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Solving Equations with Fractions

I know fractions are difficult, but with these easy step-by step instructions you'll be solving equations with fractions in no time.

Do you start to get nervous when you see fractions? Do you have to stop and review all the rules for adding, subtracting, multiplying and dividing fractions?

If so, you are just like almost every other math student out there! But... I am going to make your life so much easier when it comes to solving equations with fractions!

Our first step when solving these equations is to get rid of the fractions because they are not easy to work with!

Let see what happens with a typical two-step equation with the distributive property.

In this problem, we would typically distribute the 3/4 throughout the parenthesis and then solve. Let's see what happens:

$equations with fractions$

Yuck! That just made this problem worse! Now we have two fractions to contend with and that means subtracting fractions and multiplying fractions.
So... let's stop here and say

"We DO NOT want to do this! DO NOT distribute fractions.

We are going to learn how to get rid of the fractions and make this much more simple!

So... what do we do? We are going to get rid of just the denominator in the fraction, so we will be left with the numerator, or just an integer!

I know, easier said than done! It's really not hard, but before I get into it, I want to go over one algebra definition.

We need to discuss the word term.

In Algebra, each term within an equation is separated by a plus (+) sign, minus (-) sign or an equals sign (=). Variable or quantities that are multiplied or divided are considered the same term.

For example:

That last example is the most important to remember. If a quantity is in parenthesis, it it considered one term!

Let's look at a few examples of how to solve these crazy looking problems!

Example 1

$equations with fractions$

Hopefully you were able to follow that example. I know it's tough, but if you can get rid of the fraction, it will make these problems so much easier. Keep going, you'll get the hang of it!

Example 2

$fraction equations$

Still confused? Check out this video explaining example 2.

If you want to see this example on video, click here to visit my You Tube channel.

Example 3

$solving equations with fractions$

For additional explanation of Example 3, view the following video:

If you want to see this example on video, click here to visit my You Tube channel.

Yes, the equations are getting harder, but if you take it step-by-step, you will arrive at the correct solution. Keep at it - I know you'll get it!

If You are Still Struggling..

Use this algebra calculator to check your answers to your very own problems. Hopefully this will help you to get through your homework.

Take a look at the questions that other students have submitted on equations with fractions.

Equations with Fractions: -5 = -19-x/7

Expression with Fractions: 1/3(7y-1) +1/6(4y+7)

To ask a question, please visit my Math Forum.

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Ready to Move On?

Check out the other lessons in this unit.

Solving Equations Unit:

Balancing Equations

Solving one step equations (addition).

Solving one-step subtraction equations.

Solving one-step multiplication equations.

Solving one-step division equations.

Solving two-step equations.

Equations with the Distributive Property

Solving equations with fractions

Solving Literal Equations

Equations with variables on both sides

Writing equations given a word problem

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