Expression Simplifier Calculator

Fraction Simplifier 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 simplifyFraction() { var numeratorStr = document.getElementById("numeratorInput").value; var denominatorStr = document.getElementById("denominatorInput").value; var resultDiv = document.getElementById("simplifiedFractionResult"); var numerator = parseInt(numeratorStr); var denominator = parseInt(denominatorStr); if (isNaN(numerator) || isNaN(denominator)) { resultDiv.innerHTML = "Please enter valid numbers for both numerator and denominator."; return; } if (denominator === 0) { resultDiv.innerHTML = "Error: Denominator cannot be zero."; return; } if (numerator === 0) { resultDiv.innerHTML = "Simplified Fraction: 0/1 (or simply 0)"; return; } var commonDivisor = gcd(numerator, denominator); var simplifiedNumerator = numerator / commonDivisor; var simplifiedDenominator = denominator / commonDivisor; // Handle negative signs if (simplifiedDenominator < 0) { simplifiedNumerator *= -1; simplifiedDenominator *= -1; } resultDiv.innerHTML = "Original Fraction: " + numerator + "/" + denominator + "Simplified Fraction: " + simplifiedNumerator + "/" + simplifiedDenominator; } // Initial calculation on load for default values window.onload = simplifyFraction;

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). The goal is to express the fraction in its simplest form, where the numerator and denominator have no common factors other than 1.

Why Simplify Fractions?

• Clarity: Simplified fractions are easier to understand and visualize. For example, 1/2 is much clearer than 50/100.
• Standardization: It provides a standard way to represent a fractional value, making it easier to compare and perform operations with different fractions.
• Efficiency: Working with smaller numbers in simplified fractions reduces the chance of errors in further calculations.

How This Calculator Works

Our Fraction Simplifier Calculator uses the Euclidean algorithm to find the Greatest Common Divisor (GCD) of the numerator and the denominator you provide. Once the GCD is found, both the numerator and the denominator are divided by this GCD. The resulting numbers form the simplified fraction.

For instance, if you input 10 as the numerator and 15 as the denominator:

1. The calculator finds the GCD of 10 and 15, which is 5.
2. It then divides the numerator (10) by 5, resulting in 2.
3. It divides the denominator (15) by 5, resulting in 3.
4. The simplified fraction is therefore 2/3.

Examples of Fraction Simplification

• Example 1: Simplify 4/8
  GCD(4, 8) = 4
  Simplified: 4÷4 / 8÷4 = 1/2
• Example 2: Simplify 12/30
  GCD(12, 30) = 6
  Simplified: 12÷6 / 30÷6 = 2/5
• Example 3: Simplify 7/21
  GCD(7, 21) = 7
  Simplified: 7÷7 / 21÷7 = 1/3
• Example 4: Simplify 18/6
  GCD(18, 6) = 6
  Simplified: 18÷6 / 6÷6 = 3/1 (or simply 3)

Use this calculator to quickly and accurately simplify any fraction to its lowest terms, making your mathematical work easier and more precise.