RWM101: Foundations of Real World Math

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.

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

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

Read this section up to example 7.6. Then, do example 7.6 and Try It exercises 7.11 and 7.12.

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

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

Watch this video. You should be able to recognize an equation that shows the identity property of addition.

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.

Watch this video for additional examples.

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

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.

Watch this video for more examples.

Read this section to see this definition written formally.

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?

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.

Watch these videos for more examples.

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.

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.

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.

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

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

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.

Watch this video for more examples of negative numbers using a number line as a reference.

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.

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

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.

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

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.

Watch these two videos for additional worked examples.

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

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

Watch this video for more examples.

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

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.

Complete this assessment for more practice. If you are struggling with any of the problems, use the videos or hints for help.

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

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.

Watch this video that uses number lines to show how different fractions are equivalent, which means to have the same value.

This video will help you identify proper and improper fractions.

Read up to the "Positive Mixed Numbers" section to see some examples of proper and improper fractions using a number line.

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.

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

After you watch the videos, try this ungraded assessment. If you are unsure on any of the problems, use the hints for help.

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

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

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.

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.

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.

Read this section for an overview of adding and subtracting fractions with different denominators. Do examples 4.67–4.72 and check your answers.

Watch this video for more examples of adding and subtracting fractions with like and unlike denominators.

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.

Complete this assessment for more practice. If you need help, use the videos or hints.

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.

After you watch the videos, complete these quizzes and check your answers. If you need more practice, do problem sets 2 and 3.

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

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

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

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

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

After you watch the videos, complete these assessments.

Then, complete these assessments.

Watch this video to learn about decimal place value.

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

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

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.

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

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

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

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.

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.

Do this assessment and check your answers.

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

Do this assessment and check your answers.

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

Watch this video for an example of multiplying decimal numbers.

Do this assessment and check your answers.

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.

Watch these videos for examples of dividing with decimal numbers.

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.

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

After you watch the video, complete this assignment. The solutions to the problems are at the end of the document.

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.

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

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

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

Do this assessment. If you struggle with any of the problems, you can watch a video or get a hint.

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.

Watch this video for more examples.

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.

Watch this video for more examples.

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

Watch these videos to see how percents are related to fractions with a denominator of 100.

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

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.

Watch this video for examples of how to determine percents from real numbers. This video also shows examples of determining real numbers from percents.

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.

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

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

Watch this video to see examples of these important applications.

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

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.

Watch these three videos to see more examples, and to see what range means in the context of mathematics.

Watch this video to learn about this type of plot.

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

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.

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

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

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

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

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

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

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

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

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

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