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In this lesson we look at How To Solve Equations With Fractions on Both Sides.

Prior to doing this lesson, you need to know how to solve equations with letters and/or brackets on both sides.

If you need to find out how to do Variable Letters On Both Sides Equations, then go through our previous lesson on this at the following link:

Solving Variable Letter on Both Sides Lesson

The method for “Fractions Both Sides” is basically the same as solving equations with the letter on both sides, except that we need to do an extra cross multiplying step at the beginning.

Prior to going through our lesson on “Fractions Both Sides” :

We also recommend you check that you understand the material from the following previous lessons:

Cross Multiplying Ratio Equations Lesson

Expanding Brackets Using the Distributive Rule Lesson

Fractions Both Sides Equation

Here is a typical “Fractions Both Sides” Equation.

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These types of Equations are done the same way as “Variable Letter on Both Sides” equations, but we have one extra beginning step at the start.

Fractions Both Sides Working Out Steps

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The cross multiplying is the same as we do for Ratios.

Eg. The Ratio Equation 3/4 = 6/8 cross multiplied gives

8×3 = 6×4 which is a true equation,

and so cross multiplying is a legitimate method.

Fractions Both Sides – Example One

Here is how we do the Cross Multipying Step for a typical “Fractions Both Sides” Equation:

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Note that we need to use Brackets to make sure ALLL the terms in the top line “numerator” get multiplied.

After we have completed the Cross Multiplying, we are left with a normal “Variable Letter Both Sides” equation to solve.

We solve this as follows:

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If you do not know how to Solve for Variable Letter on Both Sides, then see our previous lesson on this at the following link:

Solving Variable Letter on Both Sides Lesson

Fractions Both Sides – Example Two

In this example, only one side has a fraction.

We do a little “trick” which involves putting the non-fraction side as being a fraction that is / 1

We can then do the Cross Multiplying Step.

Here is the example, showing the Cross Multiplying Step

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Here are the remaining steps that are required to get to the final answer:

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Videos About Fractions Both Sides Equations

These two videos show how to use the Proportions Cross Multiplying Method to Solve Equations.

And here is the second video you need to watch.

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