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  text: 'The [4zq rational numbers], being the [-field_of_fractions] of the [48l integers], have the following [481 field] structure:\n\n- Addition is given by $\\frac{a}{b} + \\frac{p}{q} = \\frac{aq+bp}{bq}$\n- Multiplication is given by $\\frac{a}{b} \\frac{c}{d} = \\frac{ac}{bd}$\n- The identity under addition is $\\frac{0}{1}$\n- The identity under multiplication is $\\frac{1}{1}$\n- The additive inverse of $\\frac{a}{b}$ is $\\frac{-a}{b}$\n- The multiplicative inverse of $\\frac{a}{b}$ (where $a \\not = 0$) is $\\frac{b}{a}$.\n\nIt additionally inherits a [540 total ordering] which respects the field structure: $0 < \\frac{c}{d}$ if and only if $c$ and $d$ are both positive or $c$ and $d$ are both negative.\nAll other information about the ordering can be derived from this fact: $\\frac{a}{b} < \\frac{c}{d}$ if and only if $0 < \\frac{c}{d} - \\frac{a}{b}$.',
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