A rational is a number that can be expressed as A/B where A and B are integers, B is positive, and A and B are co-prime.


You are to write two programs/functions, one which takes a rational and output an integer, another which takes an integer and outputs a rational.

Denote the two functions as f and g respectively.

They are meant to be inverses of each other, meaning that f(g(n)) = n and g(f(r)) = r for all integers n and all rationals r.

f(r) must be defined for all rationals r and g(n) for all integers n.

f(a) == f(b) if and only if a == b; g(p) == g(q) if and only if p == q.


  • You can take the rational and the integer in any sensible format.
  • You can choose different format for f and g, but the format must be consistent within f and within g.
  • You can assume that the rational input is simplified.
  • You do not need to simplify the rational output.
  • The two functions/programs must be stand-alone.


Below are valid rational inputs:


Below are invalid rational inputs:

2/4 (can be output)


1/2 and 2/4 must map to the same integer, although only the former will be supplied.

As always, if my problem is not clear enough, please address in the comments.

  • \$\begingroup\$ Related, related, related, related, related. \$\endgroup\$
    – Leaky Nun
    Aug 11, 2016 at 15:22
  • \$\begingroup\$ @Dada No, I just stated it there for convenience. \$\endgroup\$
    – Leaky Nun
    Aug 11, 2016 at 15:27
  • 1
    \$\begingroup\$ Half of the challenge here is just this challenge worded slightly differently ... \$\endgroup\$ Aug 11, 2016 at 15:32
  • \$\begingroup\$ @Dada My definition is still valid. Expressible as ratio of two integers <=> expressible as ratio of two co-prime integers \$\endgroup\$
    – Leaky Nun
    Aug 11, 2016 at 15:34
  • \$\begingroup\$ @TimmyD Alright, I'll hammer it myself. \$\endgroup\$
    – Leaky Nun
    Aug 11, 2016 at 15:47


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