{
  "id": "math.fractions.multiply-with-common-denominator",
  "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.multiply-with-common-denominator",
  "uuid": "116cbd32-81bd-4fbb-b5b2-31a47ff576b4",
  "version": "0.1.1",
  "status": "draft",
  "trust": "low",
  "title": "Multiplying needs a common denominator",
  "statement": "Before multiplying fractions you must write them with a common denominator, then multiply the numerators and keep the denominator.",
  "kind": "overgeneralization",
  "domain": "math.fractions",
  "about": [
    {
      "scheme": "CCSS",
      "code": "5.NF.B.4",
      "uri": "http://corestandards.org/Math/Content/5/NF/B/4/"
    }
  ],
  "level_band": [
    "primary",
    "middle"
  ],
  "locale": "en",
  "evidence_patterns": [
    {
      "item_shape": "multiply two fractions with unlike denominators",
      "signature": "converts to a common denominator, multiplies numerators and keeps the common denominator",
      "example": {
        "item": "1/2 x 1/3 = ?",
        "expected": "1/6",
        "response": "3/6 x 2/6 = 6/6 = 1"
      }
    },
    {
      "item_shape": "multiply two fractions with like denominators",
      "signature": "multiplies numerators and keeps the shared denominator",
      "example": {
        "item": "2/5 x 3/5 = ?",
        "expected": "6/25",
        "response": "6/5"
      }
    }
  ],
  "discriminators": {
    "vs_slip": "The extra common-denominator step is visible in the working and repeated across items. A slip does not add that step.",
    "vs": {
      "math.fractions.cross-multiply-to-multiply": "Cross-multipliers do not convert denominators; they give 1/2 x 1/3 = (1x3)/(2x1) = 3/2.",
      "math.fractions.add-across": "Add-across is the mirror error (addition treated like multiplication). A learner with both answers 1/2 + 1/3 = 2/5 and 1/2 x 1/3 = 6/6."
    }
  },
  "relations": {
    "conflicts_with": [
      {
        "external": "http://corestandards.org/Math/Content/5/NF/B/4/",
        "label": "CCSS 5.NF.B.4: multiply a fraction or whole number by a fraction"
      }
    ],
    "resolved_by": [
      {
        "external": "http://corestandards.org/Math/Content/5/NF/B/4/",
        "label": "CCSS 5.NF.B.4: multiply a fraction or whole number by a fraction"
      }
    ],
    "confusable_with": [
      "math.fractions.cross-multiply-to-multiply",
      "math.fractions.multiply-mixed-parts-separately"
    ]
  },
  "alignments": [
    {
      "scheme": "CCSS",
      "code": "5.NF.B.4",
      "uri": "http://corestandards.org/Math/Content/5/NF/B/4/",
      "relation": "about"
    }
  ],
  "provenance": {
    "sources": [
      {
        "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",
        "note": "Overgeneralisation of the addition procedure to multiplication."
      },
      {
        "type": "paper",
        "citation": "Siegler, R. S., & Lortie-Forgues, H. (2015). Conceptual knowledge of fraction arithmetic. Journal of Educational Psychology, 107(3), 909-918.",
        "doi": "10.1037/edu0000025"
      },
      {
        "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"
}