Protocol
Multiply successive percentage changes
The second change usually acts on what the first change left behind.
When it fits
- Several increases or reductions are applied in sequence.
When to avoid it
- Check the stated base: two adjustments explicitly calculated from the original amount follow a different rule.
Why it matters
Convert each successive change into a multiplier and apply them in order. Adding signed percentages treats their bases as identical when they are not. Write the intermediate quantity once when the result seems counterintuitive.
Steps
- Use 1 plus the decimal increase, or 1 minus the decimal decrease.
- Multiply the starting quantity by each successive factor.
- Compare the final value with the original only after the sequence is complete.
An example
Starting at 100, a 20% rise followed by a 20% fall gives 100 × 1.2 × 0.8 = 96, not 100.
Check your result
Every change uses the quantity that actually exists at that step.
Keep this limit in mind
- Check the stated base: two adjustments explicitly calculated from the original amount follow a different rule.
Evidence and sources
Supports
Successive percentage changes act on changing bases, so their multipliers combine by multiplication.
The worked example assumes the stated changes are successive, not both independently calculated from the same original base.
Prealgebra 2e, 6.2: Solve General Applications of Percent · Percent-change identity applied successively