# Find ΔX which is added to numerator and denominator both of fraction (a/b) to convert it to another fraction (c/d)

Given a fraction in form of a/b where a & b are positive integers. Find ΔX such that when it is added to numerator as well as denominator of given fraction it will result into a new Ir-reducible fraction c/d.

Examples:

Input : a = 4, b = 10, c = 1, d = 2
Output : ΔX = 2
Explanation : (a + ΔX)/(b + ΔX) =
(4 + 2) / (10 + 2) = 6/12 = 1/2 = c/d

Input : a = 4, b = 10, c = 2, d = 5
Output : ΔX = 0
Explanation : (a + ΔX) / (b + ΔX) =
(4) / (10) = 2 / 5 = c/d


## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

To solve this type of problem rather than implementing just a programming approach we have to do a little of mathematics. mathematics just necessary is as:

As per question we have to find ΔX such that:
=> (a + ΔX) / (b + ΔX) = c / d
=> ad + dΔX = bc + cΔX
=> dΔX - cΔX = bc - ad
=> ΔX (d - c) = bc -ad
=> ΔX = (bc - ad) / (d - c)


So, in a way to finding ΔX we have to only calculate .

## C++

 // C++ Program to find deltaX  #include  using namespace std;     // function to find delta X  int findDelta(int a, int b, int c, int d)  {      return (b * c - a * d) / (d - c);  }     // driver program  int main()  {      int a = 3, b = 9, c = 3, d = 5;         // u0394X is code for delta sign      cout << "\u0394X = " << findDelta(a, b, c, d);      return 0;  }

## Java

 // Java Program to  // find deltaX  import java.io.*;     class GFG  {      // function to find delta X      static int findDelta(int a, int b,                            int c, int d)      {          return (b * c - a *                   d) / (d - c);      }             // Driver Code      public static void main(String args[])      {          int a = 3, b = 9,               c = 3, d = 5;                 // u0394X is code           // for delta sign          System.out.print("\u0394X = " +                   findDelta(a, b, c, d));      }  }     // This code is contributed   // by Manish Shaw(manishshaw1)

## Python3

 # Python Program to find deltaX  # !/usr/bin/python  # coding=utf-8     # function to find delta X  def findDelta(a, b, c, d) :         return int((b * c -                 a * d) /                 (d - c));     # Driver Code  a = 3; b = 9;   c = 3; d = 5;     # u0394X is code  # for delta sign  print ("X = {}" .           format(findDelta(a, b,                            c, d)));     # This code is contributed by   # Manish Shaw(manishshaw1)

## C#

 // C# Program to  // find deltaX  using System;     class GFG  {  // function to find delta X  static int findDelta(int a, int b,                        int c, int d)  {      return (b * c - a *               d) / (d - c);  }     // Driver Code  static void Main()  {      int a = 3, b = 9,           c = 3, d = 5;         // u0394X is code       // for delta sign      Console.Write("\u0394X = " +                     findDelta(a, b, c, d));  }  }     // This code is contributed   // by Manish Shaw(manishshaw1)

## PHP

 

Output:

ΔX = 6


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Improved By : manishshaw1