Program to add two fractions

Last Updated : 21 Mar, 2025

Given two integer arrays a[] and b[] containing two integers each representing the numerator and denominator of a fraction respectively. The task is to find the sum of the two fractions and return the numerator and denominator of the result.

Examples :

Input: a = [1, 2] , b = [3, 2]
Output: [2, 1]
Explanation: 1/2 + 3/2 = 2/1
Input: a = [1, 3] , b = [3, 9]
Output: [2, 3]
Explanation: 1/3 + 3/9 = 2/3
Input: a = [1, 5] , b = [3, 15]
Output: [2, 5]
Explanation: 1/5 + 3/15 = 2/5

Algorithm to Add Two Fractions

Find a common denominator by finding the LCM (Least Common Multiple) of the two denominators.
Change the fractions to have the same denominator and add both terms.
Reduce the final fraction obtained into its simpler form by dividing both the numerator and denominator by their largest common factor.

C++

#include<bits/stdc++.h>
using namespace std;

// Function to find gcd of a and b
int gcd(int n1, int n2)
{
    if (n1 == 0)
        return n2;
    return gcd(n2%n1, n1);
}

//Function to add two fractions
vector<int> addFraction(vector<int> a, vector<int>b)
{
    vector<int> ans; 
    // Finding gcd of den1 and den2
    int den = gcd(a[1],b[1]);

    // Denominator of final fraction obtained
    // finding LCM of den1 and den2
    // LCM * GCD = a * b 
    den = (a[1]*b[1]) / den;

    // Changing the fractions to have same denominator
    // Numerator of the final fraction obtained
    int num = (a[0])*(den/a[1]) + (b[0])*(den/b[1]);

    // finding the common factor of numerator and denominator
    int common_factor = gcd(num,den);

    // Converting the result into simpler 
    // fraction by dividing them with common factor 
    den = den/common_factor;
    num = num/common_factor;
    ans.push_back(num); 
    ans.push_back(den); 
    return ans;
    
}

int main()
{
    vector<int> a = {1,2};
    vector<int> b = {3,2};
    vector<int> ans = addFraction(a, b); 
    cout<<ans[0]<<", "<<ans[1];
    return 0;
}

#include <stdio.h>

// Function to find gcd of a and b
int gcd(int n1, int n2)
{
    if (n1 == 0)
        return n2;
    return gcd(n2 % n1, n1);
}

// Function to add two fractions
void addFraction(int a[], int b[], int result[])
{
    // Finding gcd of den1 and den2
    int den = gcd(a[1], b[1]);

    // Denominator of final fraction obtained
    // finding LCM of den1 and den2
    // LCM * GCD = a * b 
    den = (a[1] * b[1]) / den;

    // Changing the fractions to have same denominator
    // Numerator of the final fraction obtained
    int num = (a[0]) * (den / a[1]) + (b[0]) * (den / b[1]);

    // finding the common factor of numerator and denominator
    int common_factor = gcd(num, den);

    // Converting the result into simpler 
    // fraction by dividing them with common factor 
    den = den / common_factor;
    num = num / common_factor;
    result[0] = num;
    result[1] = den;
}

int main()
{
    int a[] = {1,2};;
    int b[] = {3,2};;
    int ans[2];
    addFraction(a, b, ans);
    printf("%d, %d", ans[0], ans[1]);
    return 0;
}

Java

import java.util.ArrayList;
import java.util.List;

public class Main {
    // Function to find gcd of a and b
    public static int gcd(int n1, int n2) {
        if (n1 == 0)
            return n2;
        return gcd(n2 % n1, n1);
    }

    // Function to add two fractions
    public static List<Integer> addFraction(List<Integer> a, List<Integer> b) {
        List<Integer> ans = new ArrayList<>(); 
        // Finding gcd of den1 and den2
        int den = gcd(a.get(1), b.get(1));

        // Denominator of final fraction obtained
        // finding LCM of den1 and den2
        // LCM * GCD = a * b 
        den = (a.get(1) * b.get(1)) / den;

        // Changing the fractions to have same denominator
        // Numerator of the final fraction obtained
        int num = (a.get(0)) * (den / a.get(1)) + (b.get(0)) * (den / b.get(1));

        // finding the common factor of numerator and denominator
        int common_factor = gcd(num, den);

        // Converting the result into simpler 
        // fraction by dividing them with common factor 
        den = den / common_factor;
        num = num / common_factor;
        ans.add(num); 
        ans.add(den); 
        return ans;
    }

    public static void main(String[] args) {
        List<Integer> a = new ArrayList<>();
        a.add(1);
        a.add(2);
        List<Integer> b = new ArrayList<>();
        b.add(3);
        b.add(2);
        List<Integer> ans = addFraction(a, b); 
        System.out.println(ans.get(0) + ", " + ans.get(1));
    }
}

Python

from math import gcd

# Function to add two fractions
def addFraction(a, b):
    # Finding gcd of den1 and den2
    den = gcd(a[1], b[1])

    # Denominator of final fraction obtained
    # finding LCM of den1 and den2
    # LCM * GCD = a * b 
    den = (a[1] * b[1]) // den

    # Changing the fractions to have same denominator
    # Numerator of the final fraction obtained
    num = (a[0]) * (den // a[1]) + (b[0]) * (den // b[1])

    # finding the common factor of numerator and denominator
    common_factor = gcd(num, den)

    # Converting the result into simpler 
    # fraction by dividing them with common factor 
    den //= common_factor
    num //= common_factor
    return [num, den]

if __name__ == '__main__':
    a = [1, 2]
    b = [3, 2]
    ans = addFraction(a, b)
    print(f'{ans[0]}, {ans[1]}')

// Function to find gcd of a and b
int gcd(int n1, int n2)
{
    if (n1 == 0)
        return n2;
    return gcd(n2 % n1, n1);
}

// Function to add two fractions
List<int> addFraction(List<int> a, List<int> b)
{
    List<int> ans = new List<int>(); 
    // Finding gcd of den1 and den2
    int den = gcd(a[1], b[1]);

    // Denominator of final fraction obtained
    // finding LCM of den1 and den2
    // LCM * GCD = a * b 
    den = (a[1] * b[1]) / den;

    // Changing the fractions to have same denominator
    // Numerator of the final fraction obtained
    int num = (a[0]) * (den / a[1]) + (b[0]) * (den / b[1]);

    // finding the common factor of numerator and denominator
    int common_factor = gcd(num, den);

    // Converting the result into simpler 
    // fraction by dividing them with common factor 
    den = den / common_factor;
    num = num / common_factor;
    ans.Add(num); 
    ans.Add(den); 
    return ans;
}

public static void Main()
{
    List<int> a = new List<int> {1,2};
    List<int> b = new List<int> {3,2};
    List<int> ans = addFraction(a, b); 
    Console.WriteLine(ans[0] + ", " + ans[1]);
}

JavaScript

// Function to find gcd of a and b
function gcd(n1, n2) {
    if (n1 === 0)
        return n2;
    return gcd(n2 % n1, n1);
}

// Function to add two fractions
function addFraction(a, b) {
    let ans = []; 
    // Finding gcd of den1 and den2
    let den = gcd(a[1], b[1]);

    // Denominator of final fraction obtained
    // finding LCM of den1 and den2
    // LCM * GCD = a * b 
    den = (a[1] * b[1]) / den;

    // Changing the fractions to have same denominator
    // Numerator of the final fraction obtained
    let num = (a[0]) * (den / a[1]) + (b[0]) * (den / b[1]);

    // finding the common factor of numerator and denominator
    let common_factor = gcd(num, den);

    // Converting the result into simpler 
    // fraction by dividing them with common factor 
    den = den / common_factor;
    num = num / common_factor;
    ans.push(num); 
    ans.push(den); 
    return ans;
}

let a = [1, 2];
let b = [3, 2];
let ans = addFraction(a, b); 
console.log(ans[0] + ", " + ans[1]);