Adding Subtracting Fractions Calculator

Fraction Addition & Subtraction Calculator

// 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 n1 = parseInt(document.getElementById("numerator1").value); var d1 = parseInt(document.getElementById("denominator1").value); var n2 = parseInt(document.getElementById("numerator2").value); var d2 = parseInt(document.getElementById("denominator2").value); var operation = document.getElementById("operation").value; var resultDiv = document.getElementById("result"); // Input validation if (isNaN(n1) || isNaN(d1) || isNaN(n2) || isNaN(d2)) { resultDiv.innerHTML = "Please enter valid numbers for all fields."; return; } if (d1 === 0 || d2 === 0) { resultDiv.innerHTML = "Denominator cannot be zero."; return; } var commonDenominator = lcm(d1, d2); // Convert fractions to have the common denominator var newN1 = n1 * (commonDenominator / d1); var newN2 = n2 * (commonDenominator / d2); var resultNumerator; if (operation === "add") { resultNumerator = newN1 + newN2; } else { // subtract resultNumerator = newN1 – newN2; } // Simplify the resulting fraction var commonDivisor = gcd(resultNumerator, commonDenominator); var simplifiedNumerator = resultNumerator / commonDivisor; var simplifiedDenominator = commonDenominator / commonDivisor; // Handle negative denominators by moving the sign to the numerator if (simplifiedDenominator < 0) { simplifiedNumerator = -simplifiedNumerator; simplifiedDenominator = -simplifiedDenominator; } // Display result if (simplifiedDenominator === 1) { resultDiv.innerHTML = "Result: " + simplifiedNumerator; } else { resultDiv.innerHTML = "Result: " + simplifiedNumerator + " / " + simplifiedDenominator; } }

Understanding Fraction Addition and Subtraction

Fractions are a fundamental concept in mathematics, representing a part of a whole. They consist of a numerator (the top number) and a denominator (the bottom number), separated by a fraction bar. The denominator tells us how many equal parts the whole is divided into, and the numerator tells us how many of those parts we have.

What are Fractions?

A fraction like ³⁄₄ means we have 3 parts out of a total of 4 equal parts. Fractions are used in everyday life, from cooking recipes (e.g., ¹⁄₂ cup of flour) to measuring distances or time.

Adding Fractions

To add fractions, they must have a common denominator. If they don't, you need to find the Least Common Multiple (LCM) of their denominators and convert both fractions to equivalent fractions with that common denominator. Once they share a common denominator, you simply add their numerators and keep the denominator the same.

Example: Add ¹⁄₂ and ¹⁄₄

1. Find the LCM of 2 and 4, which is 4.
2. Convert ¹⁄₂ to an equivalent fraction with a denominator of 4: ^{1 × 2}⁄_{2 × 2} = ²⁄₄.
3. Now add: ²⁄₄ + ¹⁄₄ = ^{(2 + 1)}⁄₄ = ³⁄₄.

Subtracting Fractions

Subtracting fractions follows a similar principle to addition. You must first ensure both fractions have a common denominator. If not, find the LCM of their denominators and convert them. Once they have the same denominator, subtract the numerators and keep the common denominator.

Example: Subtract ¹⁄₄ from ³⁄₅

1. Find the LCM of 5 and 4, which is 20.
2. Convert ³⁄₅: ^{3 × 4}⁄_{5 × 4} = ¹²⁄₂₀.
3. Convert ¹⁄₄: ^{1 × 5}⁄_{4 × 5} = ⁵⁄₂₀.
4. Now subtract: ¹²⁄₂₀ – ⁵⁄₂₀ = ^{(12 – 5)}⁄₂₀ = ⁷⁄₂₀.

Simplifying Fractions

After adding or subtracting fractions, the resulting fraction should often be simplified to its lowest terms. This means dividing both the numerator and the denominator by their Greatest Common Divisor (GCD). A fraction is in its simplest form when the only common factor between its numerator and denominator is 1.

Example: Simplify ⁶⁄₈

1. Find the GCD of 6 and 8, which is 2.
2. Divide both numerator and denominator by 2: ^{6 ÷ 2}⁄_{8 ÷ 2} = ³⁄₄.

How to Use the Calculator

Our Fraction Addition & Subtraction Calculator makes these operations straightforward:

1. First Fraction: Enter the numerator and denominator of your first fraction in the respective fields.
2. Operation: Select whether you want to 'Add (+)' or 'Subtract (-)' the fractions using the dropdown menu.
3. Second Fraction: Enter the numerator and denominator of your second fraction.
4. Calculate: Click the "Calculate" button.

The calculator will instantly display the result, simplified to its lowest terms, making complex fraction arithmetic quick and easy.