Intro W11

    • Objectives

        The sections for this week are:
      • 8.5 Simplify Complex Rational Expressions
      • 8.6 Solve Rational Equations
      • 8.7 Solve Proportion and Similar Figure Applications
      • 8.8 Solve Uniform Motion and Work Applications

     

          Intro W11

    Intro and Learning Objectives (click on all tabs to see all sections)

    • 8.5

      Learning Outcomes

      In this section, you will:

      • Simplify a complex rational expression by writing it as division
      • Simplify a complex rational expression by using the LCD

      Intro

      In this section we will simplify complex rational expressions, which are rational expressions with rational expressions in the numerator or denominator. 

      8.6

      Learning Outcomes

      In this section, you will:

      • Solve rational equations
      • Solve a rational equation for a specific variable

      Intro

      After defining the terms expression and equation early in Foundations, we have used them throughout this book. We have simplified many kinds of expressions and solved many kinds of equations. We have simplified many rational expressions so far in this chapter. Now we will solve rational equations.

      We have already solved linear equations that contained fractions. We found the LCD of all the fractions in the equation and then multiplied both sides of the equation by the LCD to “clear” the fractions.

      We will use the same strategy to solve rational equations. We will multiply both sides of the equation by the LCD. Then we will have an equation that does not contain rational expressions and thus is much easier for us to solve.

      But because the original equation may have a variable in a denominator we must be careful that we don’t end up with a solution that would make a denominator equal to zero.

      So before we begin solving a rational equation, we examine it first to find the values that would make any denominators zero. That way, when we solve a rational equation we will know if there are any algebraic solutions we must discard.

      An algebraic solution to a rational equation that would cause any of the rational expressions to be undefined is called an extraneous solution.

      8.7

      Learning Outcomes

      In this section, you will:

      • Solve proportions
      • Solve similar figure applications

      Intro

      When two rational expressions are equal, the equation relating them is called a proportion. Proportions are used in many applications to ‘scale up’ quantities. We’ll start with a very simple example so you can see how proportions work. Even if you can figure out the answer to the example right away, make sure you also learn to solve it using proportions.

      8.8

      Learning Outcomes

      In this section, you will:

      • Solve uniform motion applications
      • Solve work applications

      Intro

      We have solved uniform motion problems using the formula D=rt in previous chapters. We used a table to organize the information and lead us to the equation. 

      The formula D=rt assumes we know r and t and use them to find D. If we know D and r and need to find t, we would solve the equation for t and get the formula t=Dr.

      We have also explained how flying with or against a current affects the speed of a vehicle. We will revisit this ideas in some examples.

    Readings

    1. Text: Read the sections from Openstax book Links to an external site. (Links to an external site.)
    2. Videos: Watch all the videos from "Resources W10"

    Assignments

    Directions

    •  Each section is accompanied by a Handout. Each Handout contains a few definitions, a few "How To" explanations, examples, and "Try It" exercises. Using the structure of the handout you have to write your own notes. Your notes must contain:
      • Your name
      • The name of the section
      • Definitions and "How To" from the provided handout (this is optional, however, it will be a good idea to have the complete notes)
      • Everywhere there is a "Read Ex nr..." you have to read the example from the ebook and write in your notes : "I read the Ex nr..." . The link for the section in the ebook is provided at the bottom of the page.
      • You have to solve ALL "Try It" exercises.

    After you complete your notes you have to submit them. See Take Notes Methods. 

     

    Directions

    • To learn the material for this sections, take notes while watching each video and then demonstrate what you learned by doing the exercise below it.

     

    Directions

    • There are 4 Practice Homework this week. This are online Homework but you do not have to leave Canvas. Just click on each link, answer the questions, and came back for the next section. There is no partial credit, each question is either 100% good or not. However you have unlimited attempts for each question. A 5% per day penalty applies for Late work if you'll do it until Tuesday night. After that the Homework will be open only for practice.

     

    Quiz 1

    Directions

    TBA

     

    The due dates for assignments are Friday, Saturday, and Sunday.

    However, you can submit them until Tuesday night next week.

    A 5% per day penalty applies for late work if you'll do it until Tuesday night.