Divide by Fractions Calculator

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 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 resultDiv = document.getElementById('result'); if (isNaN(num1) || isNaN(den1) || isNaN(num2) || isNaN(den2)) { resultDiv.innerHTML = 'Please enter valid numbers for all fields.'; return; } if (den1 === 0 || den2 === 0) { resultDiv.innerHTML = 'Denominator cannot be zero.'; return; } if (num2 === 0) { resultDiv.innerHTML = 'Cannot divide by zero (second fraction numerator is zero).'; return; } // Division of fractions: (a/b) / (c/d) = (a/b) * (d/c) = (a*d) / (b*c) var resultNumerator = num1 * den2; var resultDenominator = den1 * num2; // Handle negative signs var sign = 1; if (resultNumerator * resultDenominator < 0) { sign = -1; } resultNumerator = Math.abs(resultNumerator); resultDenominator = Math.abs(resultDenominator); // Simplify the fraction var commonDivisor = gcd(resultNumerator, resultDenominator); var simplifiedNumerator = (resultNumerator / commonDivisor) * sign; var simplifiedDenominator = resultDenominator / commonDivisor; var decimalResult = (num1 / den1) / (num2 / den2); var output = '

Result:

'; output += 'Original Division: (' + num1 + '/' + den1 + ') ÷ (' + num2 + '/' + den2 + ')'; output += 'Multiplication Equivalent: (' + num1 + '/' + den1 + ') × (' + den2 + '/' + num2 + ')'; output += 'Unsimplified Fraction: ' + (num1 * den2) + '/' + (den1 * num2) + "; output += 'Simplified Fraction: ' + simplifiedNumerator + '/' + simplifiedDenominator + "; if (simplifiedDenominator !== 0 && simplifiedNumerator % simplifiedDenominator !== 0) { var wholePart = Math.floor(Math.abs(simplifiedNumerator) / simplifiedDenominator); var remainderNumerator = Math.abs(simplifiedNumerator) % simplifiedDenominator; if (wholePart > 0) { output += 'Mixed Number: ' + (simplifiedNumerator < 0 ? '-' : '') + wholePart + ' ' + remainderNumerator + '/' + simplifiedDenominator + ''; } } else if (simplifiedDenominator !== 0 && simplifiedNumerator % simplifiedDenominator === 0) { output += 'Whole Number: ' + (simplifiedNumerator / simplifiedDenominator) + "; } output += 'Decimal Value: ' + decimalResult.toFixed(8) + "; resultDiv.innerHTML = output; }

Understanding Fraction Division

Dividing fractions might seem tricky at first, but it's actually quite straightforward once you learn the "keep, change, flip" method. This calculator helps you quickly perform fraction division and see the result in various forms: simplified fraction, mixed number, and decimal.

What is Fraction Division?

When you divide by a fraction, you're essentially asking how many times the second fraction (the divisor) fits into the first fraction (the dividend). For example, if you have 1/2 of a pizza and you want to divide it into slices that are 1/8 of a pizza each, you'd be performing (1/2) ÷ (1/8).

The "Keep, Change, Flip" Method

This is the golden rule for dividing fractions:

1. Keep the first fraction as it is.
2. Change the division sign to a multiplication sign.
3. Flip the second fraction (find its reciprocal by swapping the numerator and denominator).

Once you've applied these steps, you simply multiply the two fractions as you normally would: multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. Finally, simplify the resulting fraction if possible.

Formula:

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 Calculation:

Let's divide 3/4 by 1/2:

1. Keep the first fraction: 3/4
2. Change the division sign to multiplication: ×
3. Flip the second fraction (1/2 becomes 2/1)

Now, multiply the fractions:

(3/4) × (2/1) = (3 × 2) / (4 × 1) = 6/4

Finally, simplify the fraction 6/4. Both 6 and 4 are divisible by 2:

6 ÷ 2 = 3

4 ÷ 2 = 2

So, the simplified fraction is 3/2. This can also be written as a mixed number, 1 1/2, or as a decimal, 1.5.

Use the calculator above to practice with your own fractions and verify your results!