Cancelling terms instead of factors
"The Term Terminator"
The Mistake in Action
Simplify $\frac{x + 4}{x}$
Wrong: $\frac{x + 4}{x} = \frac{\cancel{x} + 4}{\cancel{x}} = 4$
Why It Happens
Students see an $x$ on top and bottom and cancel them without realising you can only cancel factors that multiply the entire expression.
The Fix
You can only cancel something that multiplies everything in the numerator AND denominator.
In $\frac{x + 4}{x}$, the $x$ in the numerator is being added, not multiplied.
Correct: This fraction cannot be simplified further. $\frac{x + 4}{x}$ is the final answer.
When CAN you cancel? $\frac{3x}{6x^2} = \frac{3 \times x}{6 \times x \times x} = \frac{3}{6x} = \frac{1}{2x}$ ✓
Here the $x$ is a factor of both numerator and denominator.
Spot the Mistake
Can you identify where this student went wrong?
$\frac{x + 4}{x}$
$= \frac{\cancel{x} + 4}{\cancel{x}} = 4$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: