{
  "id": "math.fractions.invert-both",
  "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.invert-both",
  "uuid": "aa675277-3fb6-44fe-aad9-20dacc62d775",
  "version": "0.1.1",
  "status": "draft",
  "trust": "low",
  "title": "Inverting both fractions when dividing",
  "statement": "To divide fractions you flip both fractions and then multiply.",
  "kind": "procedural-bug",
  "domain": "math.fractions",
  "about": [
    {
      "scheme": "CCSS",
      "code": "6.NS.A.1",
      "uri": "http://corestandards.org/Math/Content/6/NS/A/1/"
    }
  ],
  "level_band": [
    "middle",
    "secondary",
    "adult"
  ],
  "locale": "en",
  "evidence_patterns": [
    {
      "item_shape": "divide two proper fractions",
      "signature": "inverts both dividend and divisor and multiplies",
      "example": {
        "item": "1/2 / 3/4 = ?",
        "expected": "2/3",
        "response": "8/3"
      }
    }
  ],
  "discriminators": {
    "vs_slip": "Consistent across items. A slip produces one inverted-both answer; the bug produces it every time and the learner can recite 'flip them and multiply'.",
    "vs": {
      "math.fractions.invert-dividend": "Invert-dividend gives 6/4 on 1/2 / 3/4; invert-both gives 8/3."
    }
  },
  "relations": {
    "conflicts_with": [
      {
        "external": "http://corestandards.org/Math/Content/6/NS/A/1/",
        "label": "CCSS 6.NS.A.1: interpret and compute quotients of fractions"
      }
    ],
    "resolved_by": [
      {
        "external": "http://corestandards.org/Math/Content/6/NS/A/1/",
        "label": "CCSS 6.NS.A.1: interpret and compute quotients of fractions"
      }
    ],
    "confusable_with": [
      "math.fractions.invert-dividend"
    ]
  },
  "alignments": [
    {
      "scheme": "CCSS",
      "code": "6.NS.A.1",
      "uri": "http://corestandards.org/Math/Content/6/NS/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": "Newton, K. J. (2008). An extensive analysis of preservice elementary teachers' knowledge of fractions. American Educational Research Journal, 45(4), 1080-1110.",
        "doi": "10.3102/0002831208320851"
      },
      {
        "type": "paper",
        "citation": "Braithwaite, D. W., Pyke, A. A., & Siegler, R. S. (2017). A computational model of fraction arithmetic. Psychological Review, 124(5), 603-625.",
        "doi": "10.1037/rev0000072"
      }
    ],
    "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"
}