Fraction Simplify Calculator

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Fraction Simplifier

Simplified Fraction:
function gcd(a, b) { // Euclidean algorithm to find the Greatest Common Divisor (GCD) if (b === 0) { return a; } return gcd(b, a % b); } function simplifyFraction() { var numerator = parseInt(document.getElementById("numeratorInput").value); var denominator = parseInt(document.getElementById("denominatorInput").value); var resultDiv = document.getElementById("simplifiedFractionResult"); // Input validation 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"; // 0 divided by any non-zero number is 0 return; } // Determine the sign of the simplified fraction var sign = 1; if ((numerator 0) || (numerator > 0 && denominator < 0)) { sign = -1; } // Work with absolute values for GCD calculation var absNumerator = Math.abs(numerator); var absDenominator = Math.abs(denominator); var commonDivisor = gcd(absNumerator, absDenominator); var simplifiedNumerator = absNumerator / commonDivisor; var simplifiedDenominator = absDenominator / commonDivisor; // Apply the determined sign to the numerator if (sign === -1) { simplifiedNumerator = -simplifiedNumerator; } if (simplifiedDenominator === 1) { resultDiv.innerHTML = "Simplified Fraction: " + simplifiedNumerator; } else { resultDiv.innerHTML = "Simplified Fraction: " + simplifiedNumerator + " / " + simplifiedDenominator; } }

Understanding Fraction Simplification

A fraction represents a part of a whole, expressed as a ratio of two numbers: a numerator (the top number) and a denominator (the bottom number). For example, 1/2 means one part out of two equal parts.

What Does It Mean to Simplify a Fraction?

Simplifying a fraction, also known as reducing a fraction to its lowest terms, means finding an equivalent fraction where the numerator and denominator have no common factors other than 1. This makes the fraction easier to understand and work with, as it represents the same value in its most concise form.

For instance, the fraction 10/20 represents the same value as 1/2. Both mean "half." However, 1/2 is the simplified form because 1 and 2 share no common factors other than 1.

How to Simplify a Fraction

The process of simplifying a fraction involves these steps:

  1. Find the Greatest Common Divisor (GCD): Identify the largest number that divides evenly into both the numerator and the denominator. The Euclidean algorithm is a common method for finding the GCD.
  2. Divide by the GCD: Divide both the numerator and the denominator by their GCD. The resulting numbers will form the simplified fraction.

Examples of Fraction Simplification:

  • Example 1: Simplify 10/20
    • Numerator = 10, Denominator = 20
    • The GCD of 10 and 20 is 10.
    • Divide numerator by GCD: 10 ÷ 10 = 1
    • Divide denominator by GCD: 20 ÷ 10 = 2
    • Simplified Fraction: 1/2
  • Example 2: Simplify 15/45
    • Numerator = 15, Denominator = 45
    • The GCD of 15 and 45 is 15.
    • Divide numerator by GCD: 15 ÷ 15 = 1
    • Divide denominator by GCD: 45 ÷ 15 = 3
    • Simplified Fraction: 1/3
  • Example 3: Simplify 12/8
    • Numerator = 12, Denominator = 8
    • The GCD of 12 and 8 is 4.
    • Divide numerator by GCD: 12 ÷ 4 = 3
    • Divide denominator by GCD: 8 ÷ 4 = 2
    • Simplified Fraction: 3/2 (This is an improper fraction, but it's in its simplest form)
  • Example 4: Simplify -6/9
    • Numerator = -6, Denominator = 9
    • The GCD of 6 (absolute value of -6) and 9 is 3.
    • Divide absolute numerator by GCD: 6 ÷ 3 = 2
    • Divide denominator by GCD: 9 ÷ 3 = 3
    • Apply the negative sign: -2/3
    • Simplified Fraction: -2/3

Using the Fraction Simplifier Calculator

Our online Fraction Simplifier Calculator makes this process quick and effortless. Simply enter the numerator in the "Numerator" field and the denominator in the "Denominator" field, then click the "Simplify Fraction" button. The calculator will instantly display the fraction in its simplest form, helping you to easily understand and work with fractions.

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