Equations involving Fractional Forms

When we have linear equations with fractions we first take steps to transform the equation into one without fractions.

To do this:

1. Find the Lowest common denominator (LCM) for all the fractions. This is the lowest number that all the numbers in the

denominator divide into exactly.

2. We multiply each term in the equation by the LCM.

This will change the equation into one without fractions and we can solve it with the usual methods.

To see some examples of how this is done, click on the word "Example":

Example 1: Solve

Example 2: Solve

Example 3: Solve

Example 4: Solve

Word Problems:

In order to solve work problems of this type it is helpful to use the following steps:

1. Read through the problem carefully and identify what you are trying to find. This is the unknown.

2. Assign a letter to the unknown. For example x = unknown quantity.

3. Read through the problem again and write an equation for x.

4. Solve the equation using the methods for solving linear equations.

To see some examples of how this is done, click on the word "Example": 

Example 5: Find a number such that three-eighths of the number minus one half of it is 14 less than three-fourths of the number.

Example 6: The width of a rectangular parking lot is 8 feet less than three-fifths of the length. The perimeter of the lot is 400 feet. Find the length and width of the lot.

Example 7: One of two complimentary angles is 6⁰ larger than one-half of the other angle. Find the measure of each of the angles.

Example 8: Dominic’s present age is 10 years more than Michele’s present age. In 5 years Michele’s age will be three-fifths of Dominic’s age. What are their present ages?