{
  "id": "division",
  "version": "980e55dabad5",
  "status": "published",
  "name": "Division Calculator",
  "question": "What is the division result?",
  "summary": "Divides two numbers and shows the decimal quotient, the whole-number quotient, and the remainder.",
  "category": "math",
  "subcategory": "arithmetic",
  "url": "https://www.acalculator.org/math/division-calculator",
  "markdown": "https://www.acalculator.org/math/division-calculator.md",
  "kind": "function",
  "method": "Quotient = dividend ÷ divisor; dividend = divisor × q + r, with q the quotient rounded down (floored) or toward 0 (truncated).",
  "assumptions": [
    "The divisor cannot be 0.",
    "Floored (the default): the whole-number quotient is rounded down and the remainder has the sign of the divisor. Truncated: rounded toward 0, and the remainder has the sign of the dividend. Both agree when no number is negative.",
    "Decimals are taken exactly as typed: 2.4 ÷ 0.2 = 12 with remainder 0."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "dividend": {
        "title": "Dividend",
        "description": "The number being divided.",
        "type": "number"
      },
      "divisor": {
        "title": "Divisor",
        "description": "The number to divide by. It cannot be 0.",
        "type": "number"
      },
      "mode": {
        "title": "Remainder sign",
        "description": "Which sign a remainder of a negative division takes: floored follows the divisor, truncated follows the dividend.",
        "type": "string",
        "enum": [
          "floored",
          "truncated"
        ]
      }
    }
  },
  "outputs": {
    "quotient": {
      "label": "Quotient",
      "description": "The dividend divided by the divisor, as a decimal.",
      "format": "number"
    },
    "whole": {
      "label": "Whole-number quotient",
      "description": "How many whole times the divisor fits: the quotient rounded down (floored) or toward 0 (truncated).",
      "format": "number"
    },
    "remainder": {
      "label": "Remainder",
      "description": "What is left over: dividend − divisor × whole-number quotient.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "dividend": 25,
      "divisor": 4,
      "mode": "floored"
    },
    "outputs": {
      "quotient": 6.25,
      "whole": 6,
      "remainder": 1
    },
    "text": "25 ÷ 4 = 6.25, or 6 remainder 1."
  },
  "examples": [
    {
      "given": {
        "dividend": 25,
        "divisor": 4,
        "mode": "floored"
      },
      "expect": {
        "quotient": 6.25,
        "whole": 6,
        "remainder": 1
      },
      "source": "hand calculation in content.mdx: 4 × 6 = 24, 25 − 24 = 1, 25 ÷ 4 = 6.25; Ted Sundstrom, Mathematical Reasoning: Writing and Proof, §3.5 The Division Algorithm and Congruence (for integers a and b with b > 0 there are unique q and r with a = bq + r and 0 ≤ r < b, −17 = 5(−4) + 3). https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Book:_Mathematical_Reasoning__Writing_and_Proof_(Sundstrom)/03:_Constructing_and_Writing_Proofs_in_Mathematics/3.05:_The_Division_Algorithm_and_Congruence"
    },
    {
      "given": {
        "dividend": 100,
        "divisor": 7,
        "mode": "floored"
      },
      "expect": {
        "quotient": 14.285714285714286,
        "whole": 14,
        "remainder": 2
      },
      "source": "hand calculation in content.mdx: 7 × 14 = 98, 100 − 98 = 2; Python 3: 100 / 7 = 14.285714285714286; Ted Sundstrom, Mathematical Reasoning: Writing and Proof, §3.5 The Division Algorithm and Congruence (for integers a and b with b > 0 there are unique q and r with a = bq + r and 0 ≤ r < b, −17 = 5(−4) + 3). https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Book:_Mathematical_Reasoning__Writing_and_Proof_(Sundstrom)/03:_Constructing_and_Writing_Proofs_in_Mathematics/3.05:_The_Division_Algorithm_and_Congruence"
    },
    {
      "given": {
        "dividend": -17,
        "divisor": 5,
        "mode": "floored"
      },
      "expect": {
        "quotient": -3.4,
        "whole": -4,
        "remainder": 3
      },
      "source": "hand calculation in content.mdx: floor(−3.4) = −4, −17 − 5 × (−4) = 3; Ted Sundstrom, Mathematical Reasoning: Writing and Proof, §3.5 The Division Algorithm and Congruence (for integers a and b with b > 0 there are unique q and r with a = bq + r and 0 ≤ r < b, −17 = 5(−4) + 3). https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Book:_Mathematical_Reasoning__Writing_and_Proof_(Sundstrom)/03:_Constructing_and_Writing_Proofs_in_Mathematics/3.05:_The_Division_Algorithm_and_Congruence"
    },
    {
      "given": {
        "dividend": -17,
        "divisor": 5,
        "mode": "truncated"
      },
      "expect": {
        "quotient": -3.4,
        "whole": -3,
        "remainder": -2
      },
      "source": "hand calculation in content.mdx: −3.4 toward 0 is −3, −17 − 5 × (−3) = −2; Ted Sundstrom, Mathematical Reasoning: Writing and Proof, §3.5 The Division Algorithm and Congruence (for integers a and b with b > 0 there are unique q and r with a = bq + r and 0 ≤ r < b, −17 = 5(−4) + 3). https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Book:_Mathematical_Reasoning__Writing_and_Proof_(Sundstrom)/03:_Constructing_and_Writing_Proofs_in_Mathematics/3.05:_The_Division_Algorithm_and_Congruence"
    },
    {
      "given": {
        "dividend": 2.4,
        "divisor": 0.2,
        "mode": "floored"
      },
      "expect": {
        "quotient": 12,
        "whole": 12,
        "remainder": 0
      },
      "source": "hand calculation in content.mdx: 0.2 × 12 = 2.4 exactly (×10: 24 ÷ 2 = 12); Ted Sundstrom, Mathematical Reasoning: Writing and Proof, §3.5 The Division Algorithm and Congruence (for integers a and b with b > 0 there are unique q and r with a = bq + r and 0 ≤ r < b, −17 = 5(−4) + 3). https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Book:_Mathematical_Reasoning__Writing_and_Proof_(Sundstrom)/03:_Constructing_and_Writing_Proofs_in_Mathematics/3.05:_The_Division_Algorithm_and_Congruence"
    },
    {
      "given": {
        "dividend": 7.5,
        "divisor": 2.5,
        "mode": "floored"
      },
      "expect": {
        "quotient": 3,
        "whole": 3,
        "remainder": 0
      },
      "source": "hand calculation in content.mdx: 2.5 × 3 = 7.5; Ted Sundstrom, Mathematical Reasoning: Writing and Proof, §3.5 The Division Algorithm and Congruence (for integers a and b with b > 0 there are unique q and r with a = bq + r and 0 ≤ r < b, −17 = 5(−4) + 3). https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Book:_Mathematical_Reasoning__Writing_and_Proof_(Sundstrom)/03:_Constructing_and_Writing_Proofs_in_Mathematics/3.05:_The_Division_Algorithm_and_Congruence"
    }
  ],
  "sources": [
    "Ted Sundstrom, Mathematical Reasoning: Writing and Proof, §3.5 The Division Algorithm and Congruence (for integers a and b with b > 0 there are unique q and r with a = bq + r and 0 ≤ r < b; −17 = 5(−4) + 3). https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Book:_Mathematical_Reasoning__Writing_and_Proof_(Sundstrom)/03:_Constructing_and_Writing_Proofs_in_Mathematics/3.05:_The_Division_Algorithm_and_Congruence"
  ],
  "related": [],
  "changelog": [
    {
      "date": "2026-09-29",
      "note": "Worked examples name a published reference for their rule."
    }
  ]
}