Fraction Calculator Plus – Loan calculator

Fraction Arithmetic Calculator

Enter two fractions and select an operation to calculate their sum, difference, product, or quotient. The result will be automatically simplified.

Fraction 1 Numerator: Fraction 1 Denominator:

Operation: + – × ÷

Fraction 2 Numerator: Fraction 2 Denominator:

// Function to find the Greatest Common Divisor (GCD) using Euclidean algorithm 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 simplify a fraction function simplifyFraction(numerator, denominator) { if (denominator === 0) { return [numerator, denominator]; // Cannot simplify if denominator is zero } if (numerator === 0) { return [0, 1]; // 0/X simplifies to 0/1 } var commonDivisor = gcd(numerator, denominator); var simplifiedNumerator = numerator / commonDivisor; var simplifiedDenominator = denominator / commonDivisor; // Ensure the denominator is always positive. If not, move the sign to the numerator. if (simplifiedDenominator < 0) { simplifiedNumerator *= -1; simplifiedDenominator *= -1; } return [simplifiedNumerator, simplifiedDenominator]; } function calculateFractions() { 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('resultFraction'); resultDiv.style.color = '#333'; // Reset color for new calculation // Input validation if (isNaN(num1) || isNaN(den1) || isNaN(num2) || isNaN(den2)) { resultDiv.innerHTML = "Error: Please enter valid numbers for all fraction parts."; resultDiv.style.color = 'red'; return; } if (den1 === 0 || den2 === 0) { resultDiv.innerHTML = "Error: Denominator cannot be zero."; resultDiv.style.color = 'red'; return; } var resultNumerator; var resultDenominator; switch (operation) { case 'add': resultNumerator = (num1 * den2) + (num2 * den1); resultDenominator = den1 * den2; break; case 'subtract': resultNumerator = (num1 * den2) – (num2 * den1); resultDenominator = den1 * den2; break; case 'multiply': resultNumerator = num1 * num2; resultDenominator = den1 * den2; break; case 'divide': if (num2 === 0) { resultDiv.innerHTML = "Error: Cannot divide by zero (second fraction's numerator is zero)."; resultDiv.style.color = 'red'; return; } resultNumerator = num1 * den2; resultDenominator = den1 * num2; break; default: resultDiv.innerHTML = "Error: Invalid operation selected."; resultDiv.style.color = 'red'; return; } var simplified = simplifyFraction(resultNumerator, resultDenominator); var finalNumerator = simplified[0]; var finalDenominator = simplified[1]; if (finalDenominator === 1) { resultDiv.innerHTML = "Result: " + finalNumerator; } else { resultDiv.innerHTML = "Result: " + finalNumerator + " / " + finalDenominator; } }

Understanding Fractions and Their Operations

A fraction is a numerical representation of a part of a whole. It is written as two numbers separated by a horizontal line: the numerator (the top number) and the denominator (the bottom number). The numerator indicates how many parts of the whole are being considered, while the denominator indicates the total number of equal parts that make up the whole. For instance, in the fraction ³⁄₄, you have 3 parts out of a total of 4 equal parts.

Why Use a Fraction Calculator?

While performing arithmetic with fractions by hand is a fundamental skill, a dedicated fraction calculator offers significant advantages. It streamlines complex calculations, minimizes the potential for human error, and automatically simplifies results to their lowest terms. This tool is invaluable in various fields, including mathematics, science, engineering, cooking, and any scenario demanding precise calculations involving portions or ratios.

How to Add and Subtract Fractions

To add or subtract fractions, a crucial first step is to ensure they share a common denominator. If their denominators are different, you must find the least common multiple (LCM) of the denominators and convert each fraction to an equivalent fraction with this common denominator. Once the denominators are identical, you simply add or subtract the numerators and keep the common denominator. The final step is always to simplify the resulting fraction.

Example (Addition): ¹⁄₂ + ¹⁄₄

Identify the denominators: 2 and 4. The LCM of 2 and 4 is 4.
Convert ¹⁄₂ to an equivalent fraction with a denominator of 4: ²⁄₄.
Add the numerators: ²⁄₄ + ¹⁄₄ = ³⁄₄.
The calculator performs this by finding a common denominator through multiplication: (1×4 + 1×2) / (2×4) = (4+2)/8 = ⁶⁄₈, which simplifies to ³⁄₄.

Example (Subtraction): ³⁄₄ – ¹⁄₃

Identify the denominators: 4 and 3. The LCM of 4 and 3 is 12.
Convert ³⁄₄ to ⁹⁄₁₂ and ¹⁄₃ to ⁴⁄₁₂.
Subtract the numerators: ⁹⁄₁₂ – ⁴⁄₁₂ = ⁵⁄₁₂.
The calculator performs this as: (3×3 – 1×4) / (4×3) = (9-4)/12 = ⁵⁄₁₂.

How to Multiply Fractions

Multiplying fractions is quite straightforward. You simply multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. After performing the multiplication, always simplify the resulting fraction to its lowest terms.

Example: ²⁄₃ × ¹⁄₂

Multiply numerators: 2 × 1 = 2.
Multiply denominators: 3 × 2 = 6.
The initial result is ²⁄₆, which simplifies to ¹⁄₃.

How to Divide Fractions

Dividing fractions involves a simple trick often remembered as "keep, change, flip." You keep the first fraction as it is, change the division sign to a multiplication sign, and then flip (find the reciprocal of) the second fraction. Once you've done this, you proceed to multiply the fractions as described above.

Example: ³⁄₄ ÷ ¹⁄₂

Keep the first fraction: ³⁄₄.
Change the division sign to multiplication: ×.
Flip the second fraction (reciprocal of ¹⁄₂): ²⁄₁.
Multiply the fractions: ³⁄₄ × ²⁄₁ = (3 × 2) / (4 × 1) = ⁶⁄₄.
The initial result is ⁶⁄₄, which simplifies to ³⁄₂.

Fraction Simplification

Simplifying a fraction, also known as reducing it to its lowest terms, means finding an equivalent fraction where the numerator and denominator have no common factors other than 1. This is achieved by dividing both the numerator and the denominator by their greatest common divisor (GCD). For example, the fraction ⁶⁄₈ simplifies to ³⁄₄ because the GCD of 6 and 8 is 2 (6 ÷ 2 = 3, and 8 ÷ 2 = 4).