Add Two Fractions & Display Simplest Form | Step-by-Step Guide

Add Two Fractions & Display Simplest Form | Step-by-Step Guide

Add Two Fractions & Display Simplest Form | Step-by-Step Guide

This article explains how to add two fractions and simplify the result into the lowest terms. This is a common problem in arithmetic, often solved using the Least Common Denominator (LCD) method and simplifying the result using the Greatest Common Divisor (GCD).

Algorithm to Add Two Fractions

Given two fractions ab\frac{a}{b} and cd\frac{c}{d}:

  1. Calculate the numerator of the resulting fraction: x=(a×d)+(c×b)x = (a \times d) + (c \times b)
  2. Calculate the denominator of the resulting fraction: y=b×dy = b \times d
  3. Compute the GCD of xx and yy to simplify the fraction.
  4. Divide both numerator and denominator by the GCD to get the simplest form.

Python Program

python
from math import gcd

def add_fractions(a, b, c, d):
# Calculate numerator and denominator
numerator = a * d + c * b
denominator = b * d

# Simplify using GCD
common_divisor = gcd(numerator, denominator)
numerator //= common_divisor
denominator //= common_divisor

return numerator, denominator

# Input: Fractions a/b and c/d
a, b = map(int, input(“Enter numerator and denominator of first fraction (a b): “).split())
c, d = map(int, input(“Enter numerator and denominator of second fraction (c d): “).split())

# Add fractions
result_numerator, result_denominator = add_fractions(a, b, c, d)

# Output result
print(f”The sum of the fractions is: {result_numerator}/{result_denominator}“)

Examples

Input:

 
1 2 3 2

Output:

python
The sum of the fractions is: 2/1

Input:

 
1 3 3 9

Output:

python
The sum of the fractions is: 2/3

Explanation of Steps

  1. Finding Numerator and Denominator: For 12\frac{1}{2} and 32\frac{3}{2}:
    • Numerator: (1×2)+(3×2)=2+6=8(1 \times 2) + (3 \times 2) = 2 + 6 = 8
    • Denominator: 2×2=42 \times 2 = 4
  2. Simplify the Fraction:
    • GCD of 8 and 4 is 4.
    • Simplified Fraction: 84=2/1\frac{8}{4} = 2/1.

This article explains how to add two fractions and simplify the result into the lowest terms. This is a common problem in arithmetic, often solved using the Least Common Denominator (LCD) method and simplifying the result using the Greatest Common Divisor (GCD).

Algorithm to Add Two Fractions

Given two fractions ab\frac{a}{b} and cd\frac{c}{d}:

  1. Calculate the numerator of the resulting fraction: x=(a×d)+(c×b)x = (a \times d) + (c \times b)
  2. Calculate the denominator of the resulting fraction: y=b×dy = b \times d
  3. Compute the GCD of xx and yy to simplify the fraction.
  4. Divide both numerator and denominator by the GCD to get the simplest form.

Python Program

python
from math import gcd

def add_fractions(a, b, c, d):
# Calculate numerator and denominator
numerator = a * d + c * b
denominator = b * d

# Simplify using GCD
common_divisor = gcd(numerator, denominator)
numerator //= common_divisor
denominator //= common_divisor

return numerator, denominator

# Input: Fractions a/b and c/d
a, b = map(int, input(“Enter numerator and denominator of first fraction (a b): “).split())
c, d = map(int, input(“Enter numerator and denominator of second fraction (c d): “).split())

# Add fractions
result_numerator, result_denominator = add_fractions(a, b, c, d)

# Output result
print(f”The sum of the fractions is: {result_numerator}/{result_denominator}“)

Examples

Input:

 
1 2 3 2

Output:

python
The sum of the fractions is: 2/1

Input:

 
1 3 3 9

Output:

python
The sum of the fractions is: 2/3

Explanation of Steps

  1. Finding Numerator and Denominator: For 12\frac{1}{2} and 32\frac{3}{2}:
    • Numerator: (1×2)+(3×2)=2+6=8(1 \times 2) + (3 \times 2) = 2 + 6 = 8
    • Denominator: 2×2=42 \times 2 = 4
  2. Simplify the Fraction:
    • GCD of 8 and 4 is 4.
    • Simplified Fraction: 84=2/1\frac{8}{4} = 2/1.

Complexity Analysis

  1. Time Complexity: O(log⁡(min⁡(x,y)))O(\log(\min(x, y))), where xx and yy are the numerator and denominator.
  2. Space Complexity: O(1)O(1).