{
  "id": "mixed-numbers",
  "version": "6d35aca36e3e",
  "status": "published",
  "name": "Mixed Numbers Calculator",
  "question": "How do I calculate mixed numbers?",
  "summary": "Adds, subtracts, multiplies, or divides two mixed numbers or fractions exactly, as a mixed number, an improper fraction, and a decimal.",
  "category": "math",
  "subcategory": "arithmetic",
  "url": "https://www.acalculator.org/math/mixed-numbers-calculator",
  "markdown": "https://www.acalculator.org/math/mixed-numbers-calculator.md",
  "kind": "function",
  "method": "Turn each mixed number into an improper fraction, apply the operation, reduce by the GCF, and write the result as a mixed number.",
  "assumptions": [
    "A minus sign applies to the whole mixed number: −1 1/2 means −(1 + 1/2) = −3/2.",
    "All arithmetic is exact with whole-number numerators and denominators of any size.",
    "Dividing by 0 has no answer."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "a": {
        "title": "First number",
        "description": "A mixed number, fraction, or whole number, such as 1 2/3, 5/3, or 2.",
        "type": "string",
        "pattern": "^-?\\d+( \\d+)?(/\\d+)?$"
      },
      "operation": {
        "title": "Operation",
        "description": "Add, subtract, multiply, or divide the first number by the second.",
        "type": "string",
        "enum": [
          "+",
          "-",
          "*",
          "/"
        ]
      },
      "b": {
        "title": "Second number",
        "description": "A mixed number, fraction, or whole number, such as 2 1/4, 9/4, or 3.",
        "type": "string",
        "pattern": "^-?\\d+( \\d+)?(/\\d+)?$"
      }
    }
  },
  "outputs": {
    "result": {
      "label": "Result",
      "description": "The answer in lowest terms, as a mixed number such as 3 11/12 or -1 1/4.",
      "format": "text"
    },
    "improper": {
      "label": "As an improper fraction",
      "description": "The answer as one fraction in lowest terms.",
      "format": "text"
    },
    "decimal": {
      "label": "As a decimal",
      "description": "The answer as a decimal.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "a": "1 2/3",
      "operation": "+",
      "b": "2 1/4"
    },
    "outputs": {
      "result": "3 11/12",
      "improper": "47/12",
      "decimal": 3.9166666666666665
    },
    "text": "1 2/3 + 2 1/4 = 3 11/12."
  },
  "examples": [
    {
      "given": {
        "a": "1 2/3",
        "operation": "+",
        "b": "2 1/4"
      },
      "expect": {
        "result": "3 11/12",
        "improper": "47/12",
        "decimal": 3.9166666666666665
      },
      "source": "hand calculation in content.mdx: 5/3 + 9/4 = 20/12 + 27/12 = 47/12 = 3 11/12; OpenStax, Prealgebra 2e, §4.6 Add and Subtract Mixed Numbers. https://openstax.org/books/prealgebra-2e/pages/4-6-add-and-subtract-mixed-numbers"
    },
    {
      "given": {
        "a": "7/4",
        "operation": "+",
        "b": "5/6"
      },
      "expect": {
        "result": "2 7/12",
        "improper": "31/12"
      },
      "source": "hand calculation in content.mdx: 21/12 + 10/12 = 31/12 = 2 7/12; OpenStax, Prealgebra 2e, §4.6 Add and Subtract Mixed Numbers. https://openstax.org/books/prealgebra-2e/pages/4-6-add-and-subtract-mixed-numbers"
    },
    {
      "given": {
        "a": "3 1/4",
        "operation": "-",
        "b": "1 1/2"
      },
      "expect": {
        "result": "1 3/4",
        "improper": "7/4",
        "decimal": 1.75
      },
      "source": "hand calculation in content.mdx: 13/4 − 6/4 = 7/4 = 1 3/4; OpenStax, Prealgebra 2e, §4.6 Add and Subtract Mixed Numbers. https://openstax.org/books/prealgebra-2e/pages/4-6-add-and-subtract-mixed-numbers"
    },
    {
      "given": {
        "a": "2 2/3",
        "operation": "*",
        "b": "1 1/2"
      },
      "expect": {
        "result": "4",
        "improper": "4",
        "decimal": 4
      },
      "source": "hand calculation in content.mdx: 8/3 × 3/2 = 24/6 = 4; OpenStax, Prealgebra 2e, §4.6 Add and Subtract Mixed Numbers. https://openstax.org/books/prealgebra-2e/pages/4-6-add-and-subtract-mixed-numbers"
    },
    {
      "given": {
        "a": "2 1/3",
        "operation": "/",
        "b": "1 1/4"
      },
      "expect": {
        "result": "1 13/15",
        "improper": "28/15"
      },
      "source": "old page FAQ and hand calculation in content.mdx: 7/3 × 4/5 = 28/15 = 1 13/15; OpenStax, Prealgebra 2e, §4.6 Add and Subtract Mixed Numbers. https://openstax.org/books/prealgebra-2e/pages/4-6-add-and-subtract-mixed-numbers"
    },
    {
      "given": {
        "a": "-2 1/3",
        "operation": "*",
        "b": "-1 2/3"
      },
      "expect": {
        "result": "3 8/9",
        "improper": "35/9"
      },
      "source": "hand calculation in content.mdx: (−7/3) × (−5/3) = 35/9 = 3 8/9; OpenStax, Prealgebra 2e, §4.6 Add and Subtract Mixed Numbers. https://openstax.org/books/prealgebra-2e/pages/4-6-add-and-subtract-mixed-numbers"
    },
    {
      "given": {
        "a": "-1 1/2",
        "operation": "+",
        "b": "1/4"
      },
      "expect": {
        "result": "-1 1/4",
        "improper": "-5/4",
        "decimal": -1.25
      },
      "source": "hand calculation in content.mdx: −6/4 + 1/4 = −5/4 = −1 1/4; OpenStax, Prealgebra 2e, §4.6 Add and Subtract Mixed Numbers. https://openstax.org/books/prealgebra-2e/pages/4-6-add-and-subtract-mixed-numbers"
    }
  ],
  "sources": [
    "OpenStax, Prealgebra 2e, §4.1 Visualize Fractions (mixed numbers and improper fractions). https://openstax.org/books/prealgebra-2e/pages/4-1-visualize-fractions",
    "OpenStax, Prealgebra 2e, §4.6 Add and Subtract Mixed Numbers. https://openstax.org/books/prealgebra-2e/pages/4-6-add-and-subtract-mixed-numbers"
  ],
  "related": [],
  "changelog": [
    {
      "date": "2026-09-29",
      "note": "Worked examples name a published reference for their rule."
    }
  ]
}