Program to add two fractions (original) (raw)

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

Try It Yourself

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

C

#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]}')

C#

// 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 addFraction(List a, List b) { List ans = new List(); // 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 a = new List {1,2}; List b = new List {3,2}; List 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]);

`

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