Equations with Fractions and Decimals
I can clear fractions or decimals from an equation and then solve it.
The problem this sheet solves
Clearing fractions or decimals is one move in two costumes, and it fails the same way both times: the multiplier reaches the terms with denominators and skips the one without. Multiplying x/2 + x/6 = 4 by 6 and writing 3x + x = 4 leaves an equation that is no longer equivalent, and the error is invisible unless the answer is checked. This sheet names the LCD and the power of ten as the SAME move so students carry one idea rather than two, and it insists the multiplier reach every term on both sides. Every equation here has exactly one solution, keeping the difficulty on the clearing step where it belongs.
The key rule
Multiply every term on both sides by a number that clears the mess: the LCD for fractions, a power of ten for decimals. Then solve the whole-number equation you are left with.
One term missed and the equation is no longer the one you started with.
Watch out
The mistake: Multiplying x/2 + x/6 = 4 by 6 and writing 3x + x = 4.
The fix: The 6 must reach the 4 as well: 3x + x = 24. This is the A11 error wearing a different hat.
What is included
- Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
- Practice page — six problems, building from foundational to multi-step
- Apply page — a word problem, a reasoning prompt, and an error-analysis task
- Assess — a half-page exit ticket, two to a sheet, with a score box
- Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
- Ink-saver edition of all 7 pages
- 14-slide teacher deck (PowerPoint) with presenter notes on every slide
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.