This calculator helps you simplify fractions step-by-step by finding the Greatest Common Divisor (GCD) of the numerator and denominator. Simplifying fractions makes them easier to understand and work with in further calculations.
How to Use:
Enter the numerator (top number) of your fraction.
Enter the denominator (bottom number) of your fraction.
Click "Simplify Fraction" to see the step-by-step simplification process and the final reduced fraction.
Understanding Fraction Simplification
Fraction simplification, also known as reducing a fraction to its lowest terms, is the process of dividing both the numerator and the denominator by their Greatest Common Divisor (GCD). The GCD is the largest positive integer that divides two or more integers without leaving a remainder.
Why Simplify Fractions?
Clarity: Simplified fractions are easier to comprehend. For example, 50⁄100 is less intuitive than 1⁄2.
Standard Form: It's considered good mathematical practice to express fractions in their simplest form.
Easier Calculations: Working with smaller numbers in simplified fractions reduces the chance of errors in subsequent arithmetic operations.
Comparison: It's easier to compare fractions when they are in their simplest form.
The Step-by-Step Process:
To simplify a fraction N⁄D:
Identify the Numerator and Denominator: These are the top and bottom numbers of your fraction.
Find the Greatest Common Divisor (GCD): Use a method like the Euclidean algorithm to find the largest number that divides both the absolute value of the numerator and the absolute value of the denominator evenly.
Divide by the GCD: Divide both the numerator and the denominator by the GCD.
Handle Signs: Ensure the final simplified fraction has the correct sign. If the original numerator and denominator had different signs, the simplified fraction will be negative. If they had the same sign (both positive or both negative), the simplified fraction will be positive. Conventionally, the negative sign is placed in the numerator or in front of the fraction.
Example:
Let's simplify 12⁄18:
Original Fraction: 12⁄18
Find GCD of 12 and 18: The divisors of 12 are 1, 2, 3, 4, 6, 12. The divisors of 18 are 1, 2, 3, 6, 9, 18. The greatest common divisor is 6.
Divide Numerator by GCD: 12 ÷ 6 = 2
Divide Denominator by GCD: 18 ÷ 6 = 3
Simplified Fraction: 2⁄3
function gcd(a, b) {
// Euclidean algorithm to find GCD
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");
var denominatorInput = document.getElementById("denominatorInput");
var resultDiv = document.getElementById("result");
var num = parseInt(numeratorInput.value);
var den = parseInt(denominatorInput.value);
if (isNaN(num) || isNaN(den)) {
resultDiv.innerHTML = 'Please enter valid numbers for both numerator and denominator.';
return;
}
if (den === 0) {
resultDiv.innerHTML = 'The denominator cannot be zero.';
return;
}
var originalNum = num;
var originalDen = den;
// Determine the sign of the final fraction
var finalNumeratorSign = 1;
if ((num 0) || (num > 0 && den < 0)) {
finalNumeratorSign = -1;
}
// Use absolute values for GCD calculation
var absNum = Math.abs(num);
var absDen = Math.abs(den);
var commonDivisor = gcd(absNum, absDen);
var simplifiedNum = (absNum / commonDivisor) * finalNumeratorSign;
var simplifiedDen = absDen / commonDivisor;
var output = '