# 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

• 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.

#### 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?