{
  "schema": "vedokrok.public-item.v1",
  "release_id": "MHC-RPUB-20260920-75ad787a",
  "url": "/knowledge/multiply-successive-percentage-changes",
  "id": "MHC-D-RESEARCH-0246",
  "version": "0.1.0",
  "title": "Multiply successive percentage changes",
  "summary": "The second change usually acts on what the first change left behind.",
  "kind": "protocol",
  "body": "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.",
  "limits": [
    "Check the stated base: two adjustments explicitly calculated from the original amount follow a different rule."
  ],
  "topics": [
    "union-numerical-reasoning"
  ],
  "intents": [],
  "source_ids": [
    "RS-767005552D5DD114"
  ],
  "evidence": [
    {
      "claim": "Successive percentage changes act on changing bases, so their multipliers combine by multiplication.",
      "source_id": "RS-767005552D5DD114",
      "role": "supports",
      "note": "The worked example assumes the stated changes are successive, not both independently calculated from the same original base.",
      "locator": "Percent-change identity applied successively"
    }
  ],
  "use_when": [
    "Several increases or reductions are applied in sequence."
  ],
  "avoid_when": [
    "Check the stated base: two adjustments explicitly calculated from the original amount follow a different rule."
  ],
  "example": "Starting at 100, a 20% rise followed by a 20% fall gives 100 × 1.2 × 0.8 = 96, not 100.",
  "check": "Every change uses the quantity that actually exists at that step.",
  "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."
  ],
  "sources": [
    {
      "id": "RS-767005552D5DD114",
      "title": "Prealgebra 2e, 6.2: Solve General Applications of Percent",
      "url": "https://openstax.org/books/prealgebra-2e/pages/6-2-solve-general-applications-of-percent"
    }
  ],
  "relations": [],
  "collections": [
    {
      "id": "RC-D976097B2A42D9AC",
      "title": "Make the numbers answer the right question",
      "url": "/collections/make-the-numbers-answer-the-right-question"
    }
  ]
}