# Program to compare two fractions

Given two fractions a/b and c/d, compare them and print the larger of the two.

Examples :

Input: 5/6, 11/45
Output: 5/6

Input: 4/5 and 2/3
Output: 4/5

Recommended Practice

We can simply convert the fractions into floating-point values by dividing the numerator by the denominator. Once we have the two floating-point numbers corresponding to each fraction, we can compare these numbers and determine which fraction is larger.
However, the computed answer may be incorrect due to floating-point approximations and truncations during the division process. To get the most accurate answer we should avoid resorting to floating-point division.
To compare two fractions we need to make their denominators the same. We can do this by cross-multiplying numerators with denominators. Let’s see how this works

```We have two fractions a/b and c/d.
Let Y = (a/b - c/d)
Now,
if Y > 0 then a/b > c/d
if Y = 0 then a/b = c/d
if Y < o then a/b < c/d

Since bd is always positive, the sign of Y depends only on the

Complexity :
Since we perform two multiplication and one subtraction operation, the answer is computed in constant time i.e O(1)

Recommended Practice

## C++

 `// CPP program to find max between` `// two Rational numbers` `#include ` `using` `namespace` `std;`   `struct` `Fraction {` `    ``int` `num, den;` `};`   `// Get max of the two fractions` `Fraction maxFraction(Fraction first, Fraction sec)` `{` `    `  `    ``int` `a = first.num;` `    ``int` `b = first.den;` `    ``int` `c = sec.num;` `    ``int` `d = sec.den;`   `    ``// Compute ad-bc` `    ``int` `Y = a * d - b * c;`   `    ``return` `(Y > 0) ? first : sec;` `}`   `// Driver Code` `int` `main()` `{` `    ``Fraction first = { 3, 2 };` `    ``Fraction sec = { 3, 4 };`   `    ``Fraction res = maxFraction(first, sec);` `    ``cout << res.num << ``"/"` `<< res.den;` `    ``return` `0;` `}`

## Java

 `// Java program to find max between` `// two Rational numbers`   `import` `java.io.*;` `import` `java.util.*;`   `class` `Fraction {` `    `  ` ``int` `num, den;`   `//Constructor` `Fraction(``int` `n,``int` `d){` `    ``num=n;` `    ``den=d;` `}`   ` ``// Get max of the two fractions` `static` `Fraction maxFraction(Fraction first, Fraction sec)` `{` `    ``// Declare nume1 and nume2 for get the value of` `    ``// first numerator and second numerator` `    ``int` `a = first.num;` `    ``int` `b = first.den;` `    ``int` `c = sec.num;` `    ``int` `d = sec.den;` ` `  `    ``// Compute ad-bc` `    ``int` `Y = a * d - b * c;` ` `  `    ``return` `(Y > ``0``) ? first : sec;` `}`   `// Driver function` `public` `static` `void` `main (String[] args) {`   `   ``Fraction first = ``new` `Fraction( ``3``, ``2` `);` `   ``Fraction sec = ``new` `Fraction( ``3``, ``4` `);` ` `  `    ``Fraction res = maxFraction(first, sec);` `    ``System.out.println(res.num +``"/"``+ res.den); ` `    `  `}` `}`   `// This code is contributed by Gitanjali.`

## Python3

 `# Python3 program to find max ` `# between two Rational numbers`   `# Get max of the two fractions` `def` `maxFraction(first, sec):` `    `  `    ``# Declare nume1 and nume2 for get the value ` `    ``# of first numerator and second numerator` `    ``a ``=` `first[``0``]; b ``=` `first[``1``]` `    ``c ``=` `sec[``0``]; d ``=` `sec[``1``]`   `    ``# Compute ad-bc` `    ``Y ``=` `a ``*` `d ``-` `b ``*` `c`   `    ``return` `first ``if` `Y ``else` `sec`   `# Driver Code` `first ``=` `( ``3``, ``2` `)` `sec ``=` `( ``3``, ``4` `)` `res ``=` `maxFraction(first, sec)` `print``(``str``(res[``0``]) ``+` `"/"` `+` `str``(res[``1``]))`     `# This code is contributed by Ansu Kumari.`

## C#

 `// C# program to find max between` `// two Rational numbers` `using` `System;`   `class` `Fraction {` `    `  `    ``int` `num, den;` `    `  `    ``//Constructor` `    ``Fraction(``int` `n,``int` `d)` `    ``{` `        ``num=n;` `        ``den=d;` `    ``}` `    `  `    ``// Get max of the two fractions` `    ``static` `Fraction maxFraction(Fraction first, Fraction sec)` `    ``{` `        ``// Declare nume1 and nume2 for get the value of` `        ``// first numerator and second numerator` `        ``int` `a = first.num;` `        ``int` `b = first.den;` `        ``int` `c = sec.num;` `        ``int` `d = sec.den;` `    `  `        ``// Compute ad-bc` `        ``int` `Y = a * d - b * c;` `    `  `        ``return` `(Y > 0) ? first : sec;` `    ``}` `    `  `    ``// Driver function` `    ``public` `static` `void` `Main () ` `    ``{` `    `  `        ``Fraction first = ``new` `Fraction( 3, 2 );` `        ``Fraction sec = ``new` `Fraction( 3, 4 );` `        `  `        ``Fraction res = maxFraction(first, sec);` `        ``Console.WriteLine(res.num +``"/"``+ res.den); ` `        `  `    ``}` `}`   `// This code is contributed by vt_m.`

## PHP

 ``

## Javascript

 `// javascript program to find max` `// between two Rational numbers` `  `  `// Get max of the two fractions` `function` `maxFraction(first, sec) {` `      `  `    ``// Declare nume1 and nume2 for get the value` `    ``// of first numerator and second numerator` `    ``a = first[0]; b = first[1]` `    ``c = sec[0]; d = sec[1]` `  `  `    ``// Compute ad-bc` `    ``Y = a * d - b * c` `  `  `    ``return` `(Y > 0) ? first : sec;`   `}` `  `  `// Driver Code`   `first = [ 3, 2 ];` `sec = [ 3, 4 ];` `res = maxFraction(first, sec);`   `document.write(res[0] + ``"/"` `+ res[1]);`

Output

`3/2`

Time Complexity: O(1)
Auxiliary Space: O(1)

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