Fraction Calculator Division

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Fraction Division Calculator

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 calculateFractionDivision() { var numerator1 = parseFloat(document.getElementById('numerator1').value); var denominator1 = parseFloat(document.getElementById('denominator1').value); var numerator2 = parseFloat(document.getElementById('numerator2').value); var denominator2 = parseFloat(document.getElementById('denominator2').value); var resultDiv = document.getElementById('result'); if (isNaN(numerator1) || isNaN(denominator1) || isNaN(numerator2) || isNaN(denominator2)) { resultDiv.innerHTML = "Please enter valid numbers for all fields."; return; } if (denominator1 === 0 || denominator2 === 0) { resultDiv.innerHTML = "Denominator cannot be zero."; return; } if (numerator2 === 0) { resultDiv.innerHTML = "The numerator of the second fraction cannot be zero when dividing (as it would lead to division by zero after inverting)."; return; } // Division of fractions: (a/b) / (c/d) = (a/b) * (d/c) = (a*d) / (b*c) var resultNumerator = numerator1 * denominator2; var resultDenominator = denominator1 * numerator2; var commonDivisor = gcd(resultNumerator, resultDenominator); var simplifiedNumerator = resultNumerator / commonDivisor; var simplifiedDenominator = resultDenominator / commonDivisor; var output = "

Division Result:

"; output += "Original fractions: (" + numerator1 + "/" + denominator1 + ") รท (" + numerator2 + "/" + denominator2 + ")"; output += "Unsimplified Result: " + resultNumerator + "/" + resultDenominator + ""; output += "Simplified Result: " + simplifiedNumerator + "/" + simplifiedDenominator + ""; if (simplifiedDenominator === 1) { output += "Which is equivalent to the whole number: " + simplifiedNumerator + ""; } else if (Math.abs(simplifiedNumerator) > Math.abs(simplifiedDenominator)) { var wholePart = Math.floor(Math.abs(simplifiedNumerator) / Math.abs(simplifiedDenominator)); var remainder = Math.abs(simplifiedNumerator) % Math.abs(simplifiedDenominator); var sign = (simplifiedNumerator * simplifiedDenominator < 0) ? "-" : ""; if (remainder === 0) { output += "Which is equivalent to the whole number: " + sign + wholePart + ""; } else { output += "Which is equivalent to the mixed number: " + sign + wholePart + " " + remainder + "/" + Math.abs(simplifiedDenominator) + ""; } } resultDiv.innerHTML = output; }

Understanding Fraction Division

Dividing fractions might seem intimidating at first, but it's actually quite straightforward once you learn the "invert and multiply" rule. This calculator helps you quickly perform fraction division and simplifies the result for you.

What is Fraction Division?

When you divide one fraction by another, you are essentially asking how many times the second fraction "fits into" the first fraction. For example, if you divide 1/2 by 1/4, you're asking how many quarters are in a half, which is 2.

The "Invert and Multiply" Rule

The fundamental rule for dividing fractions is to:

  1. Keep the first fraction as it is.
  2. Change the division sign to a multiplication sign.
  3. Flip (or invert) the second fraction. This means swapping its numerator and denominator. The inverted fraction is called the reciprocal.
  4. Multiply the two fractions (numerator by numerator, and denominator by denominator).
  5. Simplify the resulting fraction to its lowest terms.

Mathematically, if you have two fractions (a/b) and (c/d), their division is calculated as:

(a/b) ÷ (c/d) = (a/b) × (d/c) = (a × d) / (b × c)

Example of Fraction Division

Let's divide 3⁄4 by 1⁄2:

  1. Keep 3⁄4.
  2. Change ÷ to ×.
  3. Invert 1⁄2 to 2⁄1.
  4. Multiply: 3⁄4 × 2⁄1 = (3 × 2) / (4 × 1) = 6⁄4.
  5. Simplify: The greatest common divisor (GCD) of 6 and 4 is 2. So, divide both the numerator and denominator by 2: 6 ÷ 2⁄4 ÷ 2 = 3⁄2.

The result is 3⁄2, which can also be written as the mixed number 1 1⁄2.

How to Use the Calculator

Our Fraction Division Calculator makes this process effortless:

  1. Enter the numerator of your first fraction in the "First Fraction Numerator" field.
  2. Enter the denominator of your first fraction in the "First Fraction Denominator" field.
  3. Enter the numerator of your second fraction in the "Second Fraction Numerator" field.
  4. Enter the denominator of your second fraction in the "Second Fraction Denominator" field.
  5. Click the "Calculate Division" button.

The calculator will instantly display the unsimplified result, the simplified result, and if applicable, its equivalent as a whole number or a mixed number.

Remember that denominators cannot be zero, and the numerator of the second fraction also cannot be zero, as this would lead to an undefined result.

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