{
  "aliases": [
    "irreducible-fraction",
    "reduced-fraction"
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  "body": "\n## Statement\n\nLet $q$ be a [[rational number|0NCJ5WXN6Z]].\nThen there is exactly one pair of [[integers|0C4JS9RF5M]] $a$ and $b$ with $b \u003e 0$, $\\gcd(a, b) = 1$ and $q = a / b$.\n\n## Remarks\n\nThe fraction $a / b$ is the irreducible fraction, or the fraction in lowest terms, of $q$.\nTo find it from any fraction $c / d$ with $d \\neq 0$, divide $c$ and $d$ by $\\pm \\gcd(c, d)$, with the sign that makes the denominator positive.\nFor example, $-6 / -4$ has lowest terms $3 / 2$.\n\n## Explanations\n\n### L1 human\n\nYou can simplify each fraction until the top and the bottom have no common factor larger than $1$.\nFor example, $12 / 18$ becomes $2 / 3$ when you divide both numbers by $6$.\nThe result does not depend on the order of the simplification steps.\n",
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  "front": {
    "aliases": [
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    "name": "Fraction in lowest terms",
    "role": "theorem",
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        "locator": "Uniqueness",
        "url": "https://en.wikipedia.org/wiki/Irreducible_fraction"
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      {
        "locator": "Irreducible fraction",
        "url": "https://en.wikipedia.org/wiki/Rational_number"
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  "msc": [
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  "name": "Fraction in lowest terms",
  "prov": null,
  "role": "theorem",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0R6/0R64A2CVN4.md",
  "status": null,
  "tag": "0R64A2CVN4",
  "uri": "m2://0R64A2CVN4",
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    "tag": "0R64A2CVN4",
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