O-Level E-Math and SEC G3 Mathematics K310
N3: Percentage
Handle percentage change, reverse percentage, repeated change, and financial contexts without mixing the base quantity.
Core notes
A percentage compares a change or quantity with a chosen base of . The most important decision is identifying the original base, especially in reverse and repeated percentage problems.
Expressing and comparing percentages
To express one quantity as a percentage of another, divide the comparison quantity by the stated base and multiply by . A percentage can exceed when the comparison quantity is larger than the base.
Percentage change
An increase of uses multiplier ; a decrease uses . Repeated changes multiply their successive multipliers and do not normally cancel.
Reverse percentages
If the final amount and percentage change are known, reconstruct the original by dividing the final amount by the relevant multiplier. Always label original and final values before substituting.
Formulae and methods
| Relationship | Use |
|---|---|
| Express one quantity as a percentage of another. | |
| Apply a percentage increase or decrease. |
Worked examples
Example 1: A price of is increased by and then reduced by . Find the final price.
- Use multipliers and .
- Calculate .
- Compare with the original to confirm the changes do not cancel.
Answer: The final price is .
Example 2: After a discount, a bag costs . Find its original price.
- The final price is of the original.
- Write .
- Divide: .
Answer: The original price was .
Chapter checkpoint
- Name the base quantity before calculating a percentage.
- Use a multiplier for repeated increase or decrease.
- For a reverse percentage, divide by the multiplier rather than reversing the stated change.
Exam traps and retrieval check
Avoid these traps
- Dividing by the final amount when the original is the required base.
- Adding percentage changes instead of multiplying successive multipliers.
- Trying to undo a decrease by applying the same percentage increase.
Check from memory
Can a percentage be greater than ?
Yes, when the quantity being compared is larger than the base.
What multiplier represents a decrease?
.
How do you reverse a increase?
Divide the final value by .
Official K310 coverage
This chapter maps to 5 official outcomes: N3.1, N3.2, N3.3, N3.4, N3.5. Check the official 2027 K310 syllabus for exact assessable wording and paper details.