{
  "id": "math.fractions.cancel-matching-digits",
  "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.cancel-matching-digits",
  "uuid": "9b81e6e0-ad37-42aa-9494-bc6892e7140b",
  "version": "0.1.1",
  "status": "draft",
  "trust": "low",
  "title": "Cancelling matching digits",
  "statement": "A fraction is simplified by crossing out a digit that appears in both the numerator and the denominator.",
  "kind": "notation-confusion",
  "domain": "math.fractions",
  "about": [
    {
      "scheme": "CCSS",
      "code": "4.NF.A.1",
      "uri": "http://corestandards.org/Math/Content/4/NF/A/1/"
    }
  ],
  "level_band": [
    "middle",
    "secondary"
  ],
  "locale": "en",
  "evidence_patterns": [
    {
      "item_shape": "simplify a fraction whose numerator and denominator share a digit",
      "signature": "deletes the shared digit from both numbers",
      "example": {
        "item": "Simplify 12/24",
        "expected": "1/2",
        "response": "1/4 (cancelling the 2s)"
      },
      "notes": "16/64 = 1/4 and 19/95 = 1/5 happen to be true, which reinforces the rule."
    }
  ],
  "discriminators": {
    "vs_slip": "Ask the learner to simplify 16/64 and then 12/24 and explain. The belief is 'the sixes cancel'; a slip has no digit-based rule.",
    "vs": {
      "math.fractions.equivalence-additive": "Additive reasoners subtract from both parts; digit cancellers delete a digit and leave the rest."
    }
  },
  "relations": {
    "conflicts_with": [
      {
        "external": "http://corestandards.org/Math/Content/4/NF/A/1/",
        "label": "CCSS 4.NF.A.1: explain why a fraction a/b is equivalent to (n x a)/(n x b)"
      }
    ],
    "resolved_by": [
      {
        "external": "http://corestandards.org/Math/Content/4/NF/A/1/",
        "label": "CCSS 4.NF.A.1: explain why a fraction a/b is equivalent to (n x a)/(n x b)"
      }
    ],
    "confusable_with": [
      "math.fractions.equivalence-additive"
    ]
  },
  "alignments": [
    {
      "scheme": "CCSS",
      "code": "4.NF.A.1",
      "uri": "http://corestandards.org/Math/Content/4/NF/A/1/",
      "relation": "about"
    }
  ],
  "provenance": {
    "sources": [
      {
        "type": "book",
        "citation": "Ashlock, R. B. (2010). Error Patterns in Computation: Using Error Patterns to Help Each Student Learn (10th ed.). Allyn & Bacon."
      },
      {
        "type": "paper",
        "citation": "Brown, J. S., & VanLehn, K. (1980). Repair theory: A generative theory of bugs in procedural skills. Cognitive Science, 4(4), 379-426.",
        "doi": "10.1207/s15516709cog0404_3",
        "note": "Repair theory: bugs formed by over-literal reading of a procedure's surface form."
      }
    ],
    "origin": "llm-drafted",
    "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."
  },
  "history": {
    "changelog": [
      {
        "version": "0.1.1",
        "date": "2026-09-05",
        "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."
      }
    ]
  },
  "license": "CC-BY-4.0"
}