{
  "id": "improper-fraction",
  "version": "cb2be5011f06",
  "status": "published",
  "name": "Improper Fraction Calculator",
  "question": "How do I write an improper fraction?",
  "summary": "Converts an improper fraction to a mixed number, or a mixed number to an improper fraction, with the division or multiplication shown step by step and the result in lowest terms.",
  "category": "math",
  "subcategory": "arithmetic",
  "url": "https://www.acalculator.org/math/improper-fraction-calculator",
  "markdown": "https://www.acalculator.org/math/improper-fraction-calculator.md",
  "kind": "function",
  "method": "Improper to mixed: a ÷ b = q remainder r, so a/b = q r/b. Mixed to improper: w n/d = (w × d + n)/d. Both are then reduced by the greatest common factor.",
  "assumptions": [
    "Numbers are whole numbers up to 10¹² in size; the arithmetic is exact.",
    "A minus sign applies to the whole number: −2 1/3 means −(2 + 1/3) = −7/3. In a mixed number, type the minus sign on the whole number.",
    "In a mixed number the fraction part must be less than 1 (when there is a whole part).",
    "The answer keeps the fraction as typed; \"In lowest terms\" reduces it."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "mode": {
        "title": "Convert",
        "description": "Which way to convert: an improper fraction to a mixed number, or a mixed number to a fraction.",
        "type": "string",
        "enum": [
          "improper",
          "mixed"
        ]
      },
      "w": {
        "title": "Whole number",
        "description": "The whole-number part of the mixed number. A minus sign makes the whole mixed number negative.",
        "type": "integer",
        "minimum": -1000000000000,
        "maximum": 1000000000000
      },
      "n": {
        "title": "Numerator",
        "description": "The top number of the fraction.",
        "type": "integer",
        "minimum": -1000000000000,
        "maximum": 1000000000000
      },
      "d": {
        "title": "Denominator",
        "description": "The bottom number of the fraction: how many equal parts make one whole.",
        "type": "integer",
        "minimum": 1,
        "maximum": 1000000000000
      }
    }
  },
  "outputs": {
    "typed": {
      "label": "You typed",
      "description": "The fraction or mixed number you typed.",
      "format": "text"
    },
    "result": {
      "label": "Answer",
      "description": "The mixed number (for an improper fraction) or the improper fraction (for a mixed number), with the fraction as typed.",
      "format": "text"
    },
    "simplest": {
      "label": "In lowest terms",
      "description": "The same answer with the fraction part reduced by the greatest common factor.",
      "format": "text"
    },
    "mixed": {
      "label": "Mixed number",
      "description": "The number as a whole number and a proper fraction, in lowest terms.",
      "format": "text"
    },
    "improper": {
      "label": "Improper fraction",
      "description": "The number as one fraction, in lowest terms.",
      "format": "text"
    },
    "decimal": {
      "label": "Decimal",
      "description": "The value of the number as a decimal.",
      "format": "number"
    },
    "steps": {
      "label": "Steps",
      "description": "The division (or multiplication and addition) that gives the answer.",
      "format": "text"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "mode": "improper",
      "w": 4,
      "n": 11,
      "d": 6
    },
    "outputs": {
      "typed": "11/6",
      "result": "1 5/6",
      "simplest": "1 5/6",
      "mixed": "1 5/6",
      "improper": "11/6",
      "decimal": 1.8333333333333333,
      "steps": "Divide the numerator by the denominator: 11 ÷ 6 = 1 remainder 5; The quotient 1 is the whole number, the remainder 5 is the new numerator, and 6 stays the denominator"
    },
    "text": "11/6 = 1 5/6"
  },
  "examples": [
    {
      "given": {
        "mode": "improper",
        "n": 11,
        "d": 6
      },
      "expect": {
        "result": "1 5/6",
        "mixed": "1 5/6",
        "improper": "11/6",
        "decimal": 1.8333333333333333
      },
      "source": "OpenStax, Prealgebra 2e, §4.1 Visualize Fractions (convert an improper fraction to a mixed number by dividing; a mixed number to an improper fraction by multiplying the whole number by the denominator and adding the numerator). https://openstax.org/books/prealgebra-2e/pages/4-1-visualize-fractions, retrieved 2026-10-02: 11/6 = 1 5/6"
    },
    {
      "given": {
        "mode": "improper",
        "n": 33,
        "d": 8
      },
      "expect": {
        "result": "4 1/8",
        "decimal": 4.125
      },
      "source": "OpenStax, Prealgebra 2e, §4.1 Visualize Fractions (convert an improper fraction to a mixed number by dividing; a mixed number to an improper fraction by multiplying the whole number by the denominator and adding the numerator). https://openstax.org/books/prealgebra-2e/pages/4-1-visualize-fractions, retrieved 2026-10-02: 33/8 = 4 1/8"
    },
    {
      "given": {
        "mode": "mixed",
        "w": 4,
        "n": 2,
        "d": 3
      },
      "expect": {
        "result": "14/3",
        "improper": "14/3",
        "mixed": "4 2/3"
      },
      "source": "OpenStax, Prealgebra 2e, §4.1 Visualize Fractions (convert an improper fraction to a mixed number by dividing; a mixed number to an improper fraction by multiplying the whole number by the denominator and adding the numerator). https://openstax.org/books/prealgebra-2e/pages/4-1-visualize-fractions, retrieved 2026-10-02: 4 2/3 = 14/3"
    },
    {
      "given": {
        "mode": "improper",
        "n": 10,
        "d": 4
      },
      "expect": {
        "result": "2 2/4",
        "simplest": "2 1/2",
        "improper": "5/2",
        "decimal": 2.5
      },
      "source": "hand calculation in content.mdx: 10 ÷ 4 = 2 remainder 2, so 2 2/4, which reduces to 2 1/2"
    },
    {
      "given": {
        "mode": "mixed",
        "w": -2,
        "n": 1,
        "d": 3
      },
      "expect": {
        "result": "−7/3",
        "mixed": "−2 1/3",
        "decimal": -2.3333333333333335
      },
      "source": "hand calculation in content.mdx: −2 1/3 = −(2 × 3 + 1)/3 = −7/3"
    }
  ],
  "sources": [
    "OpenStax, Prealgebra 2e, §4.1 Visualize Fractions (improper fractions and mixed numbers; convert an improper fraction to a mixed number by dividing, and a mixed number to an improper fraction by multiplying and adding). https://openstax.org/books/prealgebra-2e/pages/4-1-visualize-fractions (retrieved 2026-10-02)"
  ],
  "related": [
    "mixed-numbers",
    "fraction",
    "simplify-fraction",
    "fraction-to-decimal"
  ],
  "changelog": []
}