// Function to find the Greatest Common Divisor (GCD) using Euclidean algorithm
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 calculateDivision() {
var num1 = parseFloat(document.getElementById('firstNumerator').value);
var den1 = parseFloat(document.getElementById('firstDenominator').value);
var num2 = parseFloat(document.getElementById('secondNumerator').value);
var den2 = parseFloat(document.getElementById('secondDenominator').value);
// Input validation
if (isNaN(num1) || isNaN(den1) || isNaN(num2) || isNaN(den2)) {
document.getElementById('resultFraction').innerHTML = 'Please enter valid numbers for all fields.';
document.getElementById('simplifiedFraction').innerHTML = ";
document.getElementById('decimalResult').innerHTML = ";
return;
}
if (den1 === 0 || den2 === 0) {
document.getElementById('resultFraction').innerHTML = 'Error: Denominator cannot be zero.';
document.getElementById('simplifiedFraction').innerHTML = ";
document.getElementById('decimalResult').innerHTML = ";
return;
}
if (num2 === 0) { // If the second fraction's numerator is zero, the second fraction is zero. Division by zero is undefined.
document.getElementById('resultFraction').innerHTML = 'Error: Cannot divide by zero (second fraction is zero).';
document.getElementById('simplifiedFraction').innerHTML = ";
document.getElementById('decimalResult').innerHTML = ";
return;
}
// Division of fractions: (a/b) / (c/d) = (a/b) * (d/c) = (a*d) / (b*c)
var resultNum = num1 * den2;
var resultDen = den1 * num2;
// Display initial result
document.getElementById('resultFraction').innerHTML = 'Resulting Fraction: ' + resultNum + ' / ' + resultDen;
// Simplify the fraction
var commonDivisor = gcd(resultNum, resultDen);
var simplifiedNum = resultNum / commonDivisor;
var simplifiedDen = resultDen / commonDivisor;
// Adjust signs for simplified fraction to ensure denominator is positive
if (simplifiedDen < 0) {
simplifiedNum = -simplifiedNum;
simplifiedDen = -simplifiedDen;
}
document.getElementById('simplifiedFraction').innerHTML = 'Simplified Fraction: ' + simplifiedNum + ' / ' + simplifiedDen;
// Calculate decimal equivalent
var decimal = resultNum / resultDen;
document.getElementById('decimalResult').innerHTML = 'Decimal Equivalent: ' + decimal.toFixed(8); // Display to 8 decimal places for precision
}
// Run calculation on page load with default values
window.onload = calculateDivision;
Understanding Fraction Division
Dividing fractions might seem intimidating at first, but it's actually quite straightforward once you understand the core principle. This calculator helps you quickly find the quotient of two fractions, providing both the raw result, its simplified form, and its decimal equivalent.
What is a Fraction?
A fraction represents a part of a whole. It consists of two numbers: a numerator (the top number) and a denominator (the bottom number). The numerator tells you how many parts you have, and the denominator tells you how many equal parts make up the whole. For example, in the fraction 3/4, you have 3 parts out of a total of 4 equal parts.
How to Divide Fractions: The "Keep, Change, Flip" Method
The easiest way to divide fractions is by using the "Keep, Change, Flip" method. Here's how it works:
- Keep the first fraction as it is.
- Change the division sign to a multiplication sign.
- Flip the second fraction (find its reciprocal). To flip a fraction, you swap its numerator and denominator.
Once you've applied these three steps, you're left with a multiplication problem, which is generally easier to solve.
The Formula:
If you have two fractions, a⁄b and c⁄d, their division is calculated as follows:
(a⁄b) ÷ (c⁄d) = (a⁄b) × (d⁄c) = (a × d)⁄(b × c)
Example Calculation:
Let's divide 3⁄4 by 1⁄2 using the "Keep, Change, Flip" method:
- Keep the first fraction: 3⁄4
- Change the division sign to multiplication: ×
- Flip the second fraction (1⁄2 becomes 2⁄1): 2⁄1
Now, multiply the fractions:
3⁄4 × 2⁄1 = (3 × 2)⁄(4 × 1) = 6⁄4
Simplifying the Result
The resulting fraction 6⁄4 can be simplified. To simplify a fraction, you find the greatest common divisor (GCD) of the numerator and the denominator, and then divide both by the GCD.
- The factors of 6 are 1, 2, 3, 6.
- The factors of 4 are 1, 2, 4.
- The greatest common divisor (GCD) of 6 and 4 is 2.
Divide both the numerator and the denominator by 2:
6 ÷ 2⁄4 ÷ 2 = 3⁄2
So, 3⁄4 divided by 1⁄2 is 3⁄2, or 1 and 1⁄2 as a mixed number, or 1.5 as a decimal.
Our calculator performs all these steps for you, providing the raw fraction, the simplified fraction, and its decimal equivalent instantly.