Solving Linear Equations with Fractions - Montana State University Billings

Solving Linear Equations with Fractions

To add or subtract fractions we must have a common denominator. With algebra problems, that sometimes becomes pretty messy. One technique to solve these equations uses the least common denominator (LCD) to clear the fractions so we have a regular linear equation.

Notice what happens in this arithmetic problem:

We know that

5 8 13

77 7

When we multiply each term by the LCD, which is 7, we get

7 5 7 8 7 13 7 7 7

5 8 13

This is still a true statement but we have eliminated the fractions. This is the process of clearing the fraction.

Clearing the fraction: Multiply each term by the LCD - even terms that do not contain fractions.

Remember: 1. Terms are parts of the equation separated by +, - or =

2x 3 4

2x 1 3 4

3 terms still 3 terms

2. We can do this only because it is an equation!

Example:

4 2x 1 1 69 LCD 18

184 18 2x 1 18 1 Multiply each term by 18

6 9

72 32x 1 2

Reduce each fraction - this eliminates the

fractions and the problem becomes a regular linear equation

Be careful to distribute the minus sign correctly!!

72 6x 3 2

6x 69 2

6x 67

x 67 6

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download