Calculator Fractions Online

Online Fraction Calculator

Add (+) Subtract (-) Multiply (*) Divide (/)
function gcd(a, b) { a = Math.abs(a); // Ensure positive for GCD calculation b = Math.abs(b); // Ensure positive for GCD calculation while (b) { var temp = b; b = a % b; a = temp; } return a; } function calculateFractions() { 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'); resultDiv.style.color = '#dc3545'; // Default to error color resultDiv.style.backgroundColor = '#f8d7da'; // Default to error background // 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; } if (operation === 'divide' && n2 === 0) { resultDiv.innerHTML = 'Cannot divide by zero (second fraction numerator is zero).'; return; } var resultNumerator; var resultDenominator; switch (operation) { case 'add': resultNumerator = n1 * d2 + n2 * d1; resultDenominator = d1 * d2; break; case 'subtract': resultNumerator = n1 * d2 – n2 * d1; resultDenominator = d1 * d2; break; case 'multiply': resultNumerator = n1 * n2; resultDenominator = d1 * d2; break; case 'divide': resultNumerator = n1 * d2; resultDenominator = d1 * n2; break; default: resultDiv.innerHTML = 'Invalid operation selected.'; return; } // Simplify the fraction var commonDivisor = gcd(resultNumerator, resultDenominator); var simplifiedNumerator = resultNumerator / commonDivisor; var simplifiedDenominator = resultDenominator / commonDivisor; // Handle negative signs for simplified fraction: ensure denominator is positive if (simplifiedDenominator = simplifiedDenominator && simplifiedDenominator !== 0) { var wholePart = Math.floor(Math.abs(simplifiedNumerator) / simplifiedDenominator); var remainderNumerator = Math.abs(simplifiedNumerator) % simplifiedDenominator; if (simplifiedNumerator < 0) { wholePart *= -1; // Apply negative sign to whole part } if (remainderNumerator === 0) { mixedNumberResult = ' (or ' + wholePart + ')'; } else { mixedNumberResult = ' (or ' + wholePart + ' ' + remainderNumerator + '/' + simplifiedDenominator + ')'; } } resultDiv.style.color = '#28a745'; resultDiv.style.backgroundColor = '#e9f7ef'; resultDiv.innerHTML = 'Result: ' + fractionResult + mixedNumberResult + ' (Decimal: ' + decimalResult.toFixed(4) + ')'; }

Understanding and Using the Online Fraction Calculator

Fractions are a fundamental concept in mathematics, representing parts of a whole. They are written as a ratio of two numbers, a numerator (the top number) and a denominator (the bottom number). Our Online Fraction Calculator simplifies the process of performing arithmetic operations on fractions, making it easy to add, subtract, multiply, or divide them.

What is a Fraction?

A fraction, such as 1/2 or 3/4, indicates how many parts of a whole you have. The numerator tells you how many parts you have, and the denominator tells you how many parts make up the whole. For example, in 3/4, you have 3 parts out of a total of 4 equal parts.

How to Use the Calculator

  1. Enter Fraction 1: Input the numerator and denominator for your first fraction into the respective fields. For example, for 1/2, enter '1' in "Fraction 1 Numerator" and '2' in "Fraction 1 Denominator".
  2. Select Operation: Choose the desired arithmetic operation (+, -, *, /) from the dropdown menu.
  3. Enter Fraction 2: Input the numerator and denominator for your second fraction. For example, for 1/4, enter '1' in "Fraction 2 Numerator" and '4' in "Fraction 2 Denominator".
  4. Calculate: Click the "Calculate" button to see the result. The calculator will display the answer as a simplified fraction, a mixed number (if applicable), and its decimal equivalent.

Fraction Operations Explained

1. Adding Fractions

To add fractions, they must have a common denominator. If they don't, you find the least common multiple (LCM) of the denominators and convert the fractions. Then, you add the numerators and keep the common denominator. Finally, simplify the result.

Formula: a/b + c/d = (ad + bc) / bd

Example: Let's add 1/2 + 1/4.

  • Using the formula: (1*4 + 1*2) / (2*4) = (4 + 2) / 8 = 6/8.
  • Simplifying 6/8 gives 3/4.
  • Using the calculator: Enter 1, 2 for Fraction 1; select Add; enter 1, 4 for Fraction 2. The result will be 3/4.

2. Subtracting Fractions

Similar to addition, subtraction requires a common denominator. Once fractions have the same denominator, subtract the numerators and keep the common denominator. Simplify the result.

Formula: a/b - c/d = (ad - bc) / bd

Example: Let's subtract 3/4 - 1/2.

  • Using the formula: (3*2 - 1*4) / (4*2) = (6 - 4) / 8 = 2/8.
  • Simplifying 2/8 gives 1/4.
  • Using the calculator: Enter 3, 4 for Fraction 1; select Subtract; enter 1, 2 for Fraction 2. The result will be 1/4.

3. Multiplying Fractions

Multiplying fractions is straightforward: multiply the numerators together and multiply the denominators together. Then, simplify the resulting fraction.

Formula: a/b * c/d = (ac) / (bd)

Example: Let's multiply 2/3 * 1/2.

  • Multiply numerators: 2 * 1 = 2.
  • Multiply denominators: 3 * 2 = 6.
  • Result: 2/6, which simplifies to 1/3.
  • Using the calculator: Enter 2, 3 for Fraction 1; select Multiply; enter 1, 2 for Fraction 2. The result will be 1/3.

4. Dividing Fractions

To divide fractions, you "keep, change, flip." Keep the first fraction as it is, change the division sign to multiplication, and flip (find the reciprocal of) the second fraction. Then, multiply the fractions as usual.

Formula: a/b / c/d = a/b * d/c = (ad) / (bc)

Example: Let's divide 3/4 / 1/2.

  • Keep 3/4.
  • Change / to *.
  • Flip 1/2 to 2/1.
  • Now multiply: 3/4 * 2/1 = 6/4.
  • Simplifying 6/4 gives 3/2.
  • As a mixed number: 1 1/2.
  • Using the calculator: Enter 3, 4 for Fraction 1; select Divide; enter 1, 2 for Fraction 2. The result will be 3/2 (or 1 1/2).

This calculator is a handy tool for students, teachers, and anyone needing to quickly and accurately perform operations on fractions without manual calculation.

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