Mrs.D Math · 8th Grade

CLEAN
SWEEP

Equations with Rational Numbers · Operations
⚖️ Equations
➗ Fractions
🔢 Decimals
🧹 ×LCM clears fractions
💯 ×10 or ×100 clears decimals
⚖️ x on both sides
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📚 Clearing Fractions & Decimals

🧹 Sweep Away the Fractions

Multiply every term by the LCM of the denominators. The fractions vanish — then solve like a normal equation!

1
Find the LCM of all denominators.
x/2 + 5/3 = x/6 + 3  →  LCM of 2, 3, 6 is 6
2
Multiply every term by the LCM — even the whole numbers!
3x + 10 = x + 18
3
Solve: move the x-terms together, then the constants.
2x = 8  →  x = 4

🔢 Sweep Away the Decimals

Multiply every term by a power of 10 — ×10 for tenths, ×100 for hundredths.

1
Count decimal places. One place? ×10. Two places? ×100.
0.4x + 1.2 = 0.2x + 2.8  →  ×10
2
Multiply every term:
4x + 12 = 2x + 28
3
Solve:
2x = 16  →  x = 8

🎮 How to Play

➗
Fractions — Clear with the LCM, then solve for x.
🔢
Decimals — Clear with a power of 10, then solve for x.
🌟
Mixed — Both types together for the ultimate challenge!
🧮
Calculator — Tap the calculator button (bottom-left) anytime. Try it in your head first, then verify!
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FRACTIONS
📺 Mrs.D Math Lesson
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🧠 Try it in your head first — then verify!
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