{
  "aliases": [
    "rational-number",
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  "body": "\n## Description\n\nA rational number is a number of the form $a / b$, where $a$ and $b$ are [[integers|0C4JS9RF5M]] and $b \\neq 0$.\nWe write $\\mathbb{Q}$ for the set of rational numbers.\nTwo fractions $a / b$ and $c / d$ are the same rational number when $a d = b c$.\nWith addition and multiplication, $\\mathbb{Q}$ is a [[field|0N2WPCC00T]], and with its usual order it is an [[ordered field|09RFKMBQ63]].\nThe set $\\mathbb{Q}$ contains $\\mathbb{Z}$, because each integer $a$ is the fraction $a / 1$.\n\n## Remarks\n\nEach rational number has exactly one [[representation in lowest terms|0R64A2CVN4]] $a / b$ with $b \u003e 0$.\nThe set $\\mathbb{Q}$ is countable.\nNot every real number is rational: $\\sqrt{2}$ is [[irrational|0DZGSDHD92]].\n\n## Explanations\n\n### L1 human\n\nThe rational numbers are the fractions, such as $1/2$, $-3/4$ and $7 = 7/1$.\nMany fractions name the same number: $1/2$, $2/4$ and $3/6$ are all equal.\nIn $\\mathbb{Q}$, you can divide by any number except $0$.\n",
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