Topic Name Description
Course Introduction Page Course Syllabus
1.1: Commutative Law of Addition and Multiplication URL 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.

Page Commutative Law of Addition

Watch this video for additional explanation and examples of the commutative law of addition.

Page 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 URL 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.

Page Associative Laws of Addition and Multiplication

Watch these two videos for more examples of the associative law as it relates to addition and multiplication.

URL Properties of Addition Quiz

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

1.3: Identity Property of Addition Page 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 URL 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.

Page Inverse Property of Addition

Watch this video for additional examples.

1.5: Identity Property of Multiplication Page Identity Property of One

Watch this video for more examples of the identity property of multiplication.

1.6: Inverse Property of Multiplication URL 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.

Page Inverse Property of Multiplication

Watch this video for more examples.

1.7: Multiplication by Zero URL Properties of Identity, Inverses, and Zero

Read this section to see this definition written formally.

1.8: Dividing by Zero Is Undefined Page 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 URL 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.

Page The Distributive Property

Watch these videos for more examples.

2.1: Greatest Common Factor Page 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.

URL 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 URL 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.

Page Least Common Multiple

Watch this video for an additional example of determining the least common multiple for a set of three numbers.

Page 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 URL 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.

Page 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 Page 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.

URL Addition with Negative Numbers Exercises

After you watch the video, take this quiz and check your answers.

Page 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.

URL 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 URL 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.

Page Multiplying and Dividing Positive and Negative Numbers

Watch these two videos for additional worked examples.

2.6: Exponents Page Understanding Exponents

Watch this video to learn about how to translate a problem to exponent notation.

Page Exponent Examples

Then watch these videos to see examples of solving a problem using exponents.

Page Introduction to Exponents

Watch this video for more examples.

URL 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 URL 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 multi-step 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.

URL 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 URL Fractions of Whole Numbers

Read the "Parts of a Fraction" section to identify the different parts of a number written as a fraction.

URL 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 Page 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 Page Proper and Improper Fractions

This video will help you identify proper and improper fractions.

URL 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 URL 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 Page Changing an Improper Fraction to a Mixed Number

Watch these two videos for examples of how to perform these types of calculations.

URL 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 Page Fractions in Lowest Terms

Watch this video to learn how to reduce fractions to lowest terms.

Page Reducing Fractions

Watch this video for another explanation of how to reduce fractions to lowest terms.

URL 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 Page 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 URL 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 URL 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.

Page 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 URL 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.

URL 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 Page Adding and Subtracting Mixed Numbers Word Problems
Watch these two videos to see real-world applications to fractions and mixed numbers.
3.12: Multiplying Fractions and Mixed Numbers Page 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.

URL 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.

URL 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 Page Dividing Fractions

Watch these two videos to learn how do these calculations and see a few examples.

Page Dividing Mixed Numbers

Watch these two videos to learn how to divide mixed numbers and see a few examples.

URL 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 Page Multiplying and Dividing Fractions Word Problems

Watch these two videos for examples of multiplication and division problems.

URL Multiplying Fraction Word Problems Exercises

After you watch the videos, complete these assessments.

URL Dividing Fraction Word Problems Exercises

Then, complete these assessments.

4.1: Decimal Place Value Page Introduction to Decimals Part 1

Watch this video to learn about decimal place value.

URL Introduction to Decimals Part 1 Exercises

After you watch the video, take this quiz and check your answers.

4.2: Rounding Decimals Page Rounding Decimals

Watch this video for examples of how we can round decimals to specific decimal places.

URL 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 step-by-step directions for rounding numbers.

4.3: Converting Between Decimals and Fractions Page Introduction to Decimals Part 2

Begin by watching this video, which shows examples of converting decimals to fractions.

URL 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.

URL 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 Page Converting Repeating Decimals to Fractions

Watch these two videos for worked examples of how to handle repeating decimals.

URL 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 Page 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.

URL Adding Decimals: Hundredths Exercises

Do this assessment and check your answers.

Page Subtracting Decimals

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

URL Subtracting Decimals: Hundredths Exercises

Do this assessment and check your answers.

URL 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 Page Multiplying Decimals

Watch this video for an example of multiplying decimal numbers.

URL Multiplying Decimals Exercises

Do this assessment and check your answers.

URL 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 Page Dividing Decimals

Watch these videos for examples of dividing with decimal numbers.

URL Decimal Operations 2

Read the "Divide Decimals" section, and pay attention to the step-by-step 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 Page Applications with Decimals

Watch this video to see how to solve word problems that use decimals.

URL 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 Page 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.

Page Ratios

Watch this video on ratios to reinforce what you just learned.

URL 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 Page Finding Unit Rates and Prices

Watch these videos to see how to determine unit prices and rates.

URL 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 URL 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.

Page Solving Proportions

Watch this video for more examples.

5.4: Applications of Proportions URL Solve Proportions and their Applications

Read this section, starting at "Solve Applications using Proportions". This section gives many real-world examples of how proportions are used. Do examples 6.45–6.47 and check your answers.

Page Applications of Proportions

Watch this video for more examples.

URL 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 Page 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 Page Representing a Number as a Decimal, Percent, and Fraction

Watch these two videos for worked examples of how to do conversions with percents.

URL 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 Page 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.

URL 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 Page Calculating Percent Increase, Decrease, and Discount

Watch this video to see some examples of real-world applications of percents.

URL Percent Increase, Decrease, and Discount Exercises

After you watch the video, do this assignment. Check your answers at the end of the document.

Page Calculating Sales Tax and Commission

Watch this video to see examples of these important applications.

URL 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 URL 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.

Page 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: Stem-and-Leaf Plots Page Stem-and-Leaf Plots

Watch this video to learn about this type of plot.

URL Reading Stem and Leaf Plots Exercises

After you watch the video, do the assignment and check your answers.

7.3: Line Graphs Page 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.

URL Make Line Plots Exercises

After you watch the videos, complete this assignment and check your answers.

7.4: Bar Graphs Page Reading Bar Graphs

Watch this video to see examples of bar graphs and their applications.

URL Reading Bar Graphs Exercises

After you watch the video, do this assignment and check your answers.

URL Reading Bar Graphs Exercises 2

If you would like extra practice, you can try this assignment.

URL Create Bar Graphs Exercises

If you want even more practice, you can try this assignment too.

7.5: Box-and-Whisker Plots Page Box-and-Whisker Plots

These videos show examples of how box-and-whisker plots are used and examples of how to construct them.

URL Creating Box and Whisker Plots Exercises

After you watch the videos, take this assessment and check your answers.

7.6: Circle or Pie Graphs Page Reading Circle or Pie Graphs

Watch this video to learn how pie graphs are constructed and interpreted.

7.7: Pictographs Page Reading Pictographs

Watch this video for an example of how to interpret a pictograph.

URL Reading Pictographs Exercises

After you watch the video, do these exercises and check your answers.

Course Feedback Survey URL Course Feedback Survey