Adding Fractions and Subtracting Fractions Calculator

Fraction Addition & Subtraction Calculator

First Fraction

Operation

Second Fraction

// Function to find the Greatest Common Divisor (GCD) function gcd(a, b) { a = Math.abs(a); b = Math.abs(b); while (b) { var temp = b; b = a % b; a = temp; } return a; } // Function to find the Least Common Multiple (LCM) function lcm(a, b) { if (a === 0 || b === 0) return 0; return Math.abs(a * b) / gcd(a, b); } function calculateFraction() { var num1 = parseInt(document.getElementById('numerator1').value); var den1 = parseInt(document.getElementById('denominator1').value); var num2 = parseInt(document.getElementById('numerator2').value); var den2 = parseInt(document.getElementById('denominator2').value); var operation = document.querySelector('input[name="operation"]:checked').value; var resultDiv = document.getElementById('result'); // Input validation if (isNaN(num1) || isNaN(den1) || isNaN(num2) || isNaN(den2)) { resultDiv.innerHTML = "Please enter valid numbers for all fields."; resultDiv.style.borderColor = '#dc3545'; resultDiv.style.backgroundColor = '#ffe6e6'; resultDiv.style.color = '#dc3545'; return; } if (den1 === 0 || den2 === 0) { resultDiv.innerHTML = "Denominator cannot be zero."; resultDiv.style.borderColor = '#dc3545'; resultDiv.style.backgroundColor = '#ffe6e6'; resultDiv.style.color = '#dc3545'; return; } var commonDen = lcm(den1, den2); var newNum1 = num1 * (commonDen / den1); var newNum2 = num2 * (commonDen / den2); var resultNum; if (operation === 'add') { resultNum = newNum1 + newNum2; } else { // subtract resultNum = newNum1 – newNum2; } var resultDen = commonDen; // Simplify the fraction var commonDivisor = gcd(resultNum, resultDen); var simplifiedNum = resultNum / commonDivisor; var simplifiedDen = resultDen / commonDivisor; // Handle negative denominator by moving sign to numerator if (simplifiedDen < 0) { simplifiedNum = -simplifiedNum; simplifiedDen = -simplifiedDen; } var finalResult; if (simplifiedDen === 1) { finalResult = simplifiedNum.toString(); } else { finalResult = simplifiedNum + " / " + simplifiedDen; } resultDiv.innerHTML = "Result: " + finalResult; resultDiv.style.borderColor = '#28a745'; resultDiv.style.backgroundColor = '#e6ffe6'; resultDiv.style.color = '#28a745'; } // Initial calculation on page load (optional, but good for showing default values) document.addEventListener('DOMContentLoaded', function() { calculateFraction(); });

Understanding Fraction Addition and Subtraction

Fractions are a fundamental concept in mathematics, representing a part of a whole. They consist of two main parts: a numerator (the top number) which tells us how many parts we have, and a denominator (the bottom number) which tells us how many equal parts the whole is divided into.

Adding Fractions

Adding fractions requires a common denominator. This means that the 'whole' must be divided into the same number of equal parts for both fractions before they can be combined. Here's the process:

1. Find a Common Denominator: Determine the Least Common Multiple (LCM) of the denominators of the fractions you want to add. This will be your new common denominator.
2. Convert Fractions: For each fraction, multiply both its numerator and denominator by the factor that makes its denominator equal to the common denominator.
3. Add Numerators: Once both fractions have the same denominator, simply add their numerators. The denominator remains the common denominator.
4. Simplify (if necessary): Reduce the resulting fraction to its simplest form by dividing both the numerator and the denominator by their Greatest Common Divisor (GCD).

Example: Add 1/3 and 1/6

• LCM of 3 and 6 is 6.
• Convert 1/3: (1 * 2) / (3 * 2) = 2/6
• Now add: 2/6 + 1/6 = (2 + 1) / 6 = 3/6
• Simplify: GCD of 3 and 6 is 3. So, 3/6 simplifies to (3/3) / (6/3) = 1/2.

Subtracting Fractions

Subtracting fractions follows a very similar process to addition, also requiring a common denominator:

1. Find a Common Denominator: Just like with addition, find the LCM of the denominators.
2. Convert Fractions: Convert both fractions to equivalent fractions with the common denominator.
3. Subtract Numerators: Subtract the second numerator from the first numerator. The denominator remains the common denominator.
4. Simplify (if necessary): Reduce the resulting fraction to its simplest form.

Example: Subtract 3/4 from 7/8

• LCM of 4 and 8 is 8.
• Convert 3/4: (3 * 2) / (4 * 2) = 6/8
• Now subtract: 7/8 – 6/8 = (7 – 6) / 8 = 1/8
• The fraction 1/8 is already in its simplest form.

How the Calculator Works

Our calculator automates these steps. You simply input the numerator and denominator for your two fractions, select whether you want to add or subtract, and click 'Calculate'. The tool will automatically find the common denominator, perform the chosen operation, and simplify the final result for you, making fraction arithmetic quick and error-free.