Lesson 1 of 5 | Arithmetic Methods
Percentage Change: Always Name the Base
Arithmetic Methods
Why this matters
A percentage is incomplete until its base is named. “20% more” means 20% of the original quantity; reversing the comparison changes the base and therefore the percentage.
Method
Write new = old × (1 ± rate/100). For successive changes, multiply factors instead of adding rates. A 20% rise followed by a 20% fall gives 1.20 × 0.80 = 0.96, a net 4% fall. To reverse a change, divide by the factor: after a 25% rise, the original is new ÷ 1.25.
Worked check
A fare moves from ₹480 to ₹540. Increase = ₹60; base = ₹480; percentage increase = 60/480 × 100 = 12.5%. Reverse comparison is 60/540 × 100 ≈ 11.11%, so it answers a different question.
Review checklist
- Circle the base quantity.
- Convert each change to a multiplier.
- Estimate the direction and size before calculating.
- Substitute the result back into the original relationship.