Which common denominators are used?

The keys use the least common denominator of the terms shown. Easier uses 2 or 4; on level uses common denominators up to 12. Harder has four equations using 12 and two using 20.

What solutions are included?

Easier has six integer solutions. On level has four integer and two half-integer solutions. Harder has two integer and four half-integer solutions. Every setting includes exactly one zero solution.

What does the answer key show?

By default, every original term is multiplied and simplified. The key then combines like terms where needed, solves with reasons and checks the answer in the original equation. Choose Answers only for final answers without the worked steps.

Can students use another method?

Other exact methods are valid. This sheet asks students to practice clearing the denominators before solving.

8th grade clearing fractional coefficients

8th grade clearing fractional coefficients worksheets

These six equations practice multiplying every term on both sides by a common denominator. Easier has one variable term and one constant on each side, with denominators up to 4 and integer solutions. On level adds some collection of like terms and denominators requiring common multiples up to 12, with two half-integer solutions. Harder has four terms on each side and uses 12 and 20, more opposing signs and four half-integer solutions. The default key shows every product before collecting and solving.

Free printable PDF worksheet, aligned to Common Core 8.EE.C.7.b.

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The kind of problems you'll get

Choose a common multiple of the denominators. Multiply every term by it, then solve and check.

x − 3 = 3/2 × x − 3/2
Answer: x = −3
2 × x + 5/2 = x + 7/2
Answer: x = 1
−7/6 × z + 1/2 × z − 1/3 = −z + 2/3
Answer: z = 3

Every print pulls a fresh set of problems at this level, so a make-up test or a second sibling never gets the same sheet.

What's on an 8th grade sheet

Clearing fractional coefficients. Choose a common multiple of the denominators. Multiply every term by it, then solve and check. 6 problems per page.

Every version prints on US Letter or A4, with its answer key after the problems.

How to teach this

Find a common multiple of all the written denominators, including those in constant terms. Write the multiplier beside every term on both sides. Simplify those products before collecting like terms, and keep the original equation for the final check.

Watch for: Multiply integer terms as well as fractional terms, on both sides of the equals sign. Keep every sign when simplifying the products, and check in the original equation.

Common questions about 8th grade clearing fractional coefficients

Which common denominators are used?: The keys use the least common denominator of the terms shown. Easier uses 2 or 4; on level uses common denominators up to 12. Harder has four equations using 12 and two using 20.
What solutions are included?: Easier has six integer solutions. On level has four integer and two half-integer solutions. Harder has two integer and four half-integer solutions. Every setting includes exactly one zero solution.
What does the answer key show?: By default, every original term is multiplied and simplified. The key then combines like terms where needed, solves with reasons and checks the answer in the original equation. Choose Answers only for final answers without the worked steps.
Can students use another method?: Other exact methods are valid. This sheet asks students to practice clearing the denominators before solving.

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Aligned to Common Core 8.EE.C.7.b. Reviewed by the One more sheet team. Content version 241, updated October 2026.

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