In this lesson:
A batch needs cup of flour. You have cups to spend.
How many batches can you make — and how do you solve it cleanly?
By the end of this lesson, you should be able to:
Multiplying both sides by 3 is the multiplication property of equality.
To clear fractions, multiply every term by the LCD.
The LCD of , , and is . Multiply every term:
In , multiplying by :
The middle term is the one people forget.
Since , multiplying by clears it — just like an LCD.
Solving , isolate :
"Zero-point-three of is 2.7" — so is bigger than 2.7, not tiny.
Clearing fractions handled ugly numbers. Now: ugly structure.
From :
Work each step, then advance to check.
Say it as an operation on both sides:
The sign change is a result of subtracting — not a separate rule.
Both paths give . Which would you choose?
A student expands as:
What did they forget? Write the correct expansion.
Commit to an answer before you advance.
Solve completely, then check:
No scaffolding. Clear fractions, distribute, collect, solve, verify.
Distribute to every term — , not When clearing, multiply every term, even whole numbers "Move it" really means subtract from both sides — keep the sign right To undo , multiply by ; don't flip the division
✓ Clearing fractions or decimals turns hard equations into familiar ones ✓ Distribute and collect to tame any structure ✓ A messy equation is a clean one in a costume
You can now solve any single linear equation.
Next you'll solve systems — two equations at once (8.EE.C.8). The clearing, distributing, and collecting you mastered today are the engine inside substitution and elimination.