Enter the numerator and denominator of your fraction below to simplify it and see the step-by-step process.
Simplification Results:
Enter values and click "Simplify Fraction" to see the results.
Understanding Fraction Simplification
Fraction simplification, also known as reducing a fraction to its lowest terms, is a fundamental concept in mathematics. It involves dividing both the numerator (the top number) and the denominator (the bottom number) by their greatest common divisor (GCD) until they can no longer be divided by any common whole number other than 1.
Why Simplify Fractions?
Clarity: Simplified fractions are easier to understand and work with. For example, 1/2 is much clearer than 50/100.
Standardization: It provides a standard way to represent a fractional value, making comparisons and calculations simpler.
Foundation for Advanced Math: Understanding simplification is crucial for algebra, calculus, and other higher-level mathematical concepts.
How the Calculator Works (Step-by-Step)
Our Fraction Simplifier takes your input fraction and performs the following steps:
Identify Numerator and Denominator: It first recognizes the two parts of your fraction.
Find the Greatest Common Divisor (GCD): The calculator uses an efficient algorithm (like the Euclidean algorithm) to find the largest number that can divide both the numerator and the denominator without leaving a remainder.
Divide by the GCD: Both the original numerator and denominator are then divided by this GCD.
Display Simplified Fraction: The resulting numbers form the simplified fraction.
Show Steps: All these steps are presented clearly, so you can understand the process behind the simplification.
Example of Fraction Simplification
Let's simplify the fraction 12/18:
Original Fraction: 12/18
Find GCD of 12 and 18:
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
The greatest common factor (GCD) is 6.
Divide Numerator and Denominator by GCD:
New Numerator = 12 ÷ 6 = 2
New Denominator = 18 ÷ 6 = 3
Simplified Fraction: 2/3
This calculator automates this process, making it quick and easy to simplify any fraction.
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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 calculateSimplification() {
var numeratorInput = document.getElementById("numeratorInput").value;
var denominatorInput = document.getElementById("denominatorInput").value;
var resultDiv = document.getElementById("result");
var numerator = parseInt(numeratorInput);
var denominator = parseInt(denominatorInput);
if (isNaN(numerator) || isNaN(denominator)) {
resultDiv.innerHTML = "Please enter valid numbers for both numerator and denominator.";
return;
}
if (denominator === 0) {
resultDiv.innerHTML = "The denominator cannot be zero.";
return;
}
var commonDivisor = gcd(numerator, denominator);
var simplifiedNumerator = numerator / commonDivisor;
var simplifiedDenominator = denominator / commonDivisor;
var stepsHtml = "
";
stepsHtml += "
Step 1: Identify the original fraction: " + numerator + "/" + denominator + ".
";
stepsHtml += "
Step 2: Find the Greatest Common Divisor (GCD) of the numerator (" + numerator + ") and the denominator (" + denominator + ").";
stepsHtml += "The GCD of " + numerator + " and " + denominator + " is " + commonDivisor + ".
";
stepsHtml += "
Step 3: Divide both the numerator and the denominator by their GCD.";
stepsHtml += "New Numerator = " + numerator + " ÷ " + commonDivisor + " = " + simplifiedNumerator + "";
stepsHtml += "New Denominator = " + denominator + " ÷ " + commonDivisor + " = " + simplifiedDenominator + "
";
stepsHtml += "
Step 4: The simplified fraction is " + simplifiedNumerator + "/" + simplifiedDenominator + ".