{
  "id": "math.fractions.add-numerators-keep-denominator",
  "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.add-numerators-keep-denominator",
  "uuid": "434a29b0-8c52-4db3-a2d6-81c86e5e5d6c",
  "version": "0.1.1",
  "status": "draft",
  "trust": "low",
  "title": "Adding numerators and keeping one denominator",
  "statement": "To add fractions you add the numerators and keep the denominator, whichever denominator is written, because the denominator is just a label that does not take part in the sum.",
  "kind": "overgeneralization",
  "domain": "math.fractions",
  "about": [
    {
      "scheme": "CCSS",
      "code": "5.NF.A.1",
      "uri": "http://corestandards.org/Math/Content/5/NF/A/1/"
    }
  ],
  "level_band": [
    "primary",
    "middle"
  ],
  "locale": "en",
  "evidence_patterns": [
    {
      "item_shape": "add two fractions with unlike denominators",
      "signature": "response numerator = a + c; response denominator is one of the given denominators (usually the first or the larger), with no conversion of the addends",
      "example": {
        "item": "1/2 + 1/3",
        "expected": "5/6",
        "response": "2/3"
      },
      "notes": "Like-denominator items are answered correctly, which is the discriminator against math.fractions.add-across."
    }
  ],
  "discriminators": {
    "vs_slip": "Consistent across unlike-denominator items; the learner can state the rule (\"the bottom stays\") when asked.",
    "vs": {
      "math.fractions.add-across": "Give a like-denominator item. This belief answers 1/4 + 2/4 = 3/4 correctly; add-across gives 3/8."
    }
  },
  "relations": {
    "conflicts_with": [
      {
        "external": "http://corestandards.org/Math/Content/5/NF/A/1/",
        "label": "CCSS 5.NF.A.1: add and subtract fractions with unlike denominators"
      }
    ],
    "resolved_by": [
      {
        "external": "http://corestandards.org/Math/Content/5/NF/A/1/",
        "label": "CCSS 5.NF.A.1: add and subtract fractions with unlike denominators"
      }
    ],
    "confusable_with": [
      "math.fractions.add-across"
    ]
  },
  "alignments": [
    {
      "scheme": "CCSS",
      "code": "5.NF.A.1",
      "uri": "http://corestandards.org/Math/Content/5/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": "Ni, Y., & Zhou, Y.-D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist, 40(1), 27-52.",
        "doi": "10.1207/s15326985ep4001_3"
      }
    ],
    "origin": "literature",
    "notes": "Stub created so that math.fractions.add-across's discriminator resolves. Needs a second evidence pattern and 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"
}