{
  "id": "math.fractions.cross-multiply-to-multiply",
  "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.cross-multiply-to-multiply",
  "uuid": "fef262fa-6980-416d-bd92-851b64e59458",
  "version": "0.1.1",
  "status": "draft",
  "trust": "low",
  "title": "Cross-multiplying to multiply fractions",
  "statement": "To multiply two fractions you multiply diagonally: the first numerator by the second denominator over the first denominator by the second numerator.",
  "kind": "procedural-bug",
  "domain": "math.fractions",
  "about": [
    {
      "scheme": "CCSS",
      "code": "5.NF.B.4",
      "uri": "http://corestandards.org/Math/Content/5/NF/B/4/"
    }
  ],
  "level_band": [
    "middle",
    "secondary"
  ],
  "locale": "en",
  "evidence_patterns": [
    {
      "item_shape": "multiply two proper fractions",
      "signature": "product numerator = a x d and product denominator = b x c for a/b x c/d",
      "example": {
        "item": "2/3 x 4/5 = ?",
        "expected": "8/15",
        "response": "10/12"
      }
    }
  ],
  "discriminators": {
    "vs_slip": "Consistent across items and usually accompanied by the word 'cross-multiply'. A slip is one diagonal product.",
    "vs": {
      "math.fractions.multiply-with-common-denominator": "Common-denominator multipliers show a conversion step in their working; cross-multipliers do not."
    }
  },
  "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.multiply-with-common-denominator"
    ]
  },
  "alignments": [
    {
      "scheme": "CCSS",
      "code": "5.NF.B.4",
      "uri": "http://corestandards.org/Math/Content/5/NF/B/4/",
      "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",
        "note": "Cross-multiplication misapplied to multiplication and addition."
      }
    ],
    "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"
}