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

We can simply convert the fractions in 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 same. We can do this by cross-multiplying numerators with denominators. Lets 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)

## 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) ` `{ ` `    ``// 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 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

 ` `

Output :

```3/2
```

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