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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Two-step decimal equations worksheets
Practice ten two-step equations with decimals, fractional coefficients and grouped division. Keep exact values during the solution and round the final answer to two decimal places.
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Keep exact values while solving. Report the final answer to the nearest hundredth; use the exact solution when checking the original equation.
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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
Solve a two-operation relationship containing decimals without rounding intermediate calculations.
Worked example
Solve 0.6x + 1.4 = 3.9.
x = 25/6; to the nearest hundredth, 4.17.
Subtract 1.4 to get 0.6x = 2.5. Divide by 0.6: x = 2.5/0.6 = 25/6. This is a recurring decimal, so round only the final answer. The exact check is 0.6 × (25/6) + 1.4 = 3.9.
Teaching notes
Make the practice count
- Separate the algebraic decision from the decimal arithmetic.
- Leave a quotient as a fraction if its decimal does not terminate.
- Use the coefficient itself, including its sign, when dividing.
- Explain why a rounded value may not make both sides exactly equal.
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Includes affine, fractional-coefficient, and grouped-numerator equations. Exact solutions remain visible on the key.
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