{
  "id": "math.fractions.multiply-mixed-parts-separately",
  "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.multiply-mixed-parts-separately",
  "uuid": "89ca96fb-84d7-4b24-a0f0-c24cf282e25c",
  "version": "0.1.1",
  "status": "draft",
  "trust": "low",
  "title": "Multiplying mixed numbers part by part",
  "statement": "To multiply mixed numbers you multiply the whole numbers together and the fractions together and put the two results back together.",
  "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"
  ],
  "locale": "en",
  "evidence_patterns": [
    {
      "item_shape": "multiply two mixed numbers",
      "signature": "product = (whole x whole) and (fraction x fraction) written as a mixed number; the cross terms are dropped",
      "example": {
        "item": "2 1/2 x 3 1/3 = ?",
        "expected": "8 1/3",
        "response": "6 1/6"
      }
    }
  ],
  "discriminators": {
    "vs_slip": "The answer is too small by exactly the two cross products and the pattern holds across items. A slip is an arithmetic error within the full method.",
    "vs": {
      "math.fractions.multiply-with-common-denominator": "That bug appears on proper-fraction items; this one only appears with mixed numbers."
    }
  },
  "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"
      },
      {
        "type": "book",
        "citation": "Lamon, S. J. (2012). Teaching Fractions and Ratios for Understanding: Essential Content Knowledge and Instructional Strategies for Teachers (3rd ed.). Routledge."
      }
    ],
    "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"
}