8.4 Solve Equations with Fraction or Decimal Coefficients
Learning Objectives
By the end of this section, you will be able to:
- Solve equations with fraction coefficients
- Solve equations with decimal coefficients
Solve Equations with Fraction Coefficients
This method worked fine, but many students don’t feel very confident when they see all those fractions. So we are going to show an alternate method to solve equations with fractions. This alternate method eliminates the fractions.
We will apply the Multiplication Property of Equality and multiply both sides of an equation by the least common denominator of all the fractions in the equation. The result of this operation will be a new equation, equivalent to the first, but with no fractions. This process is called clearing the equation of fractions. Let’s solve the same equation again, but this time use the method that clears the fractions.
Notice in Example 8.37 that once we cleared the equation of fractions, the equation was like those we solved earlier in this chapter. We changed the problem to one we already knew how to solve! We then used the General Strategy for Solving Linear Equations.
How To
Solve equations with fraction coefficients by clearing the fractions.
Step 1. Find the least common denominator of all the fractions in the equation.
Step 2. Multiply both sides of the equation by that LCD. This clears the fractions.
Step 3. Solve using the General Strategy for Solving Linear Equations.
In the next example, we’ll have variables and fractions on both sides of the equation.
In Example 8.40, we’ll start by using the Distributive Property. This step will clear the fractions right away!
Many times, there will still be fractions, even after distributing.
Solve Equations with Decimal Coefficients
The next example uses an equation that is typical of the ones we will see in the money applications in the next chapter. Notice that we will distribute the decimal first before we clear all decimals in the equation.
Media
ACCESS ADDITIONAL ONLINE RESOURCES
- Solve an Equation with Fractions with Variable Terms on Both Sides
- Ex 1: Solve an Equation with Fractions with Variable Terms on Both Sides
- Ex 2: Solve an Equation with Fractions with Variable Terms on Both Sides
- Solving Multiple Step Equations Involving Decimals
- Ex: Solve a Linear Equation With Decimals and Variables on Both Sides
- Ex: Solve an Equation with Decimals and Parentheses
Section 8.4 Exercises
Practice Makes Perfect
Solve equations with fraction coefficients
In the following exercises, solve the equation by clearing the fractions.
Solve Equations with Decimal Coefficients
In the following exercises, solve the equation by clearing the decimals.
Everyday Math
Writing Exercises
Self Check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ Overall, after looking at the checklist, do you think you are well-prepared for the next Chapter? Why or why not?