Calculator with Fractions Online

Fraction Arithmetic Calculator

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+ – × ÷

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function gcd(a, b) { return b === 0 ? a : gcd(b, a % b); } function calculateFractions() { var num1 = parseFloat(document.getElementById('numerator1').value); var den1 = parseFloat(document.getElementById('denominator1').value); var num2 = parseFloat(document.getElementById('numerator2').value); var den2 = parseFloat(document.getElementById('denominator2').value); var operation = document.getElementById('operation').value; var improperFractionDisplay = document.getElementById('improperFraction'); var mixedNumberDisplay = document.getElementById('mixedNumber'); improperFractionDisplay.innerHTML = "; mixedNumberDisplay.innerHTML = "; // Input validation if (isNaN(num1) || isNaN(den1) || isNaN(num2) || isNaN(den2)) { improperFractionDisplay.innerHTML = 'Error: Please enter valid numbers for all fields.'; return; } if (den1 === 0 || den2 === 0) { improperFractionDisplay.innerHTML = 'Error: Denominators cannot be zero.'; return; } if (operation === 'divide' && num2 === 0) { improperFractionDisplay.innerHTML = 'Error: Cannot divide by zero.'; return; } var resultNum, resultDen; switch (operation) { case 'add': resultNum = num1 * den2 + num2 * den1; resultDen = den1 * den2; break; case 'subtract': resultNum = num1 * den2 – num2 * den1; resultDen = den1 * den2; break; case 'multiply': resultNum = num1 * num2; resultDen = den1 * den2; break; case 'divide': resultNum = num1 * den2; resultDen = den1 * num2; break; } // Handle negative denominator by moving sign to numerator if (resultDen = simplifiedDen) { var wholePart = Math.floor(Math.abs(simplifiedNum) / simplifiedDen); var remainderNum = Math.abs(simplifiedNum) % simplifiedDen; var sign = simplifiedNum < 0 ? '-' : ''; if (remainderNum === 0) { mixedNumberDisplay.innerHTML = 'Mixed Number: ' + sign + wholePart; } else { mixedNumberDisplay.innerHTML = 'Mixed Number: ' + sign + wholePart + ' ' + remainderNum + ' / ' + simplifiedDen; } } else if (simplifiedDen === 0) { improperFractionDisplay.innerHTML = 'Error: Resulting denominator is zero.'; mixedNumberDisplay.innerHTML = ''; } }

Understanding Fractions and How to Use This Calculator

Fractions are a fundamental concept in mathematics, representing a part of a whole. They consist of two numbers: a numerator (the top number) and a denominator (the bottom number). The numerator tells you how many parts you have, and the denominator tells you how many equal parts make up the whole.

Why Use a Fraction Calculator?

While basic fraction operations can be done by hand, they often involve finding common denominators, simplifying results, and converting between improper and mixed fractions. This online fraction calculator simplifies these tasks, allowing you to quickly and accurately perform addition, subtraction, multiplication, and division of fractions without the tedious manual steps.

How Fraction Operations Work:

• Addition (+) and Subtraction (–): To add or subtract fractions, they must have a common denominator. If they don't, you find the least common multiple (LCM) of the denominators, convert the fractions, and then add or subtract the numerators. The result is then simplified. Our calculator handles this automatically.
  Example: 1/2 + 1/4 = 2/4 + 1/4 = 3/4
• Multiplication (×): Multiplying fractions is straightforward: multiply the numerators together and multiply the denominators together. The resulting fraction is then simplified.
  Example: 1/2 × 1/4 = (1×1) / (2×4) = 1/8
• Division (÷): To divide by a fraction, you "flip" the second fraction (find its reciprocal) and then multiply.
  Example: 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2

Simplifying Fractions:

A fraction is in its simplest form when its numerator and denominator have no common factors other than 1. This calculator automatically simplifies the result by finding the Greatest Common Divisor (GCD) of the numerator and denominator and dividing both by it.

Mixed Numbers:

An improper fraction is one where the numerator is greater than or equal to the denominator (e.g., 7/3). A mixed number combines a whole number and a proper fraction (e.g., 2 1/3). Our calculator will display the result as an improper fraction and, if applicable, convert it to a mixed number for easier understanding.

How to Use the Calculator:

1. Enter Fraction 1: Input the numerator and denominator for your first fraction.
2. Select Operation: Choose whether you want to add, subtract, multiply, or divide.
3. Enter Fraction 2: Input the numerator and denominator for your second fraction.
4. Click "Calculate": The calculator will instantly display the result as a simplified improper fraction and, if appropriate, as a mixed number.

This tool is perfect for students, teachers, or anyone needing to perform quick and accurate fraction calculations.