What numbers are used?

Each equation includes fractions and decimals. Easier uses one variable term and one constant on each side. On level adds some collection of like terms; harder requires collection on both sides. Easier has six integer solutions, on level has four integer and two half-integer solutions, and harder has two integer and four half-integer solutions. Each setting includes one zero solution.

What does the answer key show?

By default, the key shows exact decimal-to-fraction conversions, collection where needed, solving steps with reasons, and the exact solution. Choose Answers only for final answers without the worked steps.

Can students use another method?

Other exact methods are valid. Fractions with repeating decimal expansions must remain exact; a rounded decimal changes the equation.

8th grade equations in mixed numeric representations

8th grade equations in mixed numeric representations worksheets

These six equations mix fractions, decimals and integers. Easier uses familiar positive decimals, 0.5 and 0.25, with integer solutions. On level adds negative decimals, tenths and values greater than one. Harder includes place-value work with 0.05 and -0.15, more opposing signs and four half-integer solutions. The default key converts to exact fractions 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 an exact fraction or decimal strategy. Show your conversions and solve.

0.75 × d − 3 = 1/2 × d − 7/2
Answer: d = −2
1.5 × p − 3/2 = p − 1/2
Answer: p = 2
−17/12 × z + 0.75 × z − 5/3 = −z − 1
Answer: z = 2

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

Equations in mixed numeric representations. Choose an exact fraction or decimal strategy. Show your conversions and solve. 6 problems per page.

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

How to teach this

Convert each decimal without changing its sign or value. For example, 0.05 is 5/100, which reduces to 1/20. Keep repeating fractions exact rather than rounding them to finite decimals. Collect each side and solve.

Watch for: Keep the sign and place value when converting a decimal to a fraction. Use exact values throughout, and check both sides of the original mixed equation.

Common questions about 8th grade equations in mixed numeric representations

What numbers are used?: Each equation includes fractions and decimals. Easier uses one variable term and one constant on each side. On level adds some collection of like terms; harder requires collection on both sides. Easier has six integer solutions, on level has four integer and two half-integer solutions, and harder has two integer and four half-integer solutions. Each setting includes one zero solution.
What does the answer key show?: By default, the key shows exact decimal-to-fraction conversions, collection where needed, solving steps with reasons, and the exact solution. Choose Answers only for final answers without the worked steps.
Can students use another method?: Other exact methods are valid. Fractions with repeating decimal expansions must remain exact; a rounded decimal changes the equation.

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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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