Topic  Name  Description 

Course Introduction  Course Syllabus  
1.1: Commutative Law of Addition and Multiplication  Commutative and Associative Properties  Read the first half of this section. Do example 7.5 and Try It exercises 7.9 and 7.10 to practice using the commutative property. 
Commutative Law of Addition  Watch this video for additional explanation and examples of the commutative law of addition. 

Commutative Law of Multiplication  Watch this video for additional explanation and examples of the commutative law of multiplication. 

1.2: Associative Law of Addition and Multiplication  Commutative and Associative Properties  Read this section up to example 7.6. Then, do example 7.6 and Try It exercises 7.11 and 7.12. 
Associative Laws of Addition and Multiplication  Watch these two videos for more examples of the associative law as it relates to addition and multiplication. 

Properties of Addition Quiz  Take this quiz to practice your understanding of the associative and commutative laws. 

1.3: Identity Property of Addition  Identity Property of Zero  Watch this video. You should be able to recognize an equation that shows the identity property of addition. 
1.4: Inverse Property of Addition  Properties of Identity, Inverses, and Zero  Read the first paragraph of this section to see examples of how the inverse property of addition is applied. Then, do example 7.34 and Try It exercises 7.67 and 7.68. 
Inverse Property of Addition  Watch this video for additional examples. 

1.5: Identity Property of Multiplication  Identity Property of One  Watch this video for more examples of the identity property of multiplication. 
1.6: Inverse Property of Multiplication  Properties of Identity, Inverses, and Zero  Read this section to see examples of how the inverse property of addition is applied. In the first multiplication example, we can use the inverse property for fractions as well as whole numbers. Do example 7.35 and Try It exercises 7.69 and 7.70. 
Inverse Property of Multiplication  Watch this video for more examples. 

1.7: Multiplication by Zero  Properties of Identity, Inverses, and Zero  Read this section to see this definition written formally. 
1.8: Dividing by Zero Is Undefined  Why Dividing by Zero Is Undefined  Watch this video. Try to sum up the argument being made in the video in your own words as to why it is impossible to divide a number by zero. What problem happens as we divide one by smaller and smaller numbers, approaching zero? What happens when we divide −1 by smaller and smaller numbers, approaching zero? What inconsistency occurs? 
1.9: Distributive Property  Mental Arithmetic: Using the Distributive Property  Read this article up to Practice Set A. The beginning explains why the distributive property works. Pay close attention to the examples in Sample Set A, which show how to use the distributive property. Do the examples in Practice Set A. 
The Distributive Property  Watch these videos for more examples. 

2.1: Greatest Common Factor  Greatest Common Factor  Watch this video for examples showing how to determine GCF for a set of numbers. Note that sometimes GCF is called the greatest common divisor. 
Greatest Common Factor  Read up to Sample Set A. Pay close attention to how to determine the greatest common factor. Complete the problems in Practice Set A and check your answers. If you feel you need more practice, you can try some of the exercises that follow. 

2.2: Least Common Multiple  Least Common Multiple  Read up to Practice Set C to learn about multiples and how to determine the least common multiple of a given set of numbers. Do Practice Set C and check your answers. 
Least Common Multiple  Watch this video for an additional example of determining the least common multiple for a set of three numbers. 

LCM and GCF Word Problems  Watch this video to see some examples of using the least common multiple and greatest common factor in the real world. 

2.3: Negative Numbers  Introduction to Integers  Read up to Try It exercise 3.10. This section explains the concept of negative numbers using number lines. Pay close attention to the section on opposite notation, which will come up frequently in the next few sections of this course. Do examples 3.2 through 3.5 and check your answer. 
Negative Numbers  Watch this video for more examples of negative numbers using a number line as a reference. 

2.4: Adding and Subtracting Negative Numbers  Adding Negative Numbers  Watch this video for examples of how to add negative numbers. When we add a negative number, we can rewrite it as subtracting the positive number. That is: 5 + (−2) = 5 − 2. 
Addition with Negative Numbers Exercises  After you watch the video, take this quiz and check your answers. 

Subtracting Negative Numbers  Watch this video for examples of how to subtract negative numbers. When we subtract negative numbers, we can rewrite it as adding the number. That is: 5 − (−4) = 5 + 4. 

Subtraction with Negative Numbers Exercises  After you watch the video, take this quiz and check your answers. 

2.5: Multiplying and Dividing Integers with Different Signs  Multiplying and Dividing Integers  Read up to the "Simplify Expressions with Integers" section. Pay special attention to how to multiply and divide signed numbers (multiplying and dividing positive and negative integers). Do examples 3.47 and 3.49, and check your answers. If you would like more practice, do Try It exercises 3.93, 3.94, 3.97, and 3.98. 
Multiplying and Dividing Positive and Negative Numbers  Watch these two videos for additional worked examples. 

2.6: Exponents  Understanding Exponents  Watch this video to learn about how to translate a problem to exponent notation. 
Exponent Examples  Then watch these videos to see examples of solving a problem using exponents. 

Introduction to Exponents  Watch this video for more examples. 

Introduction to Exponents Exercises  After you watch the videos, complete this quiz and check your answers. If you want more practice, try problem sets 2 and 3. 

2.7: Order of Operations  Use the Language of Algebra  Read the section beginning with "Simplify Expressions Using the Order of Operations". Pay special attention to the rules for performing multistep calculations. Many students remember the order of operations using the silly phrase Please Excuse My Dear Aunt Sally, where the first letter of each word corresponds to a mathematical operation: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. Do Examples
2.8–2.12 and check your answers. If you need additional practice, you can do Try It exercises 2.15–2.24. 
Order of Operations Exercises  Complete this assessment for more practice. If you are struggling with any of the problems, use the videos or hints for help. 

3.1: Identifying Parts of Fractions  Fractions of Whole Numbers  Read the "Parts of a Fraction" section to identify the different parts of a number written as a fraction. 
Visualize Fractions  Read this section up to example 4.1 to see how fractions are used to describe real world scenarios, like the pieces of a pizza. Try examples 4.1 and 4.2 to translate between the language of fractions and diagrams. 

3.2 Equivalent Fractions  Demonstrating Equivalent Fractions  Watch this video that uses number lines to show how different fractions are equivalent, which means to have the same value. 
3.3: Proper and Improper Fractions  Proper and Improper Fractions  This video will help you identify proper and improper fractions. 
Proper Fractions, Improper Fractions, and Mixed Numbers  Read up to the "Positive Mixed Numbers" section to see some examples of proper and improper fractions using a number line. 

3.4: Mixed Numbers and Improper Fractions  Visualize Fractions  Read from the "Model Improper Fractions and Mixed Numbers" section up to the "Convert Between Improper Fractions and Mixed Numbers" section. Do examples 4.5–4.8 and check your answers. If you need more practice, do Try It exercises 4.9–4.16. 
3.5: Converting Between Improper Fractions and Mixed Numbers  Changing an Improper Fraction to a Mixed Number  Watch these two videos for examples of how to perform these types of calculations. 
Converting Mixed Numbers and Improper Fractions Exercises  After you watch the videos, try this ungraded assessment. If you are unsure on any of the problems, use the hints for help. 

3.6: Fractions in Lowest Terms  Fractions in Lowest Terms  Watch this video to learn how to reduce fractions to lowest terms. 
Reducing Fractions  Watch this video for another explanation of how to reduce fractions to lowest terms. 

Reducing Fractions Exercises  After you watch the videos, complete this quiz and check your answers. You can try problem sets 2 and 3 if you feel you need more practice. 

3.7: Finding Common Denominators  Finding Common Denominators  Watch this video. Pause the video after the second example and try to determine the common denominator yourself. Then watch the rest of the video to see the solution. 
3.8: Adding and Subtracting Fractions with Like Denominators  Add and Subtract Fractions with Common Denominators  Read this section, which gives an overview of how to add and subtract fractions with the same denominator. Do examples 4.53–4.57 and 4.59–4.62 and check your answers. To see everyday examples of adding fractions, do the everyday math problems 312 and 313 at the end of the section. 
3.9: Adding and Subtracting Fractions with Unlike Denominators  Add and Subtract Fractions with Different Denominators  Read this section for an overview of adding and subtracting fractions with different denominators. Do examples 4.67–4.72 and check your answers. 
More with Fractions  Watch this video for more examples of adding and subtracting fractions with like and unlike denominators. 

3.10: Adding and Subtracting Mixed Numbers  Add and Subtract Mixed Numbers  Read the "Add Mixed Numbers" section, which explains the two methods for adding mixed numbers. Do examples 4.83 and 4.84 using the method of adding the whole numbers and fractions separately. Then, do example 4.85 using the method of converting mixed numbers to improper fractions. Then, read the "Subtract Mixed Numbers with a Common Denominator" section, which describes both methods for subtracting mixed numbers with common denominators. Do example 4.90 using the whole numbers and fraction method, and do example 4.91 using the improper fraction method. 
Adding Subtracting Mixed Numbers Exercises  Complete this assessment for more practice. If you need help, use the videos or hints. 

3.11: Applications of Adding and Subtracting Fractions  Adding and Subtracting Mixed Numbers Word Problems  Watch these two videos to see realworld applications to fractions and mixed numbers. 
3.12: Multiplying Fractions and Mixed Numbers  Multiplying Fractions and Mixed Numbers  Watch these two videos for examples of how to multiply fractions and mixed numbers. You will usually need to convert mixed numbers to improper fractions before multiplying. 
Multiplying Fractions Exercise 1  After you watch the videos, complete these quizzes and check your answers. If you need more practice, do problem sets 2 and 3. 

Multiplying Fractions Exercise 2  Here are some additional practice problems. If you need more practice, do problem sets 2 and 3. 

3.13: Dividing Fractions and Mixed Numbers  Dividing Fractions  Watch these two videos to learn how do these calculations and see a few examples. 
Dividing Mixed Numbers  Watch these two videos to learn how to divide mixed numbers and see a few examples. 

Dividing Fractions Exercises  After you watch the videos, take this quiz and check your answers. If you need more practice, do problem sets 2 and 3. 

3.14: Applications of Multiplying and Dividing Fractions  Multiplying and Dividing Fractions Word Problems  Watch these two videos for examples of multiplication and division problems. 
Multiplying Fraction Word Problems Exercises  After you watch the videos, complete these assessments. 

Dividing Fraction Word Problems Exercises  Then, complete these assessments. 

4.1: Decimal Place Value  Introduction to Decimals Part 1  Watch this video to learn about decimal place value. 
Introduction to Decimals Part 1 Exercises  After you watch the video, take this quiz and check your answers. 

4.2: Rounding Decimals  Rounding Decimals  Watch this video for examples of how we can round decimals to specific decimal places. 
Rounding Decimals Exercises  Read this section up to to Sample Set A. This section gives a set of rules for determining how to round a decimal and some stepbystep directions for rounding numbers. 

4.3: Converting Between Decimals and Fractions  Introduction to Decimals Part 2  Begin by watching this video, which shows examples of converting decimals to fractions. 
Decimals and Fractions  Read up to "Repeating Fractions". Do examples 5.28 and 5.29 and check your answers. For more practice, do Try It exercises 5.55–5.58. 

Introduction to Decimals Part 2 Exercises  Complete this quiz and check your answers. If you need more practice, you can do problem sets 2 and 3. 

4.4: Converting Repeating Decimals to Fractions  Converting Repeating Decimals to Fractions  Watch these two videos for worked examples of how to handle repeating decimals. 
Decimals and Fractions  Read the "Repeating Decimals" section. Pay attention to the notation for the repeating portion of the decimal, which is to write a line above the numbers that repeat. Do examples 5.30 and 5.31 and check your answers. If you need more practice, do Try It exercises 5.59 and 5.60. 

4.5: Adding and Subtracting Decimals  Adding Decimals  Watch this video for an example of doing an addition problem with decimal numbers. Pay attention to how the decimal point must be lined up when completing an addition problem. 
Adding Decimals: Hundredths Exercises  Do this assessment and check your answers. 

Subtracting Decimals  Watch these videos for examples of doing a subtraction problem with decimal numbers. 

Subtracting Decimals: Hundredths Exercises  Do this assessment and check your answers. 

Decimal Operations  For more examples, read the "Add and Subtract Decimals" section. Do examples 5.11–5.14 and check your answers. 

4.6: Multiplying Decimals  Multiplying Decimals  Watch this video for an example of multiplying decimal numbers. 
Multiplying Decimals Exercises  Do this assessment and check your answers. 

Decimal Operations 1  Read the "Multiply Fractions" section up to the header "Multiply by Powers of Ten". Pay attention to the overview of the steps for multiplying two fractions. Do examples 5.15–5.17 and check your answers. If you need more practice, do Try It exercises 5.29–5.34. 

4.7: Dividing Decimals  Dividing Decimals  Watch these videos for examples of dividing with decimal numbers. 
Decimal Operations 2  Read the "Divide Decimals" section, and pay attention to the stepbystep summaries of how to divide decimals. Do examples 5.19–5.23 and check your answers. If you need more practice, do Try It exercises 5.37–5.46. 

4.8: Word Problems Using Decimals  Applications with Decimals  Watch this video to see how to solve word problems that use decimals. 
Applications with Decimals Exercises  After you watch the video, complete this assignment. The solutions to the problems are at the end of the document. 

5.1: Introduction to Ratios  Introduction to Ratios  Watch this video to learn how ratios work. Ratios are essentially fractions, so you will be applying many of the concepts you learned in Unit 3. 
Ratios  Watch this video on ratios to reinforce what you just learned. 

Ratios Exercises  Do this homework assignment, which reviews writing fractions in their reduced forms. You can check your answers at the end of the document. 

5.2: Finding Unit Rates and Prices  Finding Unit Rates and Prices  Watch these videos to see how to determine unit prices and rates. 
Expressing Ratios as Fractions  Do this assessment. If you struggle with any of the problems, you can watch a video or get a hint. 

5.3: Understanding Proportions  Solve Proportions and their Applications  Read this section up to "Solve Applications using Proportions". Be sure to review how to solve for an unknown value in a proportion. Do examples 6.40–6.44 and check your answers. 
Solving Proportions  Watch this video for more examples. 

5.4: Applications of Proportions  Solve Proportions and their Applications  Read this section, starting at "Solve Applications using Proportions". This section gives many realworld examples of how proportions are used. Do examples 6.45–6.47 and check your answers. 
Applications of Proportions  Watch this video for more examples. 

Applications of Proportions Exercises  Try this assignment for more word problems about proportions. You can check your answers at the end of the document. 

6.1: Describing the Meaning of Percent  Describing the Meaning of Percent  Watch these videos to see how percents are related to fractions with a denominator of 100. 
6.2: Converting Between Decimals, Fractions, and Percents  Representing a Number as a Decimal, Percent, and Fraction  Watch these two videos for worked examples of how to do conversions with percents. 
Ratio and Rates: Percent  Read this section and pay attention to the table that shows how to convert percents to fractions and decimals. Also pay close attention to the problems in Sample Set B. Then, try Practice Set B and check your answers. 

6.3: Determine the Percent Given Two Numbers  Solving Basic Percent Problems  Watch this video for examples of how to determine percents from real numbers. This video also shows examples of determining real numbers from percents. 
Percent Exercises  After you watch the video, do this assignment to practice these types of problems. Check your answers by looking at the solutions at the end of the document. 

6.4: Percent Increase or Decrease and Other Percent Applications  Calculating Percent Increase, Decrease, and Discount  Watch this video to see some examples of realworld applications of percents. 
Percent Increase, Decrease, and Discount Exercises  After you watch the video, do this assignment. Check your answers at the end of the document. 

Calculating Sales Tax and Commission  Watch this video to see examples of these important applications. 

Sales Tax and Commission Exercises  After you watch the video, do this assignment. Check your answers at the end of the document. 

7.1: Mean, Median, Mode, and Range  Averages and Probability  Read this section up to "Use the Basic Definition of Probability". Pay close attention to the summaries of how to do mean, median, and mode calculations. After you read, do examples 5.49–5.55 and check your answers. 
Mean, Median, Mode, and Range  Watch these three videos to see more examples, and to see what range means in the context of mathematics. 

7.2: StemandLeaf Plots  StemandLeaf Plots  Watch this video to learn about this type of plot. 
Reading Stem and Leaf Plots Exercises  After you watch the video, do the assignment and check your answers. 

7.3: Line Graphs  Reading Line Graphs and Misleading Line Graphs  The first video explains the structure of a line graph using simple examples. The second video shows how line graphs can be manipulated to misrepresent data. 
Make Line Plots Exercises  After you watch the videos, complete this assignment and check your answers. 

7.4: Bar Graphs  Reading Bar Graphs  Watch this video to see examples of bar graphs and their applications. 
Reading Bar Graphs Exercises  After you watch the video, do this assignment and check your answers. 

Reading Bar Graphs Exercises 2  If you would like extra practice, you can try this assignment. 

Create Bar Graphs Exercises  If you want even more practice, you can try this assignment too. 

7.5: BoxandWhisker Plots  BoxandWhisker Plots  These videos show examples of how boxandwhisker plots are used and examples of how to construct them. 
Creating Box and Whisker Plots Exercises  After you watch the videos, take this assessment and check your answers. 

7.6: Circle or Pie Graphs  Reading Circle or Pie Graphs  Watch this video to learn how pie graphs are constructed and interpreted. 
7.7: Pictographs  Reading Pictographs  Watch this video for an example of how to interpret a pictograph. 
Reading Pictographs Exercises  After you watch the video, do these exercises and check your answers. 

Course Feedback Survey  Course Feedback Survey 