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## Course: Algebra 1 > Unit 2

- Why we do the same thing to both sides: Variable on both sides
- Intro to equations with variables on both sides
- Equations with variables on both sides: 20-7x=6x-6

## Equation with variables on both sides: fractions

## Want to join the conversation?

## Video transcript

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## ACT Math : How to solve for a variable as part of a fraction

## Example Question #2 : How To Solve For A Variable As Part Of A Fraction

## Example Question #3 : How To Solve For A Variable As Part Of A Fraction

## Example Question #7 : How To Solve For A Variable As Part Of A Fraction

Let numerator = N and denominator = D.

According to the first statement,

According to the second statement, N / 2 = 3 * D.

Let's multiply the second equation by –2 and add itthe first equation:

## Example Question #4 : How To Solve For A Variable As Part Of A Fraction

Solve the following equation for the given variable:

To solve this equation we have to multiply both sides by the denominator to get rid of the fraction.

Then to solve the last step is to isolate the variable by dividing both sides by 12. Thus,

## Example Question #5 : How To Solve For A Variable As Part Of A Fraction

When the equation is cross multiplied, it becomes

## Example Question #6 : How To Solve For A Variable As Part Of A Fraction

Reduce any fractions in your final answer.

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## Equations with Fractions - Examples & Practice - Expii

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## How To Solve Equations With Fractions

## Step 1: Find the least common denominator

## Step 2: Multiply the least common denominator

Multiply the LCD to both sides of the equation.

## Step 3: Simplify the equation

Simplify both sides of the equation and make sure we’re only working with whole numbers.

## Step 4: Simplify until there's one term on both sides

## Step 5: Divide the coefficient on both sides

## Examples of how to solve equations with fractions

First, let’s find the least common denominator (LCD) of the fractions:

Multiply 30 on both sides of the equation. Make sure to simplify after distributing 30.

Move 6x on on the left-hand side of the equation to isolate the term with the variable.

Divide 14 on both sides of the equation to solve for x.

We can let n be the unknown number. We can set up the equation to solve the problem.

Multiplying 12 to both sides of the equation, we have:

Move 4 on the right-hand side of the equation.

Divide both sides by 4 to isolate n.

Hence, the unknown fraction is equal to 5/4.

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## How to solve equations with fractions

## What is a fractional equation?

Remember that multiplying a fraction by its reciprocal will always give you a value of ???1???.

For example ???4/5??? has a reciprocal of ???5/4??? because

???\frac{4}{5}\cdot\frac{5}{4}=1???

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???2\left(5x+\frac{1}{2}=12\right)???

???2(5x)+2\left(\frac{1}{2}\right)=2(12)???

## How to solve equations when there’s a fraction somewhere in the equation

## Take the course

???\frac{5}{4}\cdot\frac{4}{5}n=\frac{5}{4}\cdot20???

???\frac{20}{20}n=\frac{100}{4}???

First isolate the fractional term.

???\frac{4}{7}x+14-14=22-14???

???\frac{7}{4}\cdot\frac{4}{7}x=\frac{7}{4}\cdot8???

???\frac{28}{28}x=\frac{56}{4}???

???7\left(\frac{4}{7}x+14=22\right)???

???7\cdot\frac{4}{7}x+7\cdot14=7\cdot22???

Now we can solve for the variable using inverse operations.

???\frac{4x}{4}=\frac{56}{4}???

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## Solving Equations with Fractions

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

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!

We need to discuss the word term.

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

## Example 1 - Equations with Fractions

Take a look at this example on video if you are feeling overwhelmed.

## Example 2 - Equations with Fractions with the Same Denominator

## Example 3 - Equations with Two Fractions with Different Denominators

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## Module 8: Growth Models

Solving equations by clearing fractions, learning outcomes.

- Use the least common denominator to eliminate fractions from a linear equation before solving it
- Solve equations with fractions that require several steps

Solve: [latex]\Large\frac{1}{8}\normalsize x+\Large\frac{1}{2}=\Large\frac{1}{4}[/latex]

https://ohm.lumenlearning.com/multiembedq.php?id=71948&theme=oea&iframe_resize_id=mom1

## Solve equations by clearing the Denominators

- Find the least common denominator of all the fractions in the equation.
- Multiply both sides of the equation by that LCD. This clears the fractions.
- Isolate the variable terms on one side, and the constant terms on the other side.
- Simplify both sides.
- Use the multiplication or division property to make the coefficient on the variable equal to [latex]1[/latex].

Now here’s a similar problem for you to try. Clear the fractions, simplify, then solve.

https://ohm.lumenlearning.com/multiembedq.php?id=71948&theme=oea&iframe_resize_id=mom2

Solve: [latex]x+\Large\frac{1}{3}=\Large\frac{1}{6}\normalsize x-\Large\frac{1}{2}[/latex]

https://ohm.lumenlearning.com/multiembedq.php?id=142514&theme=oea&iframe_resize_id=mom3

Solve: [latex]1=\Large\frac{1}{2}\normalsize\left(4x+2\right)[/latex]

https://ohm.lumenlearning.com/multiembedq.php?id=142542&theme=oea&iframe_resize_id=mom25

- Question ID 142514, 142542. Authored by : Lumen Learning. License : CC BY: Attribution . License Terms : IMathAS Community License CC-BY + GPL
- Solve a Linear Equation with Parentheses and a Fraction 2/3(9x-12)=8+2x. Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/1dmEoG7DkN4 . License : CC BY: Attribution
- Ex 1: Solve an Equation with Fractions with Variable Terms on Both Sides. Authored by : James Sousa (Mathispower4u.com). Located at : https://youtu.be/G5R9jySFMpw . License : CC BY: Attribution
- Question ID 71948. Authored by : Alyson Day. License : CC BY: Attribution . License Terms : IMathAS Community License CC-BY + GPL
- Prealgebra. Provided by : OpenStax. License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected]

## IMAGES

## VIDEO

## COMMENTS

The general rule for solving equations with fractions — whether it be only on one side or both — is to try to get rid of all of them. The most common way to

To solve an equation with a variable in a fraciton, treat the denominator as a constant value and multiply both sides of the equation by the denominator in

This video provides two examples of how to solve a linear equation in one variable that contains fractions. The fractions are not cleared

This algebra video tutorial explains how to solve linear equations with fractions.

Isolate x on one side of the equation (whether x is part of the fraction or not). · If the only terms in your equation are fractions, you can cross-multiply them

Step 1: Find the least common denominator · Step 2: Multiply the least common denominator · Step 3: Simplify the equation · Step 4: Simplify until

In this lesson we'll look at how to solve equations with numerical fractions as coefficients and terms. To clear a fraction from an equation

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

Applications · 1. Set up a Variable Dictionary. Our variable dictionary will take the form of a well labeled diagram. · 2. Set up an Equation. The

Find the least common denominator of all the fractions in the equation. · Multiply both sides of the equation by that LCD. · Isolate the variable terms on one