents
 Lecture: Khan Academy’s “Understanding Exponents” and “Understanding Exponents 2”
Link: Khan Academy’s “Understanding Exponents” (YouTube) and “Understanding Exponents 2” (YouTube)
Instructions: Please click on the links above and take notes as you watch these videos. Watch the first presentation carefully two or three times until you are able to explain how to write a problem in exponential notation. Watch the second presentation carefully two or three times until you are able to explain how to simplify a problem in exponential notation.
Watching these lectures and pausing to take notes should take approximately 15 minutes.
Terms of Use: These videos are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.  Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Exponential Notation”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Exponential Notation” (HTML or PDF)
Instructions: Please click on the link above and read the entire section titled “Exponential Notation.” Read the introductory text on exponential notation through “Sample Set A.” Then, complete “Practice Set A,” exercises 1–6. Continue with the “Reading Exponential Notation” subsection. Then, complete the oddnumbered exercises for 15–29 and 31–57. The solutions to the problems can be revealed by the “Show Solution” link under each problem. These problems will allow you to understand the basics of exponential notation.
Reading this section and completing this activity should take approximately 1 hour and 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Understanding Exponents” and “Understanding Exponents 2”

2.4.2 Level One Exponents
 Lecture: Khan Academy’s “Level 1 Exponents”
Link: Khan Academy’s “Level 1 Exponents” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to explain how to simplify exponents with a positive and negative bases as well as exponents to the zero power.
Watching this lecture and pausing to take notes should take approximately 45 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “2.4 Multiplication and Division of Integers”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “2.4 Multiplication and Division of Integers” (PDF)
Instructions: Please click on the link above and study Example 3 located on page 142 of the textbook. After reading and studying this example, complete the “You Try It” problems beside Example 3. This material provides an example of exponential notation with negative signs and bases.
Studying this example and attempting the “You Try It” example should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “2.4 Multiplication and Division of Integers Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “2.4 Multiplication and Division of Integers Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered problems for 49–59 on page 146 of the textbook. These exercises can also be located through the bookmark on the left side (2 The Integers, 2.4 Multiplication and Division of Integers, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to simplify exponent problems with negative bases. The solutions to these problems are located in the “Answers” section on page 147 of the textbook. The solutions page can also be located through the bookmark on the left side (2 The Integers, 2.4 Multiplication and Division of Integers, “Answers”).
Completing this activity should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assignment: Khan Academy’s “Positive and Zero Exponents”
Link: Khan Academy’s “Positive and Zero Exponents” (HTML)
Instructions: Please click on the link above and complete the assessment that tests your knowledge on positive and zero exponents. This incorporates concepts from positive exponents with a positive or negative base and zero exponents. You can review the concepts associated with the questions with the Khan videos in Unit 2. Answer each question by inputting your calculation into the answer box. You may click on “Check Answer” to check if your answers are correct or if you need to try again.
Completing this assessment should take approximately 30 minutes.
Terms of Use: This exercise is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Level 1 Exponents”
 2.5 Order of Operations

2.5.1 Introduction to Order of Operations
 Lecture: Khan Academy’s “Introduction to Order of Operations”
Link: Khan Academy’s “Introduction to Order of Operations” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to apply the process of the order of operations.
Watching this lecture and pausing to take notes should take approximately 45 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “2.5 Order of Operations with Integers”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “2.5 Order of Operations with Integers” (PDF)
Instructions: Please click on the link above and read the section titled “Order of Operations with Integers” on pages 148–150 of the textbook, stopping at “Evaluating Fractions.” The material can also be located through the bookmark on the left side (2 The Integers, 2.5 Order of Operations with Integers), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems beside Examples 2 and 4 on page 149. This material provides examples of order of operations with integers. Note that this reading also covers the topic outlined in subsubunit 2.5.2.
Reading this section and completing the exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “2.5 Order of Operations with Integers Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “2.5 Order of Operations with Integers Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered problems for 1–39 on page 152 of the textbook. These exercises can also be located through the bookmark on the left side (2 The Integers, 2.5 Order of Operations with Integers, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to apply the process of the order of operations. The solutions to these problems are located in the “Answers” section on page 154 of the textbook. The solutions page can also be located through the bookmark on the left side (2 The Integers, 2.5 Order of Operations with Integers, “Answers”).
Completing this activity should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Introduction to Order of Operations”

2.5.2 Introduction to Order of Operations
 Lecture: Khan Academy’s “More Complicated Order of Operations Example”
Link: Khan Academy’s “More Complicated Order of Operations Example” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to apply the process of the order of operations to a more complicated problem.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Lecture: Khan Academy’s “Order of Operations 1”
Link: Khan Academy’s “Order of Operations 1” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to apply the process of the order of operations to a more complicated problem.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “2.5 Order of Operations with Integers Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “2.5 Order of Operations with Integers Exercises” (PDF)
Instructions: The topic of this subsubunit is covered by the reading assigned below subsubunit 2.5.1. To apply your knowledge of this topic, also complete the “You Try It” problem beside Example 3 on page 149.
Completing this activity should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “2.5 Order of Operations with Integers Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “2.5 Order of Operations with Integers Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered problems for 45–53 as well as 59, 61, 67, 69, 73, 75, and 77 on page 153 of the textbook. These exercises can also be located through the bookmark on the left side (2 The Integers, 2.5 Order of Operations with Integers, “Exercises”), which will take you directly to the material. These exercises will provide you with the opportunity to apply the process of the order of operations to more complicated problems. The solutions to these problems are located in the “Answers” section on page 154 of the textbook. The solutions page can also be located through the bookmark on the left side (2 The Integers, 2.5 Order of Operations with Integers, “Answers”).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Evaluating Fractions”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Evaluating Fractions” (PDF)
Instructions: Please click on the link above and review the section titled “Evaluating Fractions,” including Example 6, on page 150 of the textbook. The material can also be located through the bookmark on the left side (2 The Integers, 2.5 Order of Operations with Integers, “Evaluating Fractions”), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problem beside Example 6 on page 150. This material provides examples of order of operations while evaluating fractions.
Reading this section and completing the exercises should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “2.5 Order of Operations with Integers Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “2.5 Order of Operations with Integers Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered problems for 81–103 on pages 153 and 154 of the textbook. These exercises can also be located through the bookmark on the left side (2 The Integers, 2.5 Order of Operations with Integers, “Exercises”), which will take you directly to the material. These exercises will provide you with the opportunity to apply the process of the order of operations to more complicated problems. The solutions to these problems are located in the “Answers” section on page 154 of the textbook. The solutions page can also be located through the bookmark on the left side (2 The Integers, 2.5 Order of Operations with Integers, “Answers”).
Completing this activity should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assignment: Khan Academy’s “Order of Operations”
Link: Khan Academy’s “Order of Operations” (HTML)
Instructions: Please click on the link above and complete the assessment, which tests your knowledge on order of operations. You can review these concepts associated with the questions with the Khan videos in subunit 2.5. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this activity should take approximately 45 minutes.
Terms of Use: This exercise is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “More Complicated Order of Operations Example”

Unit 3: Fractions
The very word – fractions – often chills the bones of math students. Working with fractions is easily the most dreaded, most feared topic in any math class. However, fractions are actually very easy to work with, if you learn the rules. After all, you cannot escape fractions in life; they are everywhere.
Unit 3 Time Advisory show close
Have you ever eaten a Hershey’s chocolate bar? It is conveniently broken up into little pieces, allowing you the option to devour in big bites or to savor tiny little morsels. Let’s say you have a Hershey’s bar sitting on your dining room table. Your oldest child cheerfully announces that she has eaten half of the bar, and her younger brother has eaten a quarter of the bar. If you know how to work with fractions, you can quickly calculate how much of the bar is left.
Fractions appear in many other situations such as sale prices, measurements, money, gardening; the list of applications is virtually endless. In this unit, you will learn to work with fractions. You will learn how to reduce them, how to add/subtract/multiply/divide them, and how to apply them to realworld situations. One suggestion: never show fear. Fractions can smell fear.
Unit 3 Learning Outcomes show close
 3.1 Fraction Basics

3.1.1 Identifying Fraction Parts
 Lecture: Khan Academy’s “Numerator and Denominator of a Fraction” and “Identifying Fraction Parts”
Link: Khan Academy’s “Numerator and Denominator of a Fraction” (YouTube) and “Identifying Fraction Parts” (YouTube)
Instructions: Please click on the links above and take notes as you watch these videos (3 minutes each). Watch the first presentation carefully two or three times until you are able to identify the numerator and denominator of a fraction. Watch the second presentation carefully two or three times until you are able to identify parts of a fraction.
Watching these lectures and pausing to take notes should take approximately 30 minutes.
Terms of Use: These videos are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.  Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Fractions of Whole Numbers”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Fractions of Whole Numbers” (HTML or PDF)
Instructions: Please click on the link above and read “Fractions of Whole Numbers,” “The Parts of a Fraction,” and “Reading and Writing Fractions” sections. Then, complete “Practice Set A,” exercises 1–5 and “Practice Set B,” exercises 6–17. The solutions to the problems are shown directly below each problem. These problems will allow you to practice identifying numerators and denominators as well as writing fractions by using words.
Reading this section and completing these exercises should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Fractions of Whole Numbers”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Fractions of Whole Numbers” (HTML or PDF)
Instructions: Please click on the link above and complete every fourth problem for 18–46 and the evennumbered problems for 4864. The solutions to the problems are shown directly below each problem. These problems will allow you to practice identifying numerators and denominators. This includes determining the numerator and denominator from problems such as “you need ¾ of a cup of sugar to make a batch of cookies.”
Completing these exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Numerator and Denominator of a Fraction” and “Identifying Fraction Parts”

3.1.2 Equivalent Fractions
 Lecture: Khan Academy’s “Equivalent Fractions” and “Comparing Fractions”
Link: Khan Academy’s “Equivalent Fractions” (YouTube) and “Comparing Fractions” (YouTube)
Instructions: Please click on the links above and take notes as you watch these videos. Watch the first presentation carefully two or three times until you are able to identify equivalent fractions. Watch the second presentation carefully two or three times until you are able to compare fractions.
Watching these lectures and pausing to take notes should take approximately 30 minutes.
Terms of Use: These videos are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.  Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Equivalent Fractions”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Equivalent Fractions” (HTML or PDF)
Instructions: Please click on the link above and read the “Equivalent Fractions” section through “Sample Set A.” Then, complete “Practice Set A,” exercises 1–5. The solutions to the problems are shown directly below each problem. These problems will allow you to practice identifying if pairs of fractions are equivalent.
Reading this section and completing these exercises should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assignment: Khan Academy’s “Equivalent Fractions” and “Equivalent Fractions 2”
Link: Khan Academy’s “Equivalent Fractions” (HTML) and “Equivalent Fractions 2” (HTML)
Instructions: Please click on the link above and complete the assignments, which test your knowledge on equivalent fractions. You can review the concepts associated with the questions the Khan videos in subunit 3.1.2. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing these assignments should take approximately 1 hour.
Terms of Use: These exercises are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.
 Lecture: Khan Academy’s “Equivalent Fractions” and “Comparing Fractions”
 3.1.3 Fraction Types

3.1.3.1 Proper and Improper Fractions
 Lecture: Khan Academy’s “Proper and Improper Fractions”
Link: Khan Academy’s “Proper and Improper Fractions” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to identify proper and improper fractions.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Proper Fractions, Improper Fractions, and Mixed Numbers”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Proper Fractions, Improper Fractions, and Mixed Numbers” (HTML or PDF)
Instructions: Please click on the link above and read the “Positive Proper Fractions” and “Positive Improper Fractions” sections. This reading provides examples of proper and improper fractions.
Reading these sections should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Proper Fractions, Improper Fractions, and Mixed Numbers”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Proper Fractions, Improper Fractions, and Mixed Numbers” (HTML or PDF)
Instructions: Please click on the link above and complete the oddnumbered problems 11–25. The solutions to the problems are shown directly below each problem. These problems will allow you to determine a proper fraction, improper fraction, or a mixed number.
Completing these exercises should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Proper and Improper Fractions”

3.1.3.2 Mixed Numbers and Improper Fractions
 Lecture: Khan Academy’s “Mixed Numbers and Improper Fractions”
Link: Khan Academy’s “Mixed Numbers and Improper Fractions” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to understand mixed numbers and improper fractions.
Watching this lecture and pausing to take notes should take approximately 30 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Mixed Numbers and Improper Fractions”
 3.1.3.3 Converting Fractions

3.1.3.3.1 Changing Improper Fractions to Mixed Numbers
 Lecture: Khan Academy’s “Changing an Improper Fraction to a Mixed Number”
Link: Khan Academy’s “Changing an Improper Fraction to a Mixed Number” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to understand changing an improper fraction to a mixed number.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Changing Improper Fractions to Mixed Fractions”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Changing Improper Fractions to Mixed Fractions” (PDF)
Instructions: Please click on the link above and review the section titled “Changing Improper Fractions to Mixed Fractions” on pages 293–295 of the textbook, stopping at “Multiplying and Dividing Mixed Fractions.” The material can also be located through the bookmark on the left side (4 Fractions, 4.5 Multiplying and Dividing Mixed Fractions, “Changing Improper Fractions to Mixed Fractions”), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems beside Examples 4–6 on pages 294 and 295. This material provides examples of converting an improper fraction to a mixed fraction.
Reading this section and completing the exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Proper Fractions, Improper Fractions, and Mixed Numbers”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Proper Fractions, Improper Fractions, and Mixed Numbers” (HTML or PDF)
Instructions: Please click on the link above and read the “Converting Improper Fractions to Mixed Numbers” section. Then, complete “Practice Set A,” exercises 1–6. The solutions to the problems are shown directly below each problem. These problems will allow you to practice converting an improper fraction to a mixed number.
Reading this section and completing these exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Proper Fractions, Improper Fractions, and Mixed Numbers”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Proper Fractions, Improper Fractions, and Mixed Numbers” (HTML or PDF)
Instructions: Please click on the link above and complete the oddnumber exercises 27–39. The solutions to the problems are shown directly below each problem. These problems will allow you to practice converting an improper fraction to a mixed number.
Completing these exercises should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Changing an Improper Fraction to a Mixed Number”

3.1.3.3.2 Changing Mixed Numbers to Improper Fractions
 Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Proper Fractions, Improper Fractions, and Mixed Numbers”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Proper Fractions, Improper Fractions, and Mixed Numbers” (HTML or PDF)
Instructions: Please click on the link above and read the “Converting Mixed Numbers to Improper Fractions” section. Then, complete “Practice Set B,” exercises 7–10. The solutions to the problems are shown directly below each problem. These problems will allow you to practice converting a mixed number to an improper fraction.
Reading this section and completing these exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Lecture: Khan Academy’s “Changing Mixed Numbers to Improper Fractions”
Link: Khan Academy’s “Changing Mixed Numbers to Improper Fractions” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to understand changing an improper fraction to a mixed number.
Watching this lecture and pausing to take notes should take approximately 30 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Proper Fractions, Improper Fractions, and Mixed Numbers”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Proper Fractions, Improper Fractions, and Mixed Numbers” (HTML or PDF)
Instructions: Please click on the link above and read the “Converting Mixed Numbers to Improper Fractions” section. Then, complete “Practice Set B,” exercises 7–10. The solutions to the problems are shown directly below each problem. These problems will allow you to practice converting a mixed number to an improper fraction.
Reading this section and completing these exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Proper Fractions, Improper Fractions, and Mixed Numbers”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Proper Fractions, Improper Fractions, and Mixed Numbers” (HTML or PDF)
Instructions: Please click on the link above and complete the oddnumbered problems 41–55. The solutions to the problems are shown directly below each problem. These problems will allow you to practice converting a mixed number and an improper fraction.
Reading this section and completing these exercises should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assignment: Khan Academy’s “Converting Mixed Numbers and Improper Fractions”
Link: Khan Academy’s “Converting Mixed Numbers and Improper Fractions” (HTML)
Instructions: Please click on the link above and complete the assignment that tests your knowledge of converting fractions. This assignment incorporates concepts from converting mixed numbers to improper fractions and vice versa. You can review the concepts associated with the questions with the Khan videos in subsubunit 3.1.3.3. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this assignment should take approximately 30 minutes.
Terms of Use: This exercise is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Proper Fractions, Improper Fractions, and Mixed Numbers”

3.1.4 Fractions in Lowest Terms
 Lecture: Khan Academy’s “Fraction in Lowest Terms”
Link: Khan Academy’s “Fraction in Lowest Terms” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to reduce fractions to lowest terms.
Watching this lecture and pausing to take notes should take approximately 30 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Equivalent Fractions, Reducing Fractions to Lowest Terms, and Raising Fractions to Higher Terms”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Equivalent Fractions, Reducing Fractions to Lowest Terms, and Raising Fractions to Higher Terms” (HTML or PDF)
Instructions: Please click on the link above and read the “Reducing Fractions to Lowest Term” section. Then, complete “Practice Set B,” exercises 6–11 and “Practice Set C,” exercises 12–17. The solutions to the problems are shown directly below each problem. These problems will allow you to practice reducing fractions to their lowest terms.
Reading this section and completing the exercises should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Equivalent Fractions, Reducing Fractions to Lowest Terms, and Raising Fractions to Higher Terms”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Equivalent Fractions, Reducing Fractions to Lowest Terms, and Raising Fractions to Higher Terms” (HTML or PDF)
Instructions: Please click on the link above and complete the oddnumbered problems for 61–77 as well as the oddnumbered problems for 89–113. The solutions to the problems are shown directly below each problem. These problems will allow you to practice reducing fractions to their lowest terms as well as determine fractional parts of a day.
Reading this section and completing the exercises should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Fraction in Lowest Terms”

3.1.5 Fractions in Highest Terms
 Lecture: Khan Academy’s “Equivalent Fractions Example”
Link: Khan Academy’s “Equivalent Fractions Example” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to solve an application of raising fractions to highest terms.
Watching this lecture and pausing to take notes should take approximately 30 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Equivalent Fractions, Reducing Fractions to Lowest Terms, and Raising Fractions to Higher Terms”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Equivalent Fractions, Reducing Fractions to Lowest Terms, and Raising Fractions to Higher Terms” (HTML or PDF)
Instructions: Please click on the link above and read the “Raising Fractions to Higher Terms” section. Then, complete “Practice Set D,” exercises 18–22. The solutions to the problems are shown directly below each problem. These problems will allow you to find the missing numerator and denominator.
Reading this section and completing these exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Equivalent Fractions, Reducing Fractions to Lowest Terms, and Raising Fractions to Higher Terms”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Equivalent Fractions, Reducing Fractions to Lowest Terms, and Raising Fractions to Higher Terms” (HTML or PDF)
Instructions: Please click on the link above and complete the oddnumbered problems for 39–53. The solutions to the problems are shown directly below each problem. These problems will allow you to practice reducing fractions to their lowest terms.
Reading this section and completing these exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Equivalent Fractions Example”

3.1.6 Finding Common Denominators
 Lecture: Khan Academy’s “Finding Common Denominators”
Link: Khan Academy’s “Finding Common Denominators” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to rewrite fractions with a least common denominator.
Watching this lecture and pausing to take notes should take approximately 30 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Finding Common Denominators”
 3.2 Fractions Operations
 3.2.1 Adding and Subtracting

3.2.1.1 Adding Fractions with Like Denominators
 Lecture: Khan Academy’s “Adding Fractions with Like Denominators”
Link: Khan Academy’s “Adding Fractions with Like Denominators” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able add fractions with common denominators.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Addition and Subtraction of Fractions with Like Denominators”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Addition and Subtraction of Fractions with Like Denominators” (HTML or PDF)
Instructions: Please click on the link above and read the “Addition of Fractions with Like Denominators” section. Then, complete “Practice Set A,” exercises 1–4. The solutions to the problems can be revealed by the “Show Solution” link under each problem. These problems will allow you to practice adding fraction with like denominators.
Reading this section and completing these exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assignment: Khan Academy’s “Adding Fractions with Common Denominators”
Link: Khan Academy’s “Adding Fractions with Common Denominators” (HTML)
Instructions: Please click on the link above and complete the assignment that tests your knowledge fn adding fractions. This assignment incorporates concepts from adding fractions with like denominators. You can review the concepts associated with the questions with the Khan videos in subsubunit 3.2.1. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this assignment should take approximately 30 minutes.
Terms of Use: This exercise is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Adding Fractions with Like Denominators”

3.2.1.2 Subtracting Fractions with Like Denominators
 Lecture: Khan Academy’s “Subtracting Fractions”
Link: Khan Academy’s “Subtracting Fractions” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able subtract fractions with common denominators.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Addition and Subtraction of Fractions with Like Denominators”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Addition and Subtraction of Fractions with Like Denominators” (HTML or PDF)
Instructions: Please click on the link above and read the “Subtraction of Fractions with Like Denominators” section. Then, complete “Practice Set B,” exercises 5–9. The solutions to the problems can be revealed by the “Show Solution” link under each problem. These problems will allow you to practice subtracting fractions with like denominators.
Reading this section and completing these exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Addition and Subtraction of Fractions with Like Denominators”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Addition and Subtraction of Fractions with Like Denominators” (HTML or PDF)
Instructions: This topic is also covered by the reading and activity in subsubunit 3.2.1.1. Please click on the link above and complete the oddnumbered problems for 11–35 and 39. The solutions to the problems can be revealed by the “Show Solution” link under each problem. These problems will allow you to practice adding and subtracting fractions with like denominators.
Reading this section and completing these exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assignment: Khan Academy’s “Subtracting Fractions with Common Denominators”
Link: Khan Academy’s “Subtracting Fractions with Common Denominators” (HTML)
Instructions: Please click on the link above and complete the assignment that tests your knowledge of subtracting fractions. This assignment incorporates concepts from subtracting fractions with like denominators. You can review the concepts associated with the questions with the Khan videos in subsubunit 3.2.1. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this assignment should take approximately 30 minutes.
Terms of Use: This exercise is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Subtracting Fractions”

3.2.1.3 Adding Fractions with Unlike Denominators
 Lecture: Khan Academy’s “Adding Fractions with Unlike Denominators” and “Adding Fractions (ex 1)”
Link: Khan Academy’s “Adding Fractions with Unlike Denominators” (YouTube) and “Adding Fractions (ex 1)” (YouTube)
Instructions: Please click on the links above and take notes as you watch these videos. View the presentations carefully two or three times until you are able add fractions with unlike denominators.
Watching these lectures and pausing to take notes should take approximately 30 minutes.
Terms of Use: These videos are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.  Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Addition and Subtraction of Fractions with Unlike Denominators”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Addition and Subtraction of Fractions with Unlike Denominators” (HTML or PDF)
Instructions: Please click on the link above and read the “Addition and Subtraction of Fractions” section stopping at “Sample Set A,” Example 3. Then, complete “Practice Set A,” exercise 1. The solutions to the problem can be revealed by the “Show Solution” link under each problem. This reading and exercise will allow you to practice adding fractions with unlike denominators.
Reading this section and completing the exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assignment: Khan Academy’s “Adding Fractions”
Link: Khan Academy’s “Adding Fractions” (HTML)
Instructions: Please click on the link above and complete the assignment that tests your knowledge of adding fractions. This assignment incorporates concepts from adding fractions with unlike denominators. You can review the concepts associated with the questions with the Khan videos in subsubunit 3.2.1. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this assignment should take approximately 45 minutes.
Terms of Use: This exercise is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Adding Fractions with Unlike Denominators” and “Adding Fractions (ex 1)”

3.2.1.4 Subtracting Fractions with Unlike Denominators
 Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Addition and Subtraction of Fractions with Unlike Denominators”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Addition and Subtraction of Fractions with Unlike Denominators” (HTML or PDF)
Instructions: Please click on the link above and starting at “Sample Set A,” Example 3, read through the “Addition and Subtraction of Fractions” section. Then, complete “Practice Set A,” exercises 2–5. The solutions to the problems are shown directly below each problem. These problems will allow you to practice subtracting fractions with unlike denominators.
Reading this section and completing these exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Addition and Subtraction of Fractions with Unlike Denominators”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Addition and Subtraction of Fractions with Unlike Denominators” (HTML or PDF)
Instructions: This topic is also covered by the reading and activity in subsubunit 3.2.1.3. Please click on the link above and complete the evennumbered problems 6–36. The solutions to the problems are shown directly below each problem. These problems will allow you to add and subtract fractions with unlike denominators.
Reading this section and completing the exercises should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assignment: Khan Academy’s “Subtracting Fractions”
Link: Khan Academy’s “Subtracting Fractions” (HTML)
Instructions: Please click on the link above and complete the assignment that tests your knowledge of subtracting fractions. This assignment incorporates concepts from subtracting fractions with unlike denominators. You can review the concepts associated with the questions with the Khan videos in subsubunit 3.2.1. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this assignment should take approximately 45 minutes.
Terms of Use: This exercise is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Addition and Subtraction of Fractions with Unlike Denominators”

3.2.1.5 Adding and Subtracting Fractions with Different Signs
 Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Adding and Subtracting Fractions with Different Denominators”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Adding and Subtracting Fractions with Different Denominators” (PDF)
Instructions: Please click on the link above and study the “Adding and Subtracting Fractions with Different Denominators” on pages 277–279 of the textbook. The material may also be located through the bookmark on the left side (4 Fractions, 4.4 Adding and Subtracting Fractions, “Adding and Subtracting Fractions with Different Denominators”), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems beside Examples 4 and 5 on page 279. This material provides examples of subtracting fractions with different signs.
Reading this section should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Adding and Subtracting Fractions Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Adding and Subtracting Fractions Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 69–103 on pages 287 through 288 of the textbook. These exercises can also be located through the bookmark on the left side (4 Fractions, 4.4 Adding and Subtracting Fractions, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to add and subtract fractions with different signs. The solutions to these problems are located in the “Answers” section on page 289 of the textbook. The solutions page can also be located through the bookmark on the left side (4 Fractions, 4.4 Adding and Subtracting Fractions, “Answers”).
Completing this activity should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assignment: Khan Academy’s “Adding and Subtracting Fractions”
Link: Khan Academy’s “Adding and Subtracting Fractions” (HTML)
Instructions: Please click on the link above and complete the assessment that tests your knowledge on adding and subtracting fractions. This quiz incorporates concepts from adding and subtracting fractions with like and unlike denominators. You can review the concepts associated with the questions with the Khan videos in subsubunit 3.2.1. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this activity should take approximately 45 minutes.
Terms of Use: This exercise is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Adding and Subtracting Fractions with Different Denominators”
 3.2.2 Adding and Subtracting Mixed Numbers

3.2.2.1 Adding Mixed Numbers with Like Denominators
 Lecture: Khan Academy’s “Adding Subtracting Mixed Numbers 0.5 (ex 1)” and “Adding Mixed Numbers”
Link: Khan Academy’s “Adding Subtracting Mixed Numbers 0.5 (ex 1)” (YouTube) and “Adding Mixed Numbers” (YouTube)
Instructions: Please click on the links above and take notes as you watch these videos. View each presentation carefully two or three times until you are able add mixed numbers with common denominators.
Watching these lectures and pausing to take notes should take approximately 15 minutes.
Terms of Use: These videos are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.
 Lecture: Khan Academy’s “Adding Subtracting Mixed Numbers 0.5 (ex 1)” and “Adding Mixed Numbers”

3.2.2.2 Subtracting Mixed Numbers with Like Denominators
 Lecture: Khan Academy’s “Adding Subtracting Mixed Numbers 0.5 (ex 2)”
Link: Khan Academy’s “Adding Subtracting Mixed Numbers 0.5 (ex 2)” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able subtract mixed numbers with common denominators.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Adding Subtracting Mixed Numbers 0.5 (ex 2)”

3.2.2.3 Adding Mixed Numbers with Unlike Denominators
 Lecture: Khan Academy’s “Adding Mixed Numbers with Unlike Denominators” and “Adding Subtracting Mixed Numbers 1 (ex 1)”
Link: Khan Academy’s “Adding Mixed Numbers with Unlike Denominators” (YouTube) and “Adding Subtracting Mixed Numbers 1 (ex 1)” (YouTube)
Instructions: Please click on the links above and take notes as you watch these videos. View each presentation carefully two or three times until you are able add mixed numbers with unlike denominators.
Watching these lectures and pausing to take notes should take approximately 30 minutes.
Terms of Use: These videos are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Adding Mixed Fractions”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Adding Mixed Fractions” (PDF)
Instructions: Please click on the link above and study the “Adding Mixed Fractions” section on pages 301–303 of the textbook. The material may also be located through the bookmark on the left side (4 Fractions, 4.6 Adding and Subtracting Mixed Fractions, “Adding Mixed Fractions”), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems beside Examples 1, 2, and 3 on pages 301 and 302. This material provides examples of subtracting fractions with different signs.
Reading this section and completing the exercises should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Adding Mixed Numbers with Unlike Denominators” and “Adding Subtracting Mixed Numbers 1 (ex 1)”

3.2.2.4 Subtracting Mixed Numbers with Unlike Denominators
 Lecture: Khan Academy’s “Subtracting Mixed Numbers”, “Subtracting Mixed Numbers 2”, and “Adding Subtracting Mixed Numbers 1 (ex 2)”
Link: Khan Academy’s “Subtracting Mixed Numbers” (YouTube), “Subtracting Mixed Numbers 2” (YouTube), and “Adding Subtracting Mixed Numbers 1 (ex 2)” (YouTube)
Instructions: Please click on the links above and take notes as you watch these videos. View each presentation carefully two or three times until you are able subtract mixed numbers with unlike denominators.
Watching these lectures and pausing to take notes should take approximately 45 minutes.
Terms of Use: These videos are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Subtracting Mixed Fractions”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Subtracting Mixed Fractions” (PDF)
Instructions: Please click on the link above and study the “Subtracting Mixed Fractions” section 9 on pages 304–307 of the textbook, stopping at Example 9. The material may also be located through the bookmark on the left side (4 Fractions, 4.6 Adding and Subtracting Mixed Fractions, “Subtracting Mixed Fractions”), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems next to Examples 5 through 8 on pages 304–306. This material provides examples of subtracting mixed fractions.
Reading this section and completing the exercises should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Addition and Subtraction of Mixed Numbers”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Addition and Subtraction of Mixed Numbers” (HTML or PDF)
Instructions: This topic is covered by the reading and activity in subsubunits 3.2.2.1, 3.2.2.2, and 3.2.2.3. Please click on the link above and complete the evennumbered problems for 6–36. The solutions to the problems are shown directly below each problem. These problems will allow you to practice with the addition and subtraction of mixed numbers.
Reading this section and completing the exercises should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Khan Academy’s “Adding Subtracting Mixed Numbers 1”
Link: Khan Academy’s “Adding Subtracting Mixed Numbers 0.5” (HTML) and “Adding Subtracting Mixed Numbers 1” (HTML)
Instructions: Please click on the link above and complete the assignments that tests your knowledge of adding and subtracting mixed numbers. These assignments incorporate concepts from adding and subtracting mixed numbers with like and unlike denominators. You can review the concepts associated with the questions with the Khan videos in subsubunit 3.2.2. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing these assignments should take approximately 1 hour and 30 minutes.
Terms of Use: These exercises is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Subtracting Mixed Numbers”, “Subtracting Mixed Numbers 2”, and “Adding Subtracting Mixed Numbers 1 (ex 2)”

3.2.3 Applications of Adding and Subtracting Fractions
 Lecture: Khan Academy’s “Adding Mixed Numbers Word Problem” and “Subtracting Mixed Numbers 1 Word Problem”
Link: Khan Academy’s “Adding Mixed Numbers Word Problem” (YouTube) and “Subtracting Mixed Numbers 1 Word Problem” (YouTube)
Instructions: Please click on the links above and take notes as you watch these videos. View each presentation carefully two or three times until you are able understand applications where you add and subtract.
Watching these lectures and pausing to take notes should take approximately 30 minutes.
Terms of Use: These videos are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Adding and Subtracting Mixed Fractions”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Adding and Subtracting Mixed Fractions” (PDF)
Instructions: Please click on the link above and review the “Adding and Subtracting Mixed Fractions” section through Example 9 on pages 301–307 of the textbook; you read this section in subsubunits 3.2.1 and 3.2.2. The material may also be located through the bookmark on the left side (4 Fractions, 4.6 Adding and Subtracting Mixed Fractions), which will take you directly to the reading. After reviewing this section, complete the “You Try It” problem next to Example 4 on page 303 and Example 9 on page 307. This material contains applications of adding and subtracting fractions.
Reading this section and completing the exercises should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Addition and Subtraction of Fractions with Like Denominators”, “Addition and Subtraction of Fractions with Unlike Denominators”, and “Addition and Subtraction of Mixed Numbers”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Addition and Subtraction of Fractions with Like Denominators” (HTML or PDF), “Addition and Subtraction of Fractions with Unlike Denominators” (HTML or PDF), and “Addition and Subtraction of Mixed Numbers” (HTML or PDF)
Instructions: Please click on the links above and complete the following problems: problem 39 for “Addition and Subtraction of Fractions with Like Denominators;” problems 50, 52, and 54 for “Addition and Subtraction of Fractions with Unlike Denominators;” problems 42, 44, and 46 for “Addition and Subtraction of Mixed Numbers.” The solutions to the problems can be revealed by the “Show Solution” link below each problem, or may be found directly below the problem. These problems will allow you to practice adding and subtracting fractions with unlike denominators, which include finding amounts needed for recipes and finding the cost after an increase.
Reading this section and completing these exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Adding Mixed Numbers Word Problem” and “Subtracting Mixed Numbers 1 Word Problem”
 3.2.4 Multiplying

3.2.4.1 Multiplying Fractions
 Lecture: Khan Academy’s “Multiplying Fractions”
Link: Khan Academy’s “Multiplying Fractions” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to multiply fractions.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Multiplying Fractions”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Multiplying Fractions” (PDF)
Instructions: Please click on the link above and study the “Multiply Fractions” section on pages 249–252, stopping at Example 5 on page 252 of the textbook. The material may also be located through the bookmark on the left side (4 Fractions, 4.2 Multiplying Fractions), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems next to Examples 2, 3, and 4 on pages 251 and 252. This material contains examples of multiplying fractions.
Reading this section and completing the exercises should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Multiplying Fraction Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Multiplying Fraction Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 5–27 on page 260 of the textbook. These exercises can also be located through the bookmark on the left side (4 Fractions, 4.2 Multiplying Fractions, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to multiply fractions. The solutions to these problems are located in the “Answers” section on page 263 of the textbook. The solutions page can also be located through the bookmark on the left side (4 Fractions, 4.2 Multiplying Fractions, “Answers”).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Multiplying Fractions”

3.2.4.2 Multiplying Mixed Numbers
 Lecture: Khan Academy’s “Multiplying Mixed Numbers” and “Multiplying Fractions and Mixed Numbers”
Link: Khan Academy’s “Multiplying Mixed Numbers” (YouTube) and “Multiplying Fractions and Mixed Numbers” (YouTube)
Instructions: Please click on the links above and take notes as you watch these videos. View the presentations carefully two or three times until you are able to multiply mixed numbers.
Watching these lectures and pausing to take notes should take approximately 45 minutes.
Terms of Use: These videos are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.  Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Multiplying Mixed Numbers”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Multiplying Mixed Numbers” (HTML or PDF)
Instructions: Please click on the link above and read “Multiplication of Mixed Numbers” section stopping at the “Powers and Roots of Fraction” section. Then, complete “Practice Set C,” exercises 17–20. The solutions to the problems are shown directly below each problem. These problems will allow you to practice multiplying mixed numbers.
Reading this section and completing these exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Multiplying and Dividing Mixed Fractions Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Multiplying and Dividing Mixed Fractions Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 25–47 on pages 297 and 298 of the textbook. These exercises can also be located through the bookmark on the left side (4 Fractions, 4.5 Multiplying and Dividing Mixed Fractions, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to multiply mixed numbers. The solutions to these problems are located in the “Answers” section on page 299 of the textbook. The solutions page can also be located through the bookmark on the left side (4 Fractions, 4.5 Multiplying and Dividing Mixed Fractions, “Answers”).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Multiplying Mixed Numbers” and “Multiplying Fractions and Mixed Numbers”
 3.2.5 Dividing

3.2.5.1 Dividing Fractions
 Lecture: Khan Academy’s “Dividing Fractions” and “Dividing Fractions Example”
Link: Khan Academy’s “Dividing Fractions” (YouTube) and “Dividing Fractions Example” (YouTube)
Instructions: Please click on the links above and take notes as you watch these videos. View the presentations carefully two or three times until you are able to divide fractions.
Watching these lectures and pausing to take notes should take approximately 45 minutes.
Terms of Use: These videos are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Division”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Division” (PDF)
Instructions: Please click on the link above and study the “Division” section on pages 267 and 268 of the textbook. The material may also be located through the bookmark on the left side (4 Fractions, 4.3 Dividing Fractions, “Division”), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems next to Examples 2, 3, and 4 on pages 267 and 268. This material contains examples of dividing fractions.
Reading this section and completing the exercises should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Dividing Fraction Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Dividing Fraction Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 33–67 on page 271 of the textbook. These exercises can also be located through the bookmark on the left side (4 Fractions, 4.3 Dividing Fractions, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to divide fractions. The solutions to these problems are located in the “Answers” section on page 273 of the textbook. The solutions page can also be located through the bookmark on the left side (4 Fractions, 4.3 Dividing Fractions, “Answers”).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Dividing Fractions” and “Dividing Fractions Example”

3.2.5.2 Dividing Mixed Numbers
 Lecture: Khan Academy’s “Dividing Mixed Numbers” and “Dividing Mixed Numbers and Fractions”
Link: Khan Academy’s “Dividing Mixed Numbers” (YouTube) and “Dividing Mixed Numbers and Fractions” (YouTube)
Instructions: Please click on the links above and take notes as you watch these videos. View the presentations carefully two or three times until you are able to divide fractions.
Watching these lectures and pausing to take notes should take approximately 45 minutes.
Terms of Use: These videos are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.  Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Division of Fractions”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Division of Fractions” (HTML or PDF)
Instructions: Please click on the link above and read Examples 7–9 under “Division of Fractions” section, stopping at the “Powers and Roots of Fraction” section. Then, complete “Practice Set B,” exercises 11–13. The solutions to the problems can be revealed by the “Show Solution” link under each problem. These problems will allow you to practice dividing mixed numbers.
Reading this section and completing these exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Multiplying and Dividing Mixed Fractions Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Multiplying and Dividing Mixed Fractions Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 49–71 on pages 298 and 299 of the textbook. These exercises can also be located through the bookmark on the left side (4 Fractions, 4.5 Multiplying and Dividing Mixed Fractions, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to divide mixed numbers. The solutions to these problems are located in the “Answers” section on page 299 of the textbook. The solutions page can also be located through the bookmark on the left side (4 Fractions, 4.5 Multiplying and Dividing Mixed Fractions, “Answers”).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Dividing Mixed Numbers” and “Dividing Mixed Numbers and Fractions”

3.2.6 Applications of Multiplying and Dividing Fractions
 Lecture: Khan Academy’s “Multiplying Fractions Word Problem” and “Dividing Fractions Word Problem”
Link: Khan Academy’s “Multiplying Fractions Word Problem” (YouTube) and “Dividing Fractions Word Problem” (YouTube)
Instructions: Please click on the links above and take notes as you watch these videos. Watch the first presentation carefully two or three times until you are able to apply the multiplication of fractions to a word problem. Watch the second presentation carefully two or three times until you are able to apply the division of fractions to a word problem.
Watching these lectures and pausing to take notes should take approximately 30 minutes.
Terms of Use: These videos are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Parallelograms”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Parallelograms” (PDF)
Instructions: Please click on the link above and study the “Parallelograms” and “Triangles” sections on pages 255–258 of the textbook, stopping at “Identifying the Base and Altitude.” The material may also be located through the bookmark on the left side (4 Fractions, 4.3 Dividing Fractions, “Parallelograms”), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems beside Examples 8 and 9 on pages 256 and 257. This material contains examples of dividing fractions.
Reading this section and completing the exercises should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Multiplying Fraction Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Multiplying Fraction Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 57–69 on page 262 of the textbook. These exercises can also be located through the bookmark on the left side (4 Fractions, 4.2 Multiplying Fractions, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to apply multiplying fractions by finding the areas of parallelograms and triangles. The solutions to these problems are located in the “Answers” section on page 263 of the textbook. The solutions page can also be located through the bookmark on the left side (4 Fractions, 4.2 Multiplying Fractions, “Answers”).
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Multiplying and Dividing Mixed Fractions Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Multiplying and Dividing Mixed Fractions Exercises” (PDF)
Instructions: Please click on the link above and complete problems 73 and 75 on page 299 of the textbook. These exercises can also be located through the bookmark on the left side (4 Fractions, 4.5 Multiplying and Dividing Mixed Fractions, “Exercises”), which will take you directly to the material. These exercises will provide you with the opportunity to practice dividing fractions by dividing fields and cutting jewelry into pieces. The solutions to these problems are located in the “Answers” section on page 299 of the textbook. The solutions page can also be located through the bookmark on the left side (4 Fractions, 4.5 Multiplying and Dividing Mixed Fractions, “Answers”).
Completing this activity should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assignment: Khan Academy’s “Multiplying Fraction Word Problems” and “Dividing Fraction Word Problems”
Link: Khan Academy’s “Multiplying Fraction Word Problems” (HTML) and “Dividing Fraction Word Problems” (HTML)
Instructions: Please click on the links above and complete the assessments that test your knowledge on applications of multiplying and dividing fractions. You can review the concepts associated with these questions with the Khan videos in subsubunits 3.2.4 and 3.2.5. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this activity should take approximately 1 hour and 30 minutes.
Terms of Use: These exercises are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.
 Lecture: Khan Academy’s “Multiplying Fractions Word Problem” and “Dividing Fractions Word Problem”
 3.3 Order of Operations

3.3.1 Order of Operations with Fractions
 Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Combination of Operations with Fractions”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Combination of Operations with Fractions” (HTML or PDF)
Instructions: Please click on the link above and read “The Order of Operations” section, stopping at “Sample Set A,” Example 5. Then, complete “Practice Set A,” exercises 1–5 and 7. The solutions to the problems are shown directly below each problem. These problems will allow you to practice the order of operations with fractions.
Reading this section and completing the exercises should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Order of Operations with Fractions Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Order of Operations with Fractions Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 17–35 on pages 321 and 322 of the textbook. These exercises can also be located through the bookmark on the left side (4 Fractions, 4.7 Order of Operations with Fractions, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to practice dividing fractions. The solutions to these problems are located in the “Answers” section on page 324 of the textbook. The solutions page can also be located through the bookmark on the left side (4 Fractions, 4.7 Order of Operations with Fractions, “Answers”).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Combination of Operations with Fractions”

3.3.2 Complex Fractions
 Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Complex Fractions”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Complex Fractions” (HTML or PDF)
Instructions: Please click on the link above and read “Simple Fractions and Complex Fractions” and “Converting Complex Fractions to Simple Fractions” sections, stopping at “Sample Set A,” Example 5. Then, complete “Practice Set A,” exercises 1–6. The solutions to the problems can be revealed by the “Show Solution” link under each problem. These problems will allow you to practice the order of operations with complex fractions.
Reading this section and completing the exercises should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Complex Fractions”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Complex Fractions” (HTML or PDF)
Instructions: Please click on the link above and complete the oddnumber problems for 7–25. The solutions to the problems can be revealed by the “Show Solution” link under each problem. These problems will allow you to use order of operations to simplify complex fractions.
Reading this section and completing the exercises should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Complex Fractions”

Unit 4: Decimals
Congratulations on surviving fractions! In this unit, you will turn your attention to the “fraternal twin” of fractions: decimals. Yes, decimals are really just fractions in disguise! Who knew? For example, look at (American) money. A dollar is 100 cents; a quarter is 25 cents, or in decimal form, $0.25. The fraction 25/100 reduces to ¼, which is read as “onequarter.” Decimals are fractions, and fractions are decimals. It’s all in how you write them.
Unit 4 Time Advisory show close
Decimals are everywhere, just like fractions. You cannot go shopping without encountering decimals. Whether you are adding up totals on your shopping list, calculating your change, or even just measuring the length of something, you will use decimals. If you add up all your purchases, find that your total comes to $17.31, and you hand the cashier $20, you need to know how to determine your change to make sure the cashier gives you back the correct amount of money. If you are measuring the length of your wall in order to fit a couch there, you might find that the wall’s length is in between two lengths, measuring at, say, 11.5 ft. You have to know how to deal with decimals to approximate distances.
In this unit, you will learn how to add/subtract/multiply/divide decimals as well as how to convert between fraction and decimal form.
Unit 4 Learning Outcomes show close
 4.1 Decimal Basics

4.1.1 Decimal Place Value
 Lecture: Khan Academy’s “Decimal Place Value” and “Decimal Place Value 2”
Link: Khan Academy’s “Decimal Place Value” (YouTube) and “Decimal Place Value 2” (YouTube)
Instructions: Please click on the links above and take notes as you watch these videos. Watch the first presentation carefully two or three times until you are able to understand place value. Watch the second presentation carefully two or three times until you are able to write decimals in word form.
Watching these lectures and pausing to take notes should take approximately 30 minutes.
Terms of Use: These videos are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Introduction to Decimals”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Introduction to Decimals” (PDF)
Instructions: Please click on the link above and study the “Introduction to Decimals,” “Decimal Notation,” and “Pronouncing Decimal Numbers” sections on pages 342–346 of the textbook, stopping at “Decimals to Fractions.” The material may also be located through the bookmark on the left side (5 Decimals, 5.1 Introduction to Decimals), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems beside Examples 1–6 on pages 344–346. This material contains examples of decimal notation and pronouncing decimal numbers.
Reading these sections and completing the exercises should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Introduction to Decimals Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Introduction to Decimals Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 1–39 on pages 353 and 354 of the textbook. These exercises can also be located through the bookmark on the left side (5 Decimals, 5.1 Introduction to Decimals, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to identify decimal places and writing out decimals numbers in expanded form and words. The solutions to these problems are located in the “Answers” section on page 356 of the textbook. The solutions page can also be located through the bookmark on the left side (5 Decimals, 5.1 Introduction to Decimals, “Answers”).
Completing this activity should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Decimal Place Value” and “Decimal Place Value 2”

4.1.2 Rounding Decimals
 Lecture: Khan Academy’s “Rounding Decimals”
Link: Khan Academy’s “Rounding Decimals” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to round decimals.
Watching this lecture and pausing to take notes should take less than 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Rounding Decimals”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Rounding Decimals” (HTML or PDF)
Instructions: Please click on the link above and read the “Rounding Decimal Numbers” section through “Sample Set A.” Then, complete “Practice Set A,” exercises 1–7. The solutions to the problems can be revealed by the “Show Solution” link under each problem. These problems will allow you to round decimals to various positions.
Reading this section and completing these exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Rounding Decimals”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Rounding Decimals” (HTML or PDF)
Instructions: Please click on the link above and complete the evennumbered problems for 8–22. The solutions to the problems can be revealed by the “Show Solution” link under each problem. These problems will help you practice rounding decimals to various positions.
Reading this section and completing the exercises should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Rounding Decimals”

4.1.3 Comparing Decimals
 Lecture: Khan Academy’s “Comparing Decimals”
Link: Khan Academy’s “Comparing Decimals” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to compare decimals accurately.
Watching this lecture and pausing to take notes should take less than 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Comparing Decimals”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Comparing Decimals” (PDF)
Instructions: Please click on the link above and study the “Comparing Decimals” section on pages 350–352 of the textbook. The material may also be located through the bookmark on the left side (5 Decimals, 5.1 Introduction to Decimals, “Comparing Decimals”), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems beside Examples 11 and 12 on pages 351 and 352. This material contains examples of comparing decimal numbers.
Reading this section and completing the exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Introduction to Decimals Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Introduction to Decimals Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 81–91 on page 355 of the textbook. These exercises can also be located through the bookmark on the left side (5 Decimals, 5.1 Introduction to Decimals, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to identify decimal places and write out decimals numbers in expanded form and words. The solutions to these problems are located in the “Answers” section on page 356 of the textbook. The solutions page can also be located through the bookmark on the left side (5 Decimals, 5.1 Introduction to Decimals, “Answers”).
Completing this activity should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Comparing Decimals”
 4.1.4 Conversion

4.1.4.1 Converting Decimals to Fractions
 Lecture: Khan Academy’s “Converting Fractions to Decimals Example”, “Converting Fractions to Decimals (Ex 1)”, “Converting Fractions to Decimals (Ex 2)”, and “Converting Fractions to Decimals”
Link: Khan Academy’s “Converting Fractions to Decimals Example” (YouTube), “Converting Fractions to Decimals (Ex 1)” (YouTube), “Converting Fractions to Decimals (Ex 2)” (YouTube), and “Converting Fractions to Decimals” (YouTube)
Instructions: Please click on the links above and take notes as you watch these videos. Watch these presentations carefully two or three times until you are able to convert fractions to decimals.
Watching these lectures and pausing to take notes should take approximately 1 hour.
Terms of Use: These videos are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.  Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Converting a Fraction to a Decimal”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Converting a Fraction to a Decimal” (HTML or PDF)
Instructions: Please click on the link above and read the “Converting a Fraction to a Decimal” section, stopping at “Sample Set A,” Example 5. Then, complete “Practice Set A,” exercises 1–4. The solutions to the problems can be revealed by the “Show Solution” link under each problem. These problems will allow you to convert fractions into decimals.
Reading this section and completing these exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Converting a Fraction to a Decimal”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Converting a Fraction to a Decimal” (HTML or PDF)
Instructions: Please click on the link above and complete the oddnumbered problems for 7–31 and 37–53. The solutions to the problems can be revealed by the “Show Solution” link under each problem. These problems will allow you to convert fractions into decimals.
Reading this section and completing these exercises should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assignment: Khan Academy’s “Converting Fractions to Decimals”
Link: Khan Academy’s “Converting Fractions to Decimals” (HTML)
Instructions: Please click on the link above and complete the assignment that tests your knowledge onf converting fractions to decimals. You can review the concepts associated with the questions with the Khan videos in subsubunit 4.1.4.1. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this assignment should take approximately 45 minutes.
Terms of Use: This exercise is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Converting Fractions to Decimals Example”, “Converting Fractions to Decimals (Ex 1)”, “Converting Fractions to Decimals (Ex 2)”, and “Converting Fractions to Decimals”

4.1.4.2 Converting Decimals to Fractions
 Lecture: Khan Academy’s “Converting Decimals to Fractions 1 (Ex 1)”, “Converting Decimals to Fractions 1 (Ex 2)”, “Converting Decimals to Fractions 1 (Ex 3)”, “Converting Decimals to Fractions 2 (Ex 1)”, and “Converting Decimals to Fractions 2 (Ex 2)”
Link: Khan Academy’s “Converting Decimals to Fractions 1 (Ex 1)” (YouTube), “Converting Decimals to Fractions 1 (Ex 2)” (YouTube), “Converting Decimals to Fractions 1 (Ex 3)” (YouTube), “Converting Decimals to Fractions 2 (Ex 1)” (YouTube), and “Converting Decimals to Fractions 2 (Ex 2)” (YouTube)
Instructions: Please click on the links above and take notes as you watch these videos. View these presentations carefully two or three times until you are able to convert decimals to fractions.
Watching these lectures and pausing to take notes should take approximately 30 minutes.
Terms of Use: These videos are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.  Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Converting a Decimal to a Fraction”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Converting a Decimal to a Fraction” (HTML or PDF)
Instructions: Please click on the link above and read the “Converting an Ordinary Decimal to a Fraction” section through “Sample Set A,” and complete “Practice Set A,” exercises 1–4. The solutions to the problems are shown directly below each problem. These problems will allow you to convert decimals into fractions.
Reading this section and completing these exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Converting a Decimal to a Fraction”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Converting a Decimal to a Fraction” (HTML or PDF)
Instructions: Please click on the link above and complete the oddnumbered problems for 9–27. The solutions to the problems are shown directly below each problem. These problems will allow you to convert decimals into fractions.
Reading this section and completing these exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assignment: Khan Academy’s “Converting Decimals to Fractions 1” and “Converting Decimals to Fractions 2”
Links: Khan Academy’s “Converting Decimals to Fractions 1” (HTML) and “Converting Decimals to Fractions 2” (HTML)
Instructions: Please click on the link above and complete the assignments that test your knowledge of converting decimals to fractions. You can review the concepts associated with the questions with the Khan videos in subsubunit 4.1.4.2. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing these assignments should take approximately 1 hour and 15 minutes.
Terms of Use: This exercise is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.
 Lecture: Khan Academy’s “Converting Decimals to Fractions 1 (Ex 1)”, “Converting Decimals to Fractions 1 (Ex 2)”, “Converting Decimals to Fractions 1 (Ex 3)”, “Converting Decimals to Fractions 2 (Ex 1)”, and “Converting Decimals to Fractions 2 (Ex 2)”

4.1.4.3 Converting Repeating Decimals to Fractions
 Lecture: Khan Academy’s “Converting Repeating Decimals to Fractions 1” and “Converting Repeating Decimals to Fractions 2”
Link: Khan Academy’s “Converting Repeating Decimals to Fractions 1” (YouTube) and “Converting Repeating Decimals to Fractions 2” (YouTube)
Instructions: Please click on the links above and take notes as you watch these videos. View these presentations carefully two or three times until you are able to convert repeating decimals to fractions.
Watching these lectures and pausing to take notes should take approximately 45 minutes.
Terms of Use: These videos are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.
 Lecture: Khan Academy’s “Converting Repeating Decimals to Fractions 1” and “Converting Repeating Decimals to Fractions 2”
 4.2 Decimal Operations
 4.2.1 Adding and Subtracting

4.2.1.1 Adding Decimals
 Lecture: Khan Academy’s “Adding Decimals”
Link: Khan Academy’s “Adding Decimals” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to add decimals.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Adding Decimals”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Adding Decimals” (PDF)
Instructions: Please click on the link above and study the “Adding Decimals” section on pages 359–361 of the textbook, stopping at “Subtracting Decimals.” The material may also be located through the bookmark on the left side (5 Decimals, 5.2 Adding and Subtracting Decimals, “Adding Decimals”), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems beside Examples 1–4 on pages 359–361. This material contains examples of adding decimal numbers.
Reading this section and completing the exercises should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Adding and Subtracting Decimals Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Adding and Subtracting Decimals Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 1–11 on page 366 of the textbook. These exercises can also be located through the bookmark on the left side (5 Decimals, 5.2 Adding and Subtracting Decimals, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to adding decimal numbers. The solutions to these problems are located in the “Answers” section on page 368 of the textbook. The solutions page can also be located through the bookmark on the left side (5 Decimals, 5.2 Adding and Subtracting Decimals, “Answers”).
Completing this activity should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assignment: Khan Academy’s “Adding Decimals 0.5” and “Adding Decimals”
Link: Khan Academy’s “Adding Decimals 0.5” (HTML) and “Adding Decimals” (HTML)
Instructions: Please click on the links above and complete the assignments that test your knowledge of adding decimals. You can review the concepts associated with the questions with the Khan videos in subsubunit 4.2.1.1. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing these assignments should take approximately 1 hour.
Terms of Use: These exercises are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.
 Lecture: Khan Academy’s “Adding Decimals”

4.2.1.2 Subtracting Decimals
 Lecture: Khan Academy’s “Subtracting Decimals” and “Subtracting Decimals Word Problem”
Link: Khan Academy’s “Subtracting Decimals” (YouTube) and “Subtracting Decimals Word Problem” (YouTube)
Instructions: Please click on the links above and take notes as you watch these videos. Watch the first presentation carefully two or three times until you are able to subtract decimals. Watch the second presentation carefully two or three times until you are able to add and subtract decimals in application.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: These videos are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Subtracting Decimals”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Subtracting Decimals” (PDF)
Instructions: Please click on the link above and study the “Subtracting Decimals” section on pages 361 and 362 of the textbook, stopping at “Adding and Subtracting Signed Decimal Numbers.” The material may also be located through the bookmark on the left side (5 Decimals, 5.2 Adding and Subtracting Decimals, “Subtracting Decimals”), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems beside Examples 5 and 6 on pages 361 and 362. This material contains examples of subtracting decimal numbers.
Reading this section and completing the exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Adding and Subtracting Decimals Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Adding and Subtracting Decimals Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 13–23 and 81–87 on page 366 of the textbook. These exercises can also be located through the bookmark on the left side (5 Decimals, 5.2 Adding and Subtracting Decimals, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to apply the addition and subtraction of decimals. The solutions to these problems are located in the “Answers” section on page 368 of the textbook. The solutions page can also be located through the bookmark on the left side (5 Decimals, 5.2 Adding and Subtracting Decimals, “Answers”).
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assignment: Khan Academy’s “Subtracting Decimals 0.5” and “Subtracting Decimals”
Links: Khan Academy’s “Subtracting Decimals 0.5” (HTML) and “Subtracting Decimals” (HTML)
Instructions: Please click on the link above and complete the assignments that test your knowledge of subtracting decimals. You can review the concepts associated with the questions with the Khan videos in subsubunit 4.2.1.2. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing these assignments should take approximately 1 hour.
Terms of Use: These exercises are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.
 Lecture: Khan Academy’s “Subtracting Decimals” and “Subtracting Decimals Word Problem”

4.2.1.3 Adding and Subtracting Signed Decimal Numbers
 Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Adding and Subtracting Signed Decimal Numbers”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Adding and Subtracting Signed Decimal Numbers” (PDF)
Instructions: Please click on the link above and study the “Adding and Subtracting Signed Decimal Numbers” section on pages 362–364 of the textbook. The material may also be located through the bookmark on the left side (5 Decimals, 5.2 Adding and Subtracting Decimals, “Adding and Subtracting Signed Decimal Numbers”), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems beside Examples 7–10 on pages 362–364. This material contains examples of adding and subtracting signed decimal numbers.
Reading this section and completing the exercises should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Adding and Subtracting Decimals Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Adding and Subtracting Decimals Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 25–63 on page 366 of the textbook. These exercises can also be located through the bookmark on the left side (5 Decimals, 5.2 Adding and Subtracting Decimals, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to add and subtract signed decimals numbers. The solutions to these problems are located in the “Answers” section on page 368 of the textbook. The solutions page can also be located through the bookmark on the left side (5 Decimals, 5.2 Adding and Subtracting Decimals, “Answers”).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Adding and Subtracting Signed Decimal Numbers”
 4.2.2 Multiplying and Dividing

4.2.2.1 Multiplying Decimals
 Lecture: Khan Academy’s “Multiplying Decimals”
Link: Khan Academy’s “Multiplying Decimals” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch the presentation carefully two or three times until you are able to multiply decimals.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Multiplying Decimals”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Multiplying Decimals” (PDF)
Instructions: Please click on the link above and study the “Multiplying Decimals” section on pages 370–373 of the textbook, stopping at “Multiplying Signed Decimal Numbers.” Then, read “The Circle” section on pages 376–380. The material may also be located through the bookmark on the left side (5 Decimals, 5.3 Multiplying Decimals) and (5 Decimals, 5.3 Multiplying Decimals, “The Circle”), which will take you directly to the readings. After reading and studying these sections, complete the “You Try It” problems beside Examples 1–3 on pages 370–373 and Examples 9 and 10 on pages 378–380. This material contains examples of multiplying decimal numbers and its applications.
Reading this section and completing the exercises should take approximately 1 hour and 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Multiplying Decimals Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Multiplying Decimals Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 127 and 89105 on page 381 of the textbook. These exercises can also be located through the bookmark on the left side (5 Decimals, 5.3 Multiplying Decimals, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to multiply decimals numbers and study applications of multiplying decimals, which include finding the total cost of items. The solutions to these problems are located in the “Answers” section on page 384 of the textbook. The solutions page can also be located through the bookmark on the left side (5 Decimals, 5.3 Multiplying Decimals, “Answers”).
Completing this activity should take approximately 1 hour and 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Multiplying Decimals”

4.2.2.2 Multiplying Signed Decimal Numbers
 Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Multiplying Signed Decimal Numbers”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Multiplying Signed Decimal Numbers” (PDF)
Instructions: Please click on the link above and study the “Multiplying Signed Decimal Numbers” section on pages 373 and 374 of the textbook, stopping at “Order of Operations.” The material may also be located through the bookmark on the left side (5 Decimals, 5.3 Multiplying Decimals, “Multiplying Signed Decimal Numbers”), which will take you directly to the material. After reading and studying this section, complete the “You Try It” problems beside Examples 4 and 5 on pages 373 and 374. This reading contains examples of multiplying signed decimal numbers.
Reading this section and completing the exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Multiplying Decimals Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Multiplying Decimals Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 29–55 on page 381 of the textbook. These exercises can also be located through the bookmark on the left side (5 Decimals, 5.3 Multiplying Decimals, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to multiply signed decimals numbers. The solutions to these problems are located in the “Answers” section on page 385 of the textbook. The solutions page can also be located through the bookmark on the left side (5 Decimals, 5.3 Multiplying Decimals, “Answers”).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assignment: Khan Academy’s “Multiplying Decimals”
Link: Khan Academy’s “Multiplying Decimals” (HTML)
Instructions: Please click on the link above and complete this assignment that tests your knowledge of operations with decimals. This assignment incorporates concepts on multiplying decimals. You can review the concepts associated with the questions with the Khan videos in subsubunit 4.2.2.1, and 4.2.2.2. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this assignment should take approximately 45 minutes.
Terms of Use: This exercise is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Multiplying Signed Decimal Numbers”

4.2.2.3 Dividing Decimals
 Lecture: Khan Academy’s “Dividing Decimals 1” and “Dividing Decimals 2”
Link: Khan Academy’s “Dividing Decimals 1” (YouTube) and “Dividing Decimals 2” (YouTube)
Instructions: Please click on the links above and take notes as you watch this video. Watch each presentation carefully two or three times until you are able to divide decimals.
Watching this lecture and pausing to take notes should take approximately 1 hour.
Terms of Use: These videos are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Dividing Decimals”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Dividing Decimals” (PDF)
Instructions: Please click on the link above and study the “Dividing Decimals” on pages 386–390 of the textbook, stopping at “Dividing Signed Decimal Numbers.” The material may also be located through the bookmark on the left side (5 Decimals, 5.4 Dividing Decimals), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems beside Examples 1–3 on pages 387–390. This reading contains examples and applications of dividing decimal numbers.
Reading this section and completing the exercises should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Dividing Decimals Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Dividing Decimals Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 1–39 and 107–113 on page 395 of the textbook. These exercises can also be located through the bookmark on the left side (5 Decimals, 5.4 Dividing Decimals, “Exercises”), which will take you directly to the material. These exercises will provide you with the opportunity to divide decimals numbers and study applications of dividing decimals, which include finding averages for a project. The solutions to these problems are located in the “Answers” section on page 399 of the textbook. The solutions page can also be located through the bookmark on the left side (5 Decimals, 5.4 Dividing Decimals, “Answers”).
Completing this activity should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Dividing Decimals 1” and “Dividing Decimals 2”

4.2.2.4 Dividing Signed Decimal Numbers
 Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Dividing Signed Decimal Numbers”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Dividing Signed Decimal Numbers” (PDF)
Instructions: Please click on the link above and study the “Dividing Signed Decimal Numbers” section on pages 390 and 391 of the textbook, stopping at “Rounding.” The material may also be located through the bookmark on the left side (5 Decimals, 5.4 Dividing Decimals, “Dividing Signed Decimal Numbers”), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems beside Example 4 on page 390. This reading contains examples of dividing signed decimal numbers.
Reading this section and completing the exercises should take approximately 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Dividing Decimals Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Dividing Decimals Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 41–63 on page 395 of the textbook. These exercises can also be located through the bookmark on the left side (5 Decimals, 5.4 Dividing Decimals, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to divide signed decimals numbers. The solutions to these problems are located in the “Answers” section on page 399 of the textbook. The solutions page can also be located through the bookmark on the left side (5 Decimals, 5.4 Dividing Decimals, “Answers”).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assessment: Khan Academy’s “Dividing Decimals”
Link: Khan Academy’s “Dividing Decimals” (HTML)
Instructions: Please click on the link above and complete this assignment that tests your knowledge of operations with decimals. This assignment incorporates concepts on dividing decimals. You can review the concepts associated with the questions with the Khan videos in subsubunit 4.2.3.1, and 4.2.3.2. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this assignment should take approximately 45 minutes.
Terms of Use: This exercise is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Dividing Signed Decimal Numbers”

4.3 Order of Operations
 Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Order of Operations”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Order of Operations” (PDF)
Instructions: Please click on the link above and study the “Order of Operations” section on pages 374 and 375 of the textbook, stopping at “Powers of Ten.” Then, read “Order of Operations” through Example 8 on pages 393 and 394. The material may also be located through the bookmark on the left side (5 Decimals, 5.3 Multiplying Decimals, “Order of Operations”)and (5 Decimals, 5.4 Dividing Decimals, “Order of Operations”), which will take you directly to the readings. Review only the processes involved with each problem and do not worry about substituting into the expression. This material contains examples of order of operations.
Reading this section should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Dividing Decimals Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Dividing Decimals Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 69–79 on page 382 and 89–99 on page 397 of the textbook. These exercises can also be located through the bookmark on the left side (5 Decimals, 5.3 Multiplying Decimals, “Exercises”) and (5 Decimals, 5.4 Dividing Decimals, “Exercises”), which will take you directly to the assignments. These exercises will provide you with the opportunity to apply order of operations to decimal numbers. The solutions to these problems are located in the “Answers” section on page 384 and page 399 of the textbook. The solutions page can also be located through the bookmark on the left side (5 Decimals, 5.3 Multiplying Decimals, “Answers”) and (5 Decimals, 5.4 Dividing Decimals, “Answers”).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Order of Operations”

Unit 5: Ratios and Proportions
In this unit, you will study ratios and proportions. These are mathematical concepts you use all the time, probably without even realizing it. Have you ever been in line at a donut store, comparing the number of chocolate donuts to the number of customers? That’s a ratio. Perhaps you are telling your vet how many times a week your dog drags you outside for an extended walk. That’s also a ratio. Have you ever been driving on a trip, going around 75 mph, and wanted to know how long it would take to reach your destination, which was only 35 miles away? You would find the answer using a proportion. In sports, statisticians use proportions to predict an athlete’s production, based on what they’ve done up to that point. In this unit, you will learn how to write ratios, how to setup and solve proportions, and how to apply these skills to realworld experiences.
Unit 5 Time Advisory show close
Unit 5 Learning Outcomes show close
 5.1 Ratios

5.1.1 Introduction to Ratios
 Lecture: Khan Academy’s “Introduction to Ratios” and “Ratios as Fractions in Simplest Form”
Link: Khan Academy’s “Introduction to Ratios” (YouTube) and “Ratios as Fractions in Simplest Form” (YouTube)
Instructions: Please click on the link above and take notes as you watch these videos. View these presentations carefully two or three times until you are able to understand the basics of ratios.
Watching these lectures and pausing to take notes should take approximately 1 hour.
Terms of Use: These videos are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Introduction to Ratios and Rates”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Introduction to Ratios and Rates” (PDF)
Instructions: Please click on the link above and study the “Introduction to Ratios and Rates” section on pages 449–451 of the textbook, stopping at “Rates.” The material may also be located through the bookmark on the left side (6 Ratio and Proportion, 6.1 Introduction to Ratios and Rates), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems beside Examples 1 and 2 on pages 449–451. This material contains examples on ratios.
Reading this section and completing the exercises should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Introduction to Ratios and Rates Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Introduction to Ratios and Rates Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 1–23 on page 454 of the textbook. These exercises can also be located through the bookmark on the left side (6 Ratio and Proportion, 6.1 Introduction to Ratios and Rates, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to write and simplify ratios. The solutions to these problems are located in the “Answers” section on page 455 of the textbook. The solutions page can also be located through the bookmark on the left side (6 Ratio and Proportion, 6.1 Introduction to Ratios and Rates, “Answers”).
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Introduction to Ratios” and “Ratios as Fractions in Simplest Form”

5.1.2 Finding Unit Rates and Prices
 Lecture: Khan Academy’s “Finding Unit Rates” and “Finding Unit Prices”
Link: Khan Academy’s “Finding Unit Rates” (YouTube) and “Finding Unit Prices” (YouTube)
Instructions: Please click on the link above and take notes as you watch these videos. Watch the first presentation carefully two or three times until you are able to find unit rates. Watch the second presentation carefully two or three times until you are able to find unit prices.
Watching these lectures and pausing to take notes should take approximately 15 minutes.
Terms of Use: These videos are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Rates”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Rates” (PDF)
Instructions: Please click on the link above and study the “Rates” and “Unit Rates” sections on pages 451–453. The material may also be located through the bookmark on the left side (6 Ratio and Proportion, 6.1 Introduction to Ratios and Rates, “Rates”), which will take you directly to the reading. After reading and studying these sections, complete the “You Try It” problems beside Examples 3–6 on pages 451–453. This material contains examples on rates and unit rates.
Reading this section and completing the exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Introduction to Rations and Rates Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Introduction to Rations and Rates Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 23–37 on page 454 of the textbook. These exercises can also be located through the bookmark on the left side (6 Ratio and Proportion, 6.1 Introduction to Ratios and Rates, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to write and simplify rates, which includes comparing rates to see the better deal on an item. The solutions to these problems are located in the “Answers” section on page 455 of the textbook. The solutions page can also be located through the bookmark on the left side (6 Ratio and Proportion, 6.1 Introduction to Ratios and Rates, “Answers”).
Completing this activity should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assignment: Khan Academy’s “Expressing Ratios as Fractions”
Link: Khan Academy’s “Expressing Ratios as Fractions” (HTML)
Instructions: Please click on the link above and complete the assignment that tests your knowledge of ratio word problems. This assignment incorporates concepts of ratios. You can review the concepts associated with the questions with the Khan video in subsubunit 5.2.1. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this activity should take approximately 30 minutes.
Terms of Use: This exercise is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Finding Unit Rates” and “Finding Unit Prices”
 5.2 Proportions

5.2.1 Understanding Proportions
 Lecture: Khan Academy’s “Understanding Proportions”
Link: Khan Academy’s “Understanding Proportions” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch this presentation carefully two or three times until you are able to understand the basics of proportions.
Watching this lecture and pausing to take notes should take less than 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Introduction to Proportions”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Introduction to Proportions” (PDF)
Instructions: Please click on the link above and study the “Introduction to Ratios and Rates” section on pages 456–459 of the textbook, stopping at “Example 4.” The material may also be located through the bookmark on the left side (6 Ratio and Proportion, 6.2 Introduction to Proportions), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems beside Examples 1–3 on pages 457–459. This material contains examples on an introduction to proportions.
Reading this section and completing the exercises should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Introduction to Proportions Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Introduction to Proportions Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 1–13, and 17, 19, 23, 27, 29, 31, and 35 on page 463 of the textbook. These exercises can also be located through the bookmark on the left side (6 Ratio and Proportion, 6.2 Introduction to Proportion, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to solve proportions. The solutions to these problems are located in the “Answers” section on page 465 of the textbook. The solutions page can also be located through the bookmark on the left side (6 Ratio and Proportion, 6.1 Introduction to Proportion, “Answers”).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Understanding Proportions”

5.2.2 Applications of Proportions
 Lecture: Khan Academy’s “Finding an Unknown in a Proportion 2”
Link: Khan Academy’s “Finding an Unknown in a Proportion 2” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch this presentation carefully two or three times until you are able to understand applications of proportions.
Watching this lecture and pausing to take notes should take approximately 30 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Introduction to Proportions”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Introduction to Proportions” (PDF)
Instructions: Please click on the link above and review the “Introduction to Ratios and Rates” section through Example 4 on pages 456–459 of the textbook; note that you already studied this material in subsubunit 5.2.1. The material may also be located through the bookmark on the left side (6 Ratio and Proportion, 6.2 Introduction to Proportions), which will take you directly to the reading. After reviewing this section, complete the “You Try It” problems beside Example 4 on page 459. This material contains examples on an introduction to proportions.
Reading this section and completing the exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Introduction to Proportions Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Introduction to Proportions Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 3753 on pages 464 and 465 of the textbook. These exercises can also be located through the bookmark on the left side (6 Ratio and Proportion, 6.2 Introduction to Proportion, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to write and solve proportions, which include finding the cost of an item. The solutions to these problems are located in the “Answers” section on page 465 of the textbook. The solutions page can also be located through the bookmark on the left side (6 Ratio and Proportion, 6.1 Introduction to Proportion, “Answers”).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Reading: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Applications of Proportions”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Applications of Proportions” (HTML or PDF)
Instructions: Please click on the link above and read the “Applications of a Proportion” section. Then, complete “Practice Set A,” exercises 1–5. The solutions to the problems can be revealed by the “Show Solution” link under each problem. These problems will allow you to practice applications of proportions.
Reading this section and completing these exercises should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Applications of Proportions”
Link: Denny Burzynski and Wade Ellis’ Fundamentals of Mathematics: “Applications of Proportions” (HTML or PDF)
Instructions: Please click on the link above and complete the oddnumbered problems for 7–25. The solutions to the problems can be revealed by the “Show Solution” link under each problem. These problems will allow you to practice applications of proportions.
Reading this section and completing the exercises should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assignment: Khan Academy’s "Writing Proportions" and “Ratio Word Problems”
Link: Khan Academy’s "Writing Proportions" (HTML) and “Ratio Word Problems” (HTML)
Instructions: Please click on the links above and complete the assignments that test your knowledge on proportion word problems. These assignments incorporate concepts of ratios and proportions. You can review the concepts associated with the questions with the Khan video in subsubunit 5.2.2. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing these assignments should take approximately 1 hour and 15 minutes.
Terms of Use: These exercises are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.
 Lecture: Khan Academy’s “Finding an Unknown in a Proportion 2”

Unit 6: Percentages
In this course, you have already studied fractions and decimals. In this unit, you will study the other “fraternal twin” of fractions: percents, which are actually fractions and decimals in disguise. (Perhaps we should call them “fraternal triplets.”) Going back to our example with decimals: we established that a dollar is 100 cents, a quarter is 25 cents, and the fraction form would be 25/100, which reduces to ¼. A percentage is simply a fraction whose denominator is 100. Therefore, 25/100 becomes 25%. Because it is also 0.25, the percent is a fraction which is a decimal, which in turn is a percent. It’s the Circle of Math. (Cue music from “The Lion King.”)
Unit 6 Time Advisory show close
Percents appear all over the place in life, especially when it comes to buying products. If you are considering whether to buy clothes at one store that has a sale with 65% off or a second store that has a sale with 50% off and an additional 15% discount off the sale price, you might be surprised to learn that the two sales are not the same. For those who follow the stock market, you might see the news talking about how your stock has had an increase of 70%. What does that mean?
In this unit, you will learn the rules of percentages and how to apply them. You will learn to convert percentages to and from fractions and decimals. You will learn about percent increase and decrease, which comes into play when you are out shopping. You will also learn (to the delight of shoppers everywhere) exactly how to calculate sale prices, restaurant tips, and other similar items.
Unit 6 Learning Outcomes show close
 6.1 Percent Basics

6.1.1 Describing the Meaning of Percent
 Lecture: Khan Academy’s “Describing the Meaning of Percent” and “Describing the Meaning of Percent 2”
Link: Khan Academy’s “Describing the Meaning of Percent” (YouTube) and “Describing the Meaning of Percent 2” (YouTube)
Instructions: Please click on the links above and take notes as you watch these videos. Watch the presentations carefully two or three times until you are able understand the basics of percents.
Watching these lectures and pausing to take notes should take approximately 30 minutes.
Terms of Use: These videos are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.
 Lecture: Khan Academy’s “Describing the Meaning of Percent” and “Describing the Meaning of Percent 2”
 6.1.2 Conversions

6.1.2.1 Decimal to Percent and Percent to Decimal
 Lecture: Khan Academy’s “Percent and Decimals”
Link: Khan Academy’s “Percent and Decimals” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch this presentation carefully two or three times until you are able to understand how to convert a decimal to a percent and a percent to a decimal.
Watching this lecture and pausing to take notes should take approximately 45 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Changing a Percent to a Decimal” and “Changing a Decimal to a Percent”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Changing a Percent to a Decimal” (PDF) and “Changing a Decimal to a Percent” (PDF)
Instructions: Please click on the links above and study the “Changing a Percent to a Decimal” and “Changing a Decimal to a Percent” sections on pages 504 and 505 of the textbook. The material may also be located through the bookmark on the left side (7 Percent, 7.1 Percent, Decimal, Fractions, “Changing a Percent to a Decimal), which will take you directly to the reading. After reading and studying these sections, complete the “You Try It” problems beside Examples 4–7 on pages 504 and 505. This reading contains examples on changing a percent to a decimal and vice versa.
Reading this section should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Percents, Decimals, Fractions Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Percents, Decimals, Fractions Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 19–49 on pages 508 and 509 of the textbook. These exercises can also be located through the bookmark on the left side (7 Percent, 7.1 Percent, Decimal, Fractions, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to change a percent to a decimal and vice versa. The solutions to these problems are located in the “Answers” section on page 510 of the textbook. The solutions page can also be located through the bookmark on the left side (7 Percent, 7.1 Percent, Decimal, Fractions, “Answers”).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assignment: Khan Academy’s Converting Percents to Decimals
Link: Khan Academy’s “Converting Percents to Decimals” (Adobe Flash)
Instructions: Please click on the link above and complete the assignment. You can review the concepts associated with the questions with the Khan videos in subsubunit 6.1.2.1. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Terms of Use: This exercise is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Assignment: Khan Academy’s Converting Decimals to Percents
Link: Khan Academy’s “Converting Decimals to Percents” (Adobe Flash)
Instructions: Please click on the link above and complete the assignment. You can review the concepts associated with the questions with the Khan videos in subsubunit 6.1.2.1. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Terms of Use: This exercise is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Percent and Decimals”

6.1.2.2 Fraction to Percent and Percent to Fraction
 Lecture: Khan Academy’s “Representing a Number as a Decimal, Percent, and Fraction” and “Representing a Number as a Decimal, Percent, and Fraction 2”
Link: Khan Academy’s “Representing a Number as a Decimal, Percent, and Fraction” (YouTube) and “Representing a Number as a Decimal, Percent, and Fraction 2” (YouTube)
Instructions: Please click on the links above and take notes as you watch these video. View these presentations carefully two or three times until you are able to understand how to convert a fraction to a percent and a percent to a fraction.
Watching this lecture and pausing to take notes should take approximately 45 minutes.
Terms of Use: These videos are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Changing a Percent to a Fraction” and “Changing a Fraction to a Percent”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Changing a Percent to a Fraction” (PDF) and “Changing a Fraction to a Percent” (PDF)
Instructions: Please click on the links above and study the “Changing a Percent to a Fraction” section on pages 502–504 of the textbook, stopping at “Changing a Percent to a Decimal.” Then, study “Changing a Fraction to a Percent” on pages 506–508 of the textbook. The material may also be located through the bookmark on the left side (7 Percent, 7.1 Percent, Decimal, Fractions, “Changing a Percent to a Fraction”), and (7 Percent, 7.1 Percent, Decimal, Fractions, “Changing a Fraction to a Percent”), which will take you directly to the readings. After reading and studying these sections, complete the “You Try It” problems beside Examples 1–4 on pages 502–504 and Examples 8–10 on pages 506–508. This reading contains examples of changing a percent to a fraction and vice versa.
Reading this section and completing the exercises should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Percent, Decimals, Fractions Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Percent, Decimals, Fractions Exercises” (PDF)
Instructions: Please click on the links above and complete the oddnumbered exercises for 1–17 and 51–79 on pages 508–510 of the textbook. These exercises can also be located through the bookmark on the left side (7 Percent, 7.1 Percent, Decimal, Fractions, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to change a percent to a decimal and vice versa. The solutions to these problems are located in the “Answers” section on page 510 of the textbook. The solutions page can also be located through the bookmark on the left side (7 Percent, 7.1 Percent, Decimal, Fractions, “Answers”).
Completing this activity should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Representing a Number as a Decimal, Percent, and Fraction” and “Representing a Number as a Decimal, Percent, and Fraction 2”
 6.2 Percent Problems

6.2.1 Find a Given Percent of Another Number
 Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Find a Given Percent of a Given Number”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Find a Given Percent of a Given Number” (PDF)
Instructions: Please click on the link above and study “Find a Given Percent of a Given Number” on pages 512–514 of the textbook, stopping at “Find a Percent Given Two Numbers.” The material may also be located through the bookmark on the left side (7 Percent, 7.1 Percent, Decimal, Fractions, “Find a Given Percent of a Given Number), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems beside Examples 1–3 on pages 512–514. This reading contains examples of finding a given percent of a given number.
Reading this section and completing the exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Find a Given Percent of a Given Number”

6.2.2 Find a Percent Given Two Numbers
 Lecture: Khan Academy’s “Solving Percent Problems 2”
Link: Khan Academy’s “Solving Percent Problems 2” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch this presentation carefully two or three times until you are able to understand how to find a percent given two numbers.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Find a Percent Given Two Numbers”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Find a Percent Given Two Numbers” (PDF)
Instructions: Please click on the link above and study “Find a Percent Given Two Numbers” on pages 514–516 of the textbook, stopping at “Find a Number That Is a Given Percent of Another Number.” The material may also be located through the bookmark on the left side (7 Percent, 7.1 Percent, Decimal, Fractions, “Find a Percent Given Two Numbers”), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems beside Examples 4 and 5 on pages 514–516. This reading contains examples of finding a percent when given two numbers.
Reading this section should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Solving Percent Problems 2”

6.2.3 Find a Number That Is a Given Percent of Another Number
 Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Find a Number that is a Given Percent of Another Number”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Find a Number that is a Given Percent of Another Number” (PDF)
Instructions: Please click on the link above and study “Find a Number That Is a Given Percent of Another Number” on pages 516 and 517 of the textbook. The material may also be located through the bookmark on the left side (7 Percent, 7.1 Percent, Decimal, Fractions, “Find a Percent Given Two Numbers”), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems beside Examples 6 and 7 on pages 516 and 517. This material contains examples of finding a number that is a given percent of another number.
Reading this section and completing the exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Solving Basic Percent Problems Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Solving Basic Percent Problems Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 1–49 on page 518 of the textbook. These exercises can also be located through the bookmark on the left side (7 Percent, 7.1 Percent, Decimal, Fractions, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to change a percent to a decimal and vice versa. The solutions to these problems are located in the “Answers” section on page 519 of the textbook. The solutions page can also be located through the bookmark on the left side (7 Percent, 7.1 Percent, Decimal, Fractions, “Answers”).
Completing this activity should take approximately 1 hour and 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Find a Number that is a Given Percent of Another Number”
 6.3 Applications of Percent

6.3.1 General Applications
 Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “General Applications of Percent”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “General Applications of Percent” (PDF)
Instructions: Please click on the link above and study “7.3 General Applications of Percent”on pages 521–524 of the textbook. The material may also be located through the bookmark on the left side (7 Percent, 7.3 General Applications of Percent), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems beside Examples 1–4 on pages 521–524. This material contains examples of percent applications.
Reading this section and completing the exercises should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “General Applications of Percent Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “General Applications of Percent Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 1–37 on pages 525–527 of the textbook. These exercises can also be located through the bookmark on the left side (7 Percent, 7.3 General Applications of Percent, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to apply concepts of percent. This includes determining the percent that you earned on a test, finding the amount of a population who fall under certain criteria, and finding the sales tax on specific items. The solutions to these problems are located in the “Answers” section on page 528 of the textbook. The solutions page can also be located through the bookmark on the left side (7 Percent, 7.3 General Applications of Percent, “Answers”).
Completing this activity should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “General Applications of Percent”

6.3.2 Percent Increase or Decrease
 Lecture: Khan Academy’s “Growing by a Percentage”
Link: Khan Academy’s “Growing by a Percentage” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch this presentation carefully two or three times until you are able to understand how to find the amount that grows or decreases by a percent.
Watching this lecture and pausing to take notes should take approximately 45 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Percent Increase or Decrease”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Percent Increase or Decrease” (PDF)
Instructions: Please click on the link above and study the “7.4 Percent Increase or Decrease” section on pages 529–537 of the textbook. The material may also be located through the bookmark on the left side (7 Percent, 7.4 Percent Increase or Decrease), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems beside Examples 1–6 on pages 529–537. This material contains applications of percent increase or decrease.
Reading this section and completing the exercises should take approximately 1 hour and 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Percent Increase or Decrease Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Percent Increase or Decrease Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 1–37 on pages 538–541 of the textbook. These exercises can also be located through the bookmark on the left side (7 Percent, 7.4 Percent Increase or Decrease, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to apply the percent of increase or decrease, which includes how much an item is discounted at the store, the percent of increase in a salary, and finding the new cost of a product. The solutions to these problems are located in the “Answers” section on page 541 of the textbook. The solutions page can also be located through the bookmark on the left side (7 Percent, 7.4 Percent Increase or Decrease, “Answers”).
Completing this activity should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assignment: Khan Academy’s “Percentage Word Problems 1”, “Discount Tax and Tip Word Problems”, and “Markup and Commission Word Problems”
Link: Khan Academy’s “Percentage Word Problems 1” (HTML), “Discount Tax and Tip Word Problems” (HTML), and “Markup and Commission Word Problems” (HTML)
Instructions: Please click on the links above and complete these assignments, which test your knowledge of percent word problems. These assignments incorporate concepts of solving applications of percents. You can review the concepts associated with the questions with the Khan videos in subsubunit 6.3.2. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this activity should take approximately 3 hours.
Terms of Use: These exercises are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.
 Lecture: Khan Academy’s “Growing by a Percentage”

Unit 7: Graphs and Charts
The list of available graph and chart applications is endless. You may have seen applications such as trying to understand voting trends and demographics for presidential campaigns and elections. Or, a business may require graphs and charts to forecast employment growth for a specific time period. Or, you may belong to a fantasy football or baseball team, and you may need to analyze the history of points that players have against certain teams as well as other statistics. In reading a news article that provides a chart, you may want to determine what information the chart provides. Using graphs and charts is a way to convey data that is easy to understand for a specific audience. Knowing how to read and interpret these items is of utmost importance in life, because charts and graphs can be manipulated to misrepresent the data.
Unit 7 Time Advisory show close
This unit discusses various topics when using graphs and charts in mathematics. For each type of graph in the unit, you will need to create a graph as well as interpret the results of this type of graph. You will learn to create charts and graphs (stemandleaf plots, line graphs, bar graphs, boxandwhisker plots, circle or pie graphs, and pictographs), read charts, and work with the measures of central tendency for a data set. (We promise it is not as scary as it sounds!)
Unit 7 Learning Outcomes show close

7.1 Mean, Median, Mode, and Range
 Lecture: Khan Academy’s “Mean Median and Mode”, “Range and Midrange”, and “Statistics the Average”
Link: Khan Academy’s “Mean Median and Mode” (YouTube), “Range and Midrange” (YouTube), and “Statistics the Average” (YouTube)
Instructions: Please click on the links above and take notes as you watch these videos. Watch these presentations carefully two or three times until you are able to understand how to find the mean, median, mode, and range of a set of numbers.
Watching these lectures and pausing to take notes should take approximately 1 hour.
Terms of Use: These videos are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.  Reading: Rory Adams’ Statistics – Grade 10: “Summarizing Data”
Link: Rory Adams’ Statistics – Grade 10: “Summarizing Data” (HTML or PDF)
Instructions: Please click on the link above and read the “Summarizing Data” section, stopping at the “Percentiles” section, and complete the exercise associated with each topic. The solutions to the problems can be revealed by the “Show Solution” link under each problem. These problems will allow you to practice and understand terms related to the measure of central tendency.
Reading this section and completing these exercises should take approximately 1 hour.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: Rory Adams’ Statistics – Grade 10: “Summarizing Data”
Link: Rory Adams’ Statistics – Grade 10: “Summarizing Data” (HTML or PDF)
Instructions: Please click on the link above and complete exercises 14, 5b, 5c, 78. The solutions to the problems can be revealed by the “Show Solution” link under each problem. These problems will allow you to practice and understand terms related to the measure of central tendency.
Reading this section and completing the exercises should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Mean Median and Mode”, “Range and Midrange”, and “Statistics the Average”

7.2 StemandLeaf Plots
 Lecture: Khan Academy’s “StemandLeaf Plots”
Link: Khan Academy’s “StemandLeaf Plots” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch this presentation carefully two or three times until you are able to understand how to find information from a stemandleaf plot.
Watching this lecture and pausing to take notes should take approximately 30 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “StemandLeaf Graphs (Stemplots)”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “StemandLeaf Graphs (Stemplots)” (HTML or PDF)
Instructions: Please click on the link above and read the “StemandLeaf Graphs” section, stopping at the “Line Graphs” section. Then, complete Example 2. The solution to the problems can be revealed by the “Show Solution” link under each problem. These problems will allow you to practice how to read and create a stemandleaf graph.
Reading this section and completing the exercises should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Homework”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Homework” (HTML or PDF)
Instructions: Please click on the link above and complete exercises 1m, 3m, and 23. The solutions to the problems can be revealed by the “Show Solution” link under each problem. These problems will allow you to read and create a stemandleaf graph.
Reading this section and completing these exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assignment: Khan Academy’s “Reading Stem and Leaf Plots”
Link: Khan Academy’s “Reading Stem and Leaf Plots” (HTML)
Instructions: Please click on the link above and complete the assignment on reading stem and leaf plots. You can review the concepts associated with the questions with the Khan videos in subunit 7.2. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
This assignment should take approximately 45 minutes to complete.
Terms of Use: This exercise is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “StemandLeaf Plots”

7.3 Line Graphs
 Lecture: Khan Academy’s “Reading Line Graphs” and “Misleading Line Graphs”
Link: Khan Academy’s “Reading Line Graphs” (YouTube) and “Misleading Line Graphs” (YouTube)
Instructions: Please click on the links above and take notes as you watch these videos. Watch the first presentation carefully two or three times until you are able to understand how to read line graphs. Watch the second presentation carefully two or three times until you are able to understand how line graphs can be misleading.
Watching these lectures and pausing to take notes should take approximately 30 minutes.
Terms of Use: These videos are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.  Assignment: Khan Academy’s “Reading Line Charts 1”
Link: Khan Academy’s “Reading Line Charts 1” (HTML)
Instructions: Please click on the link above and complete the assignment on reading line charts. You can review the concepts associated with the questions with the Khan videos in subunit 7.3. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this assignment should take approximately 45 minutes.
Terms of Use: This exercise is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Reading Line Graphs” and “Misleading Line Graphs”

7.4 Bar Graphs
 Lecture: Khan Academy’s “Reading Bar Graphs”
Link: Khan Academy’s “Reading Bar Graphs” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch this presentation carefully two or three times until you are able to understand how to find information from a bar graph.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Assignment: Khan Academy’s “Reading Bar Charts 3” and “Creating Bar Charts 1”
Link: Khan Academy’s “Reading Bar Charts 3” (HTML) and “Creating Bar Charts 1” (HTML)
Instructions: Please click on the links above and complete these assignments, which test your knowledge of reading and creating bar graphs. These assignments incorporate concepts of reading and creating bar charts. You can review the concepts associated with the questions with the Khan videos in subunit 7.4. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing these assignments should take approximately 1 hour and 30 minutes.
Terms of Use: These exercises are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.
 Lecture: Khan Academy’s “Reading Bar Graphs”

7.5 BoxandWhisker Plots
 Lecture: Khan Academy’s “Reading BoxandWhisker Plots” and “BoxandWhisker Plots”
Link: Khan Academy’s “Reading BoxandWhisker Plots” (YouTube) and “BoxandWhisker Plots” (YouTube)
Instructions: Please click on the links above and take notes as you watch these videos. Watch the first presentation carefully two or three times until you are able to understand how to read a boxandwhisker plot. Watch the second presentation carefully two or three times until you are able to understand how to create a boxandwhisker plot.
Watching these lectures and pausing to take notes should take approximately 1 hour.
Terms of Use: These videos are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.  Reading: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Box Plots”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Box Plots” (HTML or PDF)
Instructions: Please click on the link above and read the “Box Plots” section. Then, complete Examples 1 and 2. The solutions to the problems can be revealed by the “Show Solution” link under each problem. These problems will allow you to practice how to read and create a boxandwhisker plot.
Reading this section and completing the exercises should take approximately 45 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Homework”
Link: Barbara Illowsky and Susan Dean’s Collaborative Statistics: “Homework” (HTML or PDF)
Instructions: Please click on the link above and complete exercises 5ae, 17a, 17b, 17e, and 21. The solutions to the problems can be revealed by the “Show Solution” link under each problem. These problems will allow you to read and create a boxandwhisker plot.
Reading this section and completing these exercises should take approximately 30 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Assignment: Khan Academy’s “Creating Box and Whisker Plots”
Link: Khan Academy’s “Creating Box and Whisker Plots” (HTML)
Instructions: Please click on the link above and complete the assessment, which tests your knowledge on creating boxandwhisker plots. This quiz incorporates concepts of creating boxandwhisker plots, means, and quartiles. You can review the concepts associated with the questions with the Khan videos in subunit 7.5. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing this activity should take approximately 1 hour and 30 minutes.
Terms of Use: This exercise is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.
 Lecture: Khan Academy’s “Reading BoxandWhisker Plots” and “BoxandWhisker Plots”

7.6 Circle or Pie Graphs
 Lecture: Khan Academy’s “Reading Pie Graphs (Circle Graphs)”
Link: Khan Academy’s “Reading Pie Graphs (Circle Graphs)” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch this presentation carefully two or three times until you are able to understand how to find information from a pie/circle graph.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Reading: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Pie Charts”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Pie Charts” (PDF)
Instructions: Please click on the link above and study the “Pie Charts” section on pages 552–559 of the textbook. The material may also be located through the bookmark on the left side (7 Percent, 7.6 Pie Charts), which will take you directly to the reading. After reading and studying this section, complete the “You Try It” problems beside Examples 1 and 2 on pages 554 and 556. This material contains examples on how to interpret and represent data with a pie chart.
Reading this section and completing the exercises should take approximately 1 hour and 15 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.  Activity: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2nd Edition: “Pie Charts Exercises”
Link: College of the Redwoods: Department of Mathematics’ PreAlgebra Textbook, 2^{nd} Edition: “Pie Charts Exercises” (PDF)
Instructions: Please click on the link above and complete the oddnumbered exercises for 1–29 on pages 560–565 of the textbook. These exercises can also be located through the bookmark on the left side (7 Percent, 7.6 Pie Charts, “Exercises”), which will take you directly to the assignment. These exercises will provide you with the opportunity to interpret and represent data with a pie chart. The solutions to these problems are located in the “Answers” section on page 566 of the textbook. The solutions page can also be located through the bookmark on the left side (7 Percent, 7.6 Pie Charts, “Answers”).
This activity will take approximately 2 hours to complete.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
 Lecture: Khan Academy’s “Reading Pie Graphs (Circle Graphs)”

7.7 Pictographs
 Lecture: Khan Academy’s “Reading Pictographs”
Link: Khan Academy’s “Reading Pictographs” (YouTube)
Instructions: Please click on the link above and take notes as you watch this video. Watch this presentation carefully two or three times until you are able to understand how to find information from a pictograph.
Watching this lecture and pausing to take notes should take approximately 15 minutes.
Terms of Use: This video is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. It is attributed to the Khan Academy.  Assignment: Khan Academy’s “Reading Pictographs 1” and “Reading Pictographs 2”
Link: Khan Academy’s “Reading Pictographs 1” (HTML) and “Reading Pictographs 2” (HTML)
Instructions: Please click on the links above and complete the assignments, which test your knowledge of interpreting pictographs. You can review the concepts associated with the questions with the Khan videos in subunit 7.7. Compute the answer to the given problem, and input your response into the answer box. Then, click on “Check Answer” to see if you were correct or if you need to try again.
Completing these assignments should take approximately 1 hour and 30 minutes.
Terms of Use: These exercises are licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 United States License. They are attributed to the Khan Academy.
 Lecture: Khan Academy’s “Reading Pictographs”

Final Exam
 Final Exam: The Saylor Foundation’s “RWM101 Final Exam”
Link: The Saylor Foundation’s “RWM101 Final Exam”
Instructions: You must be logged into your Saylor Foundation School account in order to access this exam. If you do not yet have an account, you will be able to create one, free of charge, after clicking the link.
 Final Exam: The Saylor Foundation’s “RWM101 Final Exam”