Equations
One-step decimal equations worksheets
Practice ten one-step equations with decimal operands and exact terminating solutions. Use inverse operations and check each solution with the original decimal values.
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One-step fraction equations worksheets
Solve ten equations containing proper fractions and signed mixed numbers. Practice fractional coefficients and inverse operations, with exact working and answers rounded to hundredths.
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Solve each equation using exact fractions, then give the answer to the nearest hundredth. The key retains the exact value before showing the rounded answer.
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Customize this worksheetKeep exact working separate from final rounding
These equations can have fractional or recurring-decimal solutions. The worksheet asks for the nearest hundredth; the key also retains an exact solution, shows the intermediate equations and substitutes the exact value back into the original relationship.
A rounded decimal is a report of the solution, not necessarily an exact substitute for it. Round only at the end. In the two-step sets, a fractional coefficient may appear alongside integer or decimal constants.
Learning objective
What this activity builds
Interpret fractional or mixed-number quantities and undo one operation without losing the sign or denominator.
Worked example
Solve −(2 1/2)x = 3 3/4.
x = −3/2; to the nearest hundredth, −1.50.
Write the mixed quantities as −5/2 and 15/4. Divide 15/4 by −5/2, or multiply by −2/5, to obtain −3/2. Check: (−5/2)(−3/2) = 15/4.
Teaching notes
Make the practice count
- Read a mixed number as one signed quantity.
- Convert mixed numbers before multiplying or dividing.
- Keep an exact fraction until the final rounding step.
- Compare the exact substitution check with the rounded decimal report.
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Ten equations cover addition, subtraction, and fractional multiplication with proper and mixed numbers in both equality orientations.
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