Dividing Fractions Calculator

Easily divide two fractions and see the step-by-step simplification.

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Result:

How to Use the Dividing Fractions Calculator

Dividing fractions might seem complex, but it follows a simple set of rules known as the "Keep, Change, Flip" method. This calculator automates the process, providing you with both the raw product and the simplified final fraction.

Step-by-Step Guide to Dividing Fractions

To divide one fraction by another manually, follow these three simple steps:

1. Keep: Keep the first fraction (the dividend) exactly as it is.
2. Change: Change the division sign (÷) to a multiplication sign (×).
3. Flip: Flip the second fraction (the divisor) upside down. This is called finding the "reciprocal."

Once you have flipped the second fraction, you simply multiply the numerators together and the denominators together, then simplify the result if possible.

Practical Example

Let's say you want to divide 1/2 by 1/4:

• Keep: 1/2
• Change: 1/2 ×
• Flip: 1/2 × 4/1
• Multiply: (1 × 4) / (2 × 1) = 4/2
• Simplify: 4 ÷ 2 = 2

Important Mathematical Rules

When using this calculator, keep in mind that denominators cannot be zero. In mathematics, division by zero is undefined. Additionally, when you divide by a fraction, if the divisor's numerator is zero, the operation is also impossible because the "flipped" fraction would result in a zero denominator.

Common Questions (FAQ)

What is a reciprocal?
A reciprocal is simply a fraction turned upside down. For example, the reciprocal of 3/4 is 4/3.

Can I divide a whole number by a fraction?
Yes. Simply treat the whole number as a fraction with a denominator of 1. For example, 5 becomes 5/1.

Does order matter?
Yes. Unlike multiplication, division is not commutative. 1/2 ÷ 1/4 is not the same as 1/4 ÷ 1/2.

function getGCD(a, b) { a = Math.abs(a); b = Math.abs(b); while (b) { var t = b; b = a % b; a = t; } return a; } function calculateFractionDivision() { var n1 = parseInt(document.getElementById('num1').value); var d1 = parseInt(document.getElementById('den1').value); var n2 = parseInt(document.getElementById('num2').value); var d2 = parseInt(document.getElementById('den2').value); var resultArea = document.getElementById('fraction-result-area'); var stepsArea = document.getElementById('calculation-steps'); var displayArea = document.getElementById('final-result-display'); if (isNaN(n1) || isNaN(d1) || isNaN(n2) || isNaN(d2)) { alert("Please enter valid numbers in all fields."); return; } if (d1 === 0 || d2 === 0) { alert("Denominators cannot be zero."); return; } if (n2 === 0) { alert("Cannot divide by a fraction with a numerator of zero (division by zero)."); return; } // Calculation: (n1/d1) / (n2/d2) = (n1*d2) / (d1*n2) var finalNum = n1 * d2; var finalDen = d1 * n2; // Handle signs if (finalDen < 0) { finalNum = -finalNum; finalDen = -finalDen; } var commonDivisor = getGCD(finalNum, finalDen); var simplifiedNum = finalNum / commonDivisor; var simplifiedDen = finalDen / commonDivisor; resultArea.style.display = "block"; stepsArea.innerHTML = "Step: " + n1 + "/" + d1 + " × " + d2 + "/" + n2 + " = " + finalNum + "/" + finalDen; if (simplifiedDen === 1) { displayArea.innerHTML = "Result: " + simplifiedNum; } else { displayArea.innerHTML = "Result: " + simplifiedNum + " / " + simplifiedDen; } }