#5
Top 50 Mistake
Dividing by the new value instead of the original
"The Denominator Disaster"
The Mistake in Action
A phone's price increased from £400 to £500. Calculate the percentage increase.
Wrong: $$\frac{100}{500} \times 100 = 20\%$$
Why It Happens
Students divide by the new value (500) instead of the original value (400).
The Fix
In percentage change, you always divide by the ORIGINAL value.
$$\text{Percentage change} = \frac{\text{Change}}{\text{ORIGINAL}} \times 100$$
Correct calculation:
- Change = $500 - 400 = £100$
- Original = £400
- Percentage increase = $\frac{100}{400} \times 100 = 25\%$
Memory aid: "Original" starts with "O" — the "O"riginal goes "O"n the bottom.
Spot the Mistake
Can you identify where this student went wrong?
A phone's price increased from £400 to £500. Find the percentage increase.
Change = $500 - 400 = £100$
Percentage = $\frac{100}{500} \times 100$
$= 20\%$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: