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Solving Equations: Clearing Fractions

11 questions

8th - 8th Grade

Mathematics

This Grade 8 mathematics worksheet gives students focused practice with solving linear equations by clearing fractions. Across 11 multiple-choice questions, students identify the least common denominator (LCD), recognize what a common denominator means, determine the correct first and next steps, and decide which number to multiply across every term of an equation. The set also includes equations requiring students to apply the process and select the solution, including equations with fractional coefficients on one or both sides. Use this worksheet to reinforce the connection between finding an LCD and transforming a fractional equation into a form that is easier to solve. It is suitable for independent practice, a quick formative check, or review after direct instruction in Grade 8 algebra. Students can use the answer choices to explain why an LCD—not a greatest common factor or an arbitrary number—is needed. This is a free printable worksheet with a complete answer key for efficient checking.

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Worksheets

Solving Equations: Clearing Fractions

Total questions: 11

Name
Class
Date
1.

Find the least common denominator of these fractions: 

 27      221\frac{2}{7}\ \ \ \ \ \ \frac{2}{21}  

a)

7

b)

21

c)

18

d)

147

2.

To have a common denominator means two or more fractions have the same number on the ___________ of the fraction line.

a)

top

b)

bottom

3.
What is the least common denominator of 1/9 and 2/3?
a)
6
b)
3
c)
9
d)
21
4.
What do you multiply each term of an equation by to clear fractions?
a)
The greatest common factor
b)
The least common denominator
c)
whatever number you want
d)
zero
5.

Solve the equation by first clearing fractions:

a)

x = 1/8

b)

x = 4

c)

x = 3

d)

solution not listed

6.

Solve for c by clearing the fractions.

a)

1/3

b)

2/3

c)

1

d)

2

7.

What is the first step to solve this equation?

a)

Move all the variables to one side.

b)

Move all the constants to one side.

c)

Find the least common denominator.

d)

Plug in a number for X.

8.

What should you do next after finding the LCD?

a)

Move all the constants to one side.

b)

Move all the variables to one side.

c)

Multiply the LCD to all the variables

d)

Multiply the LCD to every term of the equation.

9.

When solving this equation by clearing the fractions, what number would you multiply each term in the equation by?

 23a+14a−8=7\frac{2}{3}a+\frac{1}{4}a-8=7  

a)

3

b)

4

c)

12

d)

15

10.

Solve this equation by clearing the fraction.

a)

x = -18

b)

x = 66

c)

x = 5

d)

x = -3

11.

Solve the equation by clearing the fraction.

 3+65x=9+85x3+\frac{6}{5}x=9+\frac{8}{5}x  

a)

x = -15

b)

x = -60

c)

x = 30

d)

x = 120

Answer Key

Solving Equations: Clearing Fractions

Total questions: 11

1.
b)

21

2.
b)

bottom

3.
c) 9
4.
b) The least common denominator
5.
c)

x = 3

6.
d)

2

7.
c)

Find the least common denominator.

8.
d)

Multiply the LCD to every term of the equation.

9.
c)

12

10.
b)

x = 66

11.
a)

x = -15

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FAQs

What does the Solving Equations: Clearing Fractions worksheet cover?

This Grade 8 worksheet covers solving linear equations by finding the least common denominator and multiplying every term by it to clear the fractions. Its 11 multiple-choice questions move from identifying LCDs and the meaning of a common denominator to applying the process and selecting solutions for equations with fractional coefficients.

How can I use this worksheet to teach students to clear fractions in equations?

Introduce the worksheet by modeling how to find the LCD, then emphasize that the LCD must multiply every term on both sides of the equation. Have students explain the sequence reflected in the questions—find the LCD, multiply every term, and then solve—before completing the equation-solving items independently. Ask students to justify why a choice such as a greatest common factor or multiplying only the variable is incorrect.

What mistakes should I watch for when students complete this worksheet?

Watch for students choosing the greatest common factor instead of the least common denominator, identifying the numerator rather than the denominator as the common part of a fraction, or using only one denominator when a shared LCD is required. In the application questions, students may multiply only the fractional terms instead of every term, skip finding the LCD first, or make sign and isolation errors after the fractions are cleared.

How do I assign and grade this clearing-fractions worksheet?

On Wayground, assign this worksheet as a printable PDF or as a digital quiz, and use its complete answer key to check the 11 multiple-choice responses. For printable submissions, scan student work with the Wayground for Teachers app to streamline grading. The printable format also supports schools that want to reduce screen time.

How can I differentiate this worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or increase the font size so the fraction-based equations and answer choices are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language when those options support access to the clearing-fractions practice.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across subjects, including downloadable PDFs and answer keys that support mastery of essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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