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Q&A Why always rationalize a denominator?

posted 4y ago by r~~‭  ·  edited 4y ago by r~~‭

Answer
#2: Post edited by user avatar r~~‭ · 2020-12-21T07:12:49Z (almost 4 years ago)
  • Mathematically, absolutely nothing is wrong with fractions that don't have the smallest positive integer denominator that they could have, as far as I know.
  • Pedagogically, the policy does help with there being a unique answer that can be checked quickly.
  • Mathematically, absolutely nothing is wrong with fractions that don't have the smallest positive integer denominator that they could have, as far as I know.
  • Pedagogically, the policy does help with there being a unique answer that can be checked quickly, when grading multiple homework assignments or tests. I imagine that property can also be useful at times outside of the classroom, though of course any working mathematician would be comfortable with the idea of there being multiple equivalent representations of a mathematical object; I don't think anyone outside of an educational context is likely to bat an eye at $1/\sqrt{3}$ in practice.
#1: Initial revision by user avatar r~~‭ · 2020-12-21T07:04:07Z (almost 4 years ago)
Mathematically, absolutely nothing is wrong with fractions that don't have the smallest positive integer denominator that they could have, as far as I know.

Pedagogically, the policy does help with there being a unique answer that can be checked quickly.