A rational number can be represented in the form of a/b where a and b are integers and b≠0. a and b should be co-prime. My question is why do a and b need to be co-prime?
Asked
Active
Viewed 142 times
0
-
1In my eyes - we don't, but we say that to create equivalence classes (i.e., simplified fractions). – Sean Roberson Dec 21 '22 at 08:45
1 Answers
2
There is no objective mathematical reason to require $a$ and $b$ to be coprime. $\frac 46$ is as valid a fraction as $\frac23$. However, it's a little difficult to see that $$ \frac{30971726}{46457589} $$ is also exactly the same number, so we like our fractions to be reduced for aesthetic and practical reasons. Educators also often like to insist that fractions are "reduced to lowest terms" or some such. Presumably this insistence ultimately stems from these same practical and aesthetic considerations.
Arthur
- 199,419