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]);

Output

2, 1

Time Complexity : O(log(min(a, b))
Auxiliary Space : O(1)

Fraction to Recurring Decimal

Rahul Agrawal

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Program to add two fractions

Algorithm to Add Two Fractions

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