Description

After learning how to manipulate fractions such as reducing, multiplying, dividing, adding and subtracting, we combine these skills with factoring and simplifying polynomaisl to learn how to perform fraction operations with rational expressions. Besides learning how to reduce, simplify, multiply, divide, add, and subtract rational expressions, we investigate complex fractions (fractions within fractions that are used in higher mathematics), solving rational equations, exploring ratios and proportions as well as variations.

Sections of this topic include:

1. Simplifying Rational Expressions

   The first stage of working with rational expressions is to simplify or reduce rational expressions. Groups in this section include Simplifying fractions; simplifying rational expressions; factoring and simplifying rational expressions.

2. Multiplying and Dividing Rational Expressions

   The next stage of working with rational expressions or fractions is to multiply or divide rational expressions. This group includes multiplying rational expressions; dividing rational expressions; multiplying and dividing harder rational expressions.

3. Adding and Subtracting Rational Expressions; The Least Commond Denominator

   The last stage of working with rational expressions is to be able to add or subtraction rational expressions that either have common denominators or that don't have common denominators. Groups in this section includes finding the least common denominator (the LCD); adding and subtracting rational expressions.

4. Complex Fractions

   An improvement of our knowledge of working with rational expressions or fractions is simplifying complex fractions (fractions composed of other fractions). The group in this section is named simplifying Complex Fractions.

5. Solving Rational Equations

   Combining our knowledge or rational expressions and solving equations, we explore how to solve rational equations. Groups within this section include solving rational equations and solving rational equations by factoring.

6. Ratio and Proportion

   A very useful application of rational expressions is using ratios and proportions to solve many common real world scenarios. Groups within this section include writing ratios in simplest form; solving proportions; using proportions to find the unknown sides of similar triangles.

7. Variation

   Another useful application of rational expressions is variation. Many scenarios in the real world involve direct, inverse or joint variation. Groups in this section include writing variation equations; writing variation equations and solving for the variation constant; writing variation equations then solving as indicated; solving variation applications; writing a phrase for a variation equation.