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Math Help - Congruence classes and rings

  1. #1
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    Congruence classes and rings

    For  a/b and c/d rational numbers, say a/b \equiv c/d (mod 1) if (a/b) - (c/d) is an integer. Call the set of congruence classes mod 1, \mathbb{Q}/\mathbb{Z}.

    Show that every rational number is congruent (mod 1) to a rational number a/b with 0 \leq a/b \leq 1.
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by Zennie View Post
    For  a/b and c/d rational numbers, say a/b \equiv c/d (mod 1) if (a/b) - (c/d) is an integer. Call the set of congruence classes mod 1, \mathbb{Q}/\mathbb{Z}.

    Show that every rational number is congruent (mod 1) to a rational number a/b with 0 \leq a/b \leq 1.
    HINT: Use its decimal expansion.
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