Fraction

A fraction is a ratio of two values. Fractions have the form a/b where a is called the numerator, b is called the denominator and b cannot equal 0 (since division by 0 is undefined).The denominator gives how many equal parts are there. The numerator represents how many of these are taken. For example, one-half, eight-fifths, three-quarters (1/2, 8/5, 3/4). Fact about Fraction :

1. Fractions can be reduced if the numerator and denominator have a greatest common divisor(gcd) greater than 1.
2. Addition and Subtraction of Fractions : When adding or subtracting fractions, they must have the same denominator. If they do not have the same denomimator, we must find a common one for both. To do this, we first need to find the lowest common multiple(lcm) of the two denominators or multiply each fraction by the proper integers so that there will be the same denominator.
3. Multiplication and Division of Fractions : When multiplying two fractions, simply multiply the two numerators and multiply the two denominators.When dividing two fractions, the first fraction must be multiplied by the reciprocal of the second fraction.
4. There are three types of fractions :
• Proper Fractions:The numerator is less than the denominator. For Example, 1/3, 3/4, 2/7
• Improper Fractions:The numerator is greater than (or equal to) the denominator. For Example, 4/3, 11/4, 7/7.
• Mixed Fractions: A whole number and proper fraction together. For Example, 1 1/3, 2 1/4, 16 2/5.

How to add two fraction ?
Add two fraction a/b and c/d and print answer in simplest form.

Examples :

Input:  1/2 + 3/2
Output: 2/1

Input:  1/3 + 3/9
Output: 2/3

Input:  1/5 + 3/15
Output: 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 numerator and denominator by there largest common factor.

C++

 // C++ program to add 2 fractions #include using namespace std;    // Function to return gcd of a and b int gcd(int a, int b) {     if (a == 0)         return b;     return gcd(b % a, a); }    // Function to convert the obtained fraction // into it's simplest form void lowest(int& den3, int& num3) {     // Finding gcd of both terms     int common_factor = gcd(num3, den3);        // Converting both terms into simpler     // terms by dividing them by common factor     den3 = den3 / common_factor;     num3 = num3 / common_factor; }    // Function to add two fractions void addFraction(int num1, int den1, int num2,                  int den2, int& num3, int& den3) {     // Finding gcd of den1 and den2     den3 = gcd(den1, den2);        // Denominator of final fraction obtained     // finding LCM of den1 and den2     // LCM * GCD = a * b     den3 = (den1 * den2) / den3;        // Changing the fractions to have same denominator     // Numerator of the final fraction obtained     num3 = (num1) * (den3 / den1) + (num2) * (den3 / den2);        // Calling function to convert final fraction     // into it's simplest form     lowest(den3, num3); }    // Driver program int main() {     int num1 = 1, den1 = 500, num2 = 2, den2 = 1500, den3, num3;        addFraction(num1, den1, num2, den2, num3, den3);        printf("%d/%d + %d/%d is equal to %d/%d\n", num1, den1,            num2, den2, num3, den3);     return 0; }

Java

 // Java program to add 2 fractions import java.util.*;    class GFG { static int den3, num3;     // Function to return gcd of a and b static int gcd(int a, int b) {     if (a == 0)         return b;     return gcd(b % a, a); }    // Function to convert the obtained fraction // into it's simplest form static void lowest() {     // Finding gcd of both terms     int common_factor = gcd(num3, den3);        // Converting both terms into simpler     // terms by dividing them by common factor     den3 = den3 / common_factor;     num3 = num3 / common_factor; }    // Function to add two fractions static void addFraction(int num1, int den1,                         int num2, int den2) {     // Finding gcd of den1 and den2     den3 = gcd(den1, den2);        // Denominator of final fraction obtained     // finding LCM of den1 and den2     // LCM * GCD = a * b     den3 = (den1 * den2) / den3;        // Changing the fractions to have      // same denominator.      // Numerator of the final fraction obtained     num3 = (num1) * (den3 / den1) +             (num2) * (den3 / den2);        // Calling function to convert final fraction     // into it's simplest form     lowest(); }    // Driver Code public static void main(String[] args)  {     int num1 = 1, den1 = 500,         num2 = 2, den2 = 1500;        addFraction(num1, den1, num2, den2);        System.out.printf("%d/%d + %d/%d is equal to %d/%d\n",                        num1, den1, num2, den2, num3, den3); } }    // This code is contributed by Rajput-Ji

Python3

 # Python3 program to add 2 fractions     # Function to return gcd of a and b  def gcd(a, b):     if (a == 0):          return b      return gcd(b % a, a)     # Function to convert the obtained  # fraction into it's simplest form  def lowest(den3, num3):         # Finding gcd of both terms      common_factor = gcd(num3, den3)         # Converting both terms      # into simpler terms by      # dividing them by common factor      den3 = int(den3 / common_factor)      num3 = int(num3 / common_factor)     print(num3, "/", den3)    # Function to add two fractions  def addFraction(num1, den1, num2, den2):         # Finding gcd of den1 and den2      den3 = gcd(den1, den2)         # Denominator of final      # fraction obtained finding      # LCM of den1 and den2      # LCM * GCD = a * b      den3 = (den1 * den2) / den3         # Changing the fractions to      # have same denominator Numerator      # of the final fraction obtained      num3 = ((num1) * (den3 / den1) +             (num2) * (den3 / den2))         # Calling function to convert      # final fraction into it's      # simplest form      lowest(den3, num3)    # Driver Code  num1 = 1; den1 = 500 num2 = 2; den2 = 1500    print(num1, "/", den1, " + ", num2, "/",      den2, " is equal to ", end = "")        addFraction(num1, den1, num2, den2)

C#

 // C# program to add 2 fractions using System;        class GFG { static int den3, num3;     // Function to return gcd of a and b static int gcd(int a, int b) {     if (a == 0)         return b;     return gcd(b % a, a); }    // Function to convert the obtained fraction // into it's simplest form static void lowest() {     // Finding gcd of both terms     int common_factor = gcd(num3, den3);        // Converting both terms into simpler     // terms by dividing them by common factor     den3 = den3 / common_factor;     num3 = num3 / common_factor; }    // Function to add two fractions static void addFraction(int num1, int den1,                         int num2, int den2) {     // Finding gcd of den1 and den2     den3 = gcd(den1, den2);        // Denominator of final fraction obtained     // finding LCM of den1 and den2     // LCM * GCD = a * b     den3 = (den1 * den2) / den3;        // Changing the fractions to have      // same denominator.      // Numerator of the final fraction obtained     num3 = (num1) * (den3 / den1) +             (num2) * (den3 / den2);        // Calling function to convert final fraction     // into it's simplest form     lowest(); }    // Driver Code public static void Main(String[] args)  {     int num1 = 1, den1 = 500,         num2 = 2, den2 = 1500;        addFraction(num1, den1, num2, den2);        Console.Write("{0}/{1} + {2}/{3} is equal to {4}/{5}\n",                          num1, den1, num2, den2, num3, den3); } }    // This code is contributed by PrinciRaj1992

PHP



Output :

1/500 + 2/1500 is equal to 1/300

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Improved By : Rajput-Ji, princiraj1992