Mixed Number to an Improper Fraction

In this challenge you will be converting a mixed number to an improper fraction.

Because improper fractions use fewer numbers, your code will need to be as short as possible.


4 1/2

12 2/4

0 0/2

11 23/44


You may assume the denominator of the input will never be 0. The input will always be in the format x y/z where x,y,z are arbitrary nonnegative integers. You do not need to simplify the output.

This is so shortest code in bytes wins.

  • 5
    \$\begingroup\$ You should add the tag "parsing". I'm sure most answers will spend more bytes on parsing the input and formatting the output than on doing the math. \$\endgroup\$ – nimi Dec 17 '15 at 18:31
  • 3
    \$\begingroup\$ Can the output be a rational number type or does it have to be a string? \$\endgroup\$ – Martin Ender Dec 17 '15 at 18:33
  • 2
    \$\begingroup\$ @AlexA.: ... but a large part of the challenge. According to it's description the tag should be used in such cases. \$\endgroup\$ – nimi Dec 17 '15 at 18:38
  • 7
    \$\begingroup\$ Can x, y and z be negative? \$\endgroup\$ – Dennis Dec 17 '15 at 19:21
  • 2
    \$\begingroup\$ Based on the challenge I'm assuming it is, but is the input format "x y/z" mandatory, or can the space be a new-line, and/or the x,y,z be separated inputs? Most answers are assuming the input format is indeed mandatory to be x y/z, but some aren't, hence this question to have a definitive answer. \$\endgroup\$ – Kevin Cruijssen Jun 15 '18 at 13:04

31 Answers 31


Ouroboros, 16 bytes


Try it here!


The reason why Ouroboros is great for this challenge: its integer-reading primitive, r, skips over any non-digit characters until it comes to a number. So no parsing is required; we just read three numbers and process them.

rr                Read the first two numbers
                   Stack: 11 23
  \r              Swap and read the third one
                   Stack: 44 23 11
    .             Duplicate
                   Stack: 44 44 23 11
     @            Rotate (moving third item to top of stack)
                   Stack: 23 44 44 11
      *           Multiply
                   Stack: 1012 44 11
       @+         Rotate and add
                   Stack: 1023 44
         n        Output as number
                   Stack: 44  Output: 1023
          47o     Push 47 and output as character
                   Stack: 44  Output: 1023/
             n    Output as number
                   Output: 1023/44
              1(  Terminate
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