Percent to Fraction Calculator

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Percent to Fraction Converter

// Function to find the Greatest Common Divisor (GCD) using Euclidean algorithm function gcd(a, b) { if (b === 0) { return a; } return gcd(b, a % b); } function calculateFraction() { var percentageInput = document.getElementById("percentageValue").value; var percentage = parseFloat(percentageInput); if (isNaN(percentage)) { document.getElementById("fractionResult").innerHTML = "Please enter a valid number for the percentage."; return; } if (percentage < 0) { document.getElementById("fractionResult").innerHTML = "Percentage must be non-negative."; return; } // Convert percentage to a decimal var decimal = percentage / 100; // Determine the number of decimal places in the original percentage input var decimalPlaces = 0; if (percentageInput.includes('.')) { decimalPlaces = percentageInput.split('.')[1].length; } // To convert decimal to fraction, we need to handle the decimal places // Multiply by 10^max_decimal_places to get integers var multiplier = Math.pow(10, decimalPlaces); var numerator = percentage * multiplier; // This is the original percentage value, scaled var denominator = 100 * multiplier; // This is 100, scaled by the same factor // Find the GCD of the numerator and denominator var commonDivisor = gcd(numerator, denominator); // Simplify the fraction var simplifiedNumerator = numerator / commonDivisor; var simplifiedDenominator = denominator / commonDivisor; document.getElementById("fractionResult").innerHTML = "" + percentage + "% is equal to " + simplifiedNumerator + "/" + simplifiedDenominator + ""; } // Calculate on page load with default value window.onload = calculateFraction;

Understanding Percentages and Fractions

Percentages and fractions are two fundamental ways to represent parts of a whole. While percentages express a value out of one hundred, fractions represent a part of a whole using a numerator and a denominator. Converting between these forms is a common mathematical task, useful in various real-world scenarios from finance to cooking.

What is a Percentage?

The word "percent" literally means "per one hundred." A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%". For example, 25% means 25 out of 100, or 25/100.

What is a Fraction?

A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, or three-quarters. A common, vulgar, or simple fraction consists of an integer numerator displayed above a line (or before a slash), and a non-zero integer denominator displayed below (or after) that line.

Why Convert Percent to Fraction?

Converting percentages to fractions can be beneficial for several reasons:

  • Simplification: Fractions often provide a simpler, more intuitive representation of a proportion, especially when dealing with common values like 50% (1/2) or 25% (1/4).
  • Calculations: In some mathematical operations, working with fractions can be more straightforward than percentages, particularly when multiplying or dividing.
  • Understanding Ratios: Fractions directly show the ratio of one quantity to another, which can be clearer than a percentage in certain contexts.

How to Convert Percent to Fraction

The process of converting a percentage to a fraction involves a few simple steps:

  1. Write the percentage as a fraction over 100: Since a percentage means "per one hundred," any percentage value 'P' can be written as P/100.
  2. Remove any decimal points from the numerator: If your percentage has a decimal (e.g., 12.5%), multiply both the numerator and the denominator by a power of 10 (10, 100, 1000, etc.) until the numerator is a whole number. The power of 10 should correspond to the number of decimal places. For 12.5%, you'd multiply by 10 to get 125/1000.
  3. Simplify the fraction: Find the greatest common divisor (GCD) of the numerator and the denominator. Divide both the numerator and the denominator by their GCD to reduce the fraction to its simplest form.

Examples of Percent to Fraction Conversion

Let's walk through a few examples:

Example 1: Convert 50% to a fraction

  1. Write as a fraction over 100: 50/100
  2. No decimals in the numerator.
  3. Simplify: The GCD of 50 and 100 is 50.
    • 50 ÷ 50 = 1
    • 100 ÷ 50 = 2
    So, 50% = 1/2.

Example 2: Convert 75% to a fraction

  1. Write as a fraction over 100: 75/100
  2. No decimals in the numerator.
  3. Simplify: The GCD of 75 and 100 is 25.
    • 75 ÷ 25 = 3
    • 100 ÷ 25 = 4
    So, 75% = 3/4.

Example 3: Convert 12.5% to a fraction

  1. Write as a fraction over 100: 12.5/100
  2. Remove decimal: Multiply numerator and denominator by 10 (since there's one decimal place).
    • 12.5 × 10 = 125
    • 100 × 10 = 1000
    The fraction becomes 125/1000.
  3. Simplify: The GCD of 125 and 1000 is 125.
    • 125 ÷ 125 = 1
    • 1000 ÷ 125 = 8
    So, 12.5% = 1/8.

Using the calculator above, you can quickly convert any percentage value into its simplest fractional form, making these conversions effortless.

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