To convert a percentage to a fraction, follow these steps: (1) Write the percentage as a fraction with denominator 100 (e.g., 45% = 45/100). (2) If the percentage has a decimal, multiply both numerator and denominator by 10 for each decimal place to eliminate the decimal (e.g., 12.5% = 12.5/100 = 125/1000). (3) Simplify the fraction by dividing both numerator and denominator by their greatest common divisor (GCD). For 45/100, GCD=5, so 45÷5=9, 100÷5=20, giving 9/20. Our tool does all of this automatically and shows every step.

50% as a fraction is 1/2 (one-half). Here's why: 50% means 50 per 100, so 50/100. The greatest common divisor of 50 and 100 is 50. Dividing both by 50 gives 1/2. This is one of the most common percentage-to-fraction conversions used in everyday math, finance, and statistics.

25% = 1/4 (one-quarter). Since 25/100 simplifies by GCD=25 to 1/4.
75% = 3/4 (three-quarters). Since 75/100 simplifies by GCD=25 to 3/4.
These three fractions — 1/4, 1/2 (50%), and 3/4 (75%) — are the most commonly used quarter-based percentages and appear frequently in discounts, test scores, and statistical data.

For decimal percentages like 12.5%, the process has an extra step: (1) Write as 12.5/100. (2) Multiply numerator and denominator by 10 (since there's 1 decimal place) → 125/1000. (3) Find the GCD of 125 and 1000, which is 125. (4) Divide: 125÷125=1, 1000÷125=8. Result: 1/8. Other common decimal percentage conversions include 37.5% = 3/8, 62.5% = 5/8, and 87.5% = 7/8. Our calculator handles decimal percentages with precision up to several decimal places.

33.33% converts exactly to 3333/10000, which is already in its simplest form (GCD=1). However, 33.33% is commonly understood as an approximation of 1/3 (which equals approximately 33.333...% with repeating decimals). Since 33.33% has only two decimal places, our tool gives the exact mathematical fraction 3333/10000. For reference, the exact fraction for 33.333...% (repeating) is 1/3. When precision matters, use the exact value shown.

Fraction simplification uses the Greatest Common Divisor (GCD) algorithm — also known as the Euclidean algorithm. The GCD is the largest number that divides both the numerator and denominator without leaving a remainder. For example, with 60/100: the GCD of 60 and 100 is 20. Dividing both by 20 yields 3/5. The Euclidean algorithm repeatedly subtracts the smaller number from the larger (or uses modulo division) until only the GCD remains, making it extremely efficient even for large numbers. Our calculator performs GCD simplification instantly for all inputs.

A mixed number combines a whole number with a proper fraction (e.g., 1½, 3¼). It's used when a fraction represents a value greater than 1 and the improper fraction format (like 3/2) is less intuitive. For percentages over 100%, mixed numbers are especially helpful. For example, 150% = 3/2 = 1½, and 275% = 11/4 = 2¾. Our tool automatically displays the mixed number format when the simplified fraction is greater than 1, making results easier to understand at a glance.

Yes! Every percentage — whether a whole number, decimal, or even a repeating decimal — can be expressed as a fraction because percentages are inherently ratios (per hundred). Whole number percentages like 40% become simple fractions (40/100 → 2/5). Decimal percentages like 12.5% become fractions by scaling (125/1000 → 1/8). Even percentages with many decimal places follow the same rule. The only theoretical exception would be irrational percentages, but those don't occur in practical applications. Our tool handles percentages with precision across a wide range of values.

Proper fraction: Numerator is less than denominator (e.g., 3/4, value < 1).
Improper fraction: Numerator is greater than or equal to denominator (e.g., 5/3, value ≥ 1).
Mixed number: A whole number plus a proper fraction (e.g., 1⅔).
Percentages under 100% yield proper fractions (e.g., 75% = 3/4). Percentages over 100% yield improper fractions which are often displayed as mixed numbers (e.g., 150% = 3/2 = 1½). Our tool shows both formats when applicable, giving you complete flexibility.