Module 6 Summary

In a tug of war, one team competes against another. Like tug of war, many games are competitive. The objective of such games is often for one player or team to achieve a certain objective before the opponent achieves the same objective.

 

There are often steps required to achieve the objectives in a game. In this module you learned to describe the steps needed to solve equations. When solving equations you often have to navigate through several steps in order to find the unknown variable, or the “hidden object.”

 

You investigated the following questions:

• How are rational expressions an extension of rational numbers?

• How can rational expressions be used to model situations related to competition and cooperative games?

You learned that the operations you previously performed on rational numbers can be extended to rational expressions. The table below summarizes the similarities.

 

Operation	Similiarities
Addition or Subtraction	terms must be expressed over a common denominator before the addition or subtraction of numerators can take place the denominator must not be equal to zero
Multiplication	numerators are multiplied together; denominators are multiplied together the product can be simplified according to the property of 1 the denominator must not be equal to zero
Division	division is done by multiplying the first term by the reciprocal of the second term the quotient can be simplified according to the property of 1 the denominator must not be equal to 0

 

You investigated rational equations and their applications. You learned that rational expressions must not have denominators equal to 0. As a result, you must identify non-permissible values of the variable when simplifying rational expressions and solving rational equations.

 

The first step in solving rational equations is to clear the denominator. Once this is done, the resulting equation will be linear or quadratic. You can then use an appropriate strategy to solve this equivalent equation.

 

This module has addressed the theme of competitive and cooperative games. You learned how to model given scenarios with rational expressions and equations. You discovered how to use rational equations to solve problems related to court dimensions, motion problems, cooperative work situations, and proportions.

 

Module 6: Rational Expressions and Equations, Video Summary is a look back at the math you explored. Watch Module 6: Rational Expressions and Equations, Video Summary to review what you learned and to confirm your answers to the module questions.

The following table summarizes the learning outcomes in Module 6. Complete a table like this one by listing the activities you undertook to address each outcome. You can use Module 6: Rational Expressions and Equations, Video Summary to help you recall major activities. You can also revisit the lessons.

 

Save a copy of your completed table in your course folder for review.

 

Outcomes for This Module	Learning Activities in Which I Addressed This Outcome
Determine equivalent forms of rational expressions.
Perform operations on rational expressions.
Solve problems that involve rational equations.