#18
Top 50 Mistake
Not applying operations to entire expressions
"The Partial Operation"
The Mistake in Action
Make $r$ the subject of $A = 2\pi r + 3$
Wrong:
$\frac{A}{2\pi} = r + 3$
$r = \frac{A}{2\pi} - 3$
Why It Happens
When dividing, students only divide the term with $r$, not the constant. They forget that division must apply to everything on that side.
The Fix
You must divide BOTH terms on the right side by $2\pi$:
Correct method: $$A = 2\pi r + 3$$
First subtract 3: $$A - 3 = 2\pi r$$
Then divide by $2\pi$: $$\frac{A - 3}{2\pi} = r$$
Key insight: Deal with addition/subtraction BEFORE multiplication/division (reverse of BIDMAS).
Spot the Mistake
Can you identify where this student went wrong?
Make $r$ the subject of $A = 2\pi r + 3$
$\frac{A}{2\pi} = r + 3$
$r = \frac{A}{2\pi} - 3$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: