Fraction Calculator Adding and Subtracting

Fraction Addition & Subtraction Calculator

Add (+) Subtract (-)
Result:
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.getElementById("operation").value; var resultDiv = document.getElementById("fractionResult"); if (isNaN(num1) || isNaN(den1) || isNaN(num2) || isNaN(den2)) { resultDiv.innerHTML = "Error: Please enter valid numbers for all fields."; return; } if (den1 === 0 || den2 === 0) { resultDiv.innerHTML = "Error: Denominator cannot be zero."; return; } var resultNum, resultDen; 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 lcm(a, b) { if (a === 0 || b === 0) return 0; return (Math.abs(a * b)) / gcd(a, b); } if (operation === "add") { var commonDen = lcm(den1, den2); resultNum = (num1 * (commonDen / den1)) + (num2 * (commonDen / den2)); resultDen = commonDen; } else if (operation === "subtract") { var commonDen = lcm(den1, den2); resultNum = (num1 * (commonDen / den1)) – (num2 * (commonDen / den2)); resultDen = commonDen; } var commonDivisor = gcd(resultNum, resultDen); var simplifiedNum = resultNum / commonDivisor; var simplifiedDen = resultDen / commonDivisor; if (simplifiedDen < 0) { simplifiedNum = -simplifiedNum; simplifiedDen = -simplifiedDen; } if (simplifiedDen === 1) { resultDiv.innerHTML = "Result: " + simplifiedNum; } else { resultDiv.innerHTML = "Result: " + simplifiedNum + " / " + simplifiedDen; } }

Understanding Fraction Addition and Subtraction

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 denominator indicates how many equal parts the whole is divided into, and the numerator indicates how many of those parts are being considered.

Adding Fractions

To add fractions, you must first ensure they have a common denominator. If they don't, you need to find the least common multiple (LCM) of the denominators and convert each fraction to an equivalent fraction with that common denominator. Once the denominators are the same, you simply add the numerators and keep the common denominator. Finally, simplify the resulting fraction if possible.

Steps for Adding Fractions:

  1. Find a Common Denominator: Determine the least common multiple (LCM) of the denominators.
  2. Convert Fractions: Rewrite each fraction as an equivalent fraction with the common denominator. To do this, multiply both the numerator and denominator of each fraction by the factor that makes its denominator equal to the common denominator.
  3. Add Numerators: Add the numerators of the new fractions. The denominator remains the common denominator.
  4. Simplify: Reduce the resulting fraction to its simplest form by dividing both the numerator and denominator by their greatest common divisor (GCD).

Example of Fraction Addition:

Let's add 1/3 and 1/6.

  • Common Denominator: The LCM of 3 and 6 is 6.
  • Convert Fractions: 1/3 becomes 2/6 (multiply numerator and denominator by 2). 1/6 remains 1/6.
  • Add Numerators: 2/6 + 1/6 = (2+1)/6 = 3/6.
  • Simplify: The GCD of 3 and 6 is 3. So, 3/6 simplifies to 1/2.

Therefore, 1/3 + 1/6 = 1/2.

Subtracting Fractions

Subtracting fractions follows a very similar process to adding them. The crucial first step is again to find a common denominator. Once the denominators are the same, you subtract the numerators and keep the common denominator. The final step is to simplify the result.

Steps for Subtracting Fractions:

  1. Find a Common Denominator: Determine the least common multiple (LCM) of the denominators.
  2. Convert Fractions: Rewrite each fraction as an equivalent fraction with the common denominator.
  3. Subtract Numerators: Subtract the numerator of the second fraction from the numerator of the first fraction. The denominator remains the common denominator.
  4. Simplify: Reduce the resulting fraction to its simplest form.

Example of Fraction Subtraction:

Let's subtract 1/4 from 3/8.

  • Common Denominator: The LCM of 4 and 8 is 8.
  • Convert Fractions: 3/8 remains 3/8. 1/4 becomes 2/8 (multiply numerator and denominator by 2).
  • Subtract Numerators: 3/8 – 2/8 = (3-2)/8 = 1/8.
  • Simplify: The fraction 1/8 is already in its simplest form (GCD of 1 and 8 is 1).

Therefore, 3/8 – 1/4 = 1/8.

Using the Calculator

Our Fraction Addition & Subtraction Calculator simplifies these processes for you. Simply enter the numerator and denominator for your first fraction, select whether you want to add or subtract, then enter the numerator and denominator for your second fraction. Click "Calculate Fraction," and the tool will instantly provide the simplified result.

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