Percentage to Fraction Converter Formula

Understand the math behind the percentage to fraction converter. Each variable explained with a worked example.

Use the Percentage to Fraction Converter

Formulas Used

Simplified Numerator

numerator = round(percentage * 100) / gcd(round(percentage * 100), 10000)

Simplified Denominator

denominator = 10000 / gcd(round(percentage * 100), 10000)

Decimal Value

decimal_value = percentage / 100

Variables

VariableDescriptionDefault
percentagePercentage(%)75

How It Works

Percentage to Fraction Converter

Method

1. Write the percentage as a fraction over 100: e.g., 75% = 75/100 2. Simplify by finding the GCD of numerator and denominator 3. Divide both by the GCD

Example: 75% = 75/100, GCD(75,100)=25, so 75/25 = 3 and 100/25 = 4 → 3/4

For decimals like 12.5%, we multiply by 100 to avoid fractions in the numerator: 1250/10000, then simplify.

Worked Example

Convert 75% to a fraction.

percentage = 75
  1. 0175% = 7500/10000 (multiplied by 100 for precision)
  2. 02GCD(7500, 10000) = 2500
  3. 03Numerator = 7500 / 2500 = 3
  4. 04Denominator = 10000 / 2500 = 4
  5. 05Result: 3/4

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Open Percentage to Fraction Converter