How to Convert Percentages to Fractions — Step by Step
Blog › Math · 6 min read · Published 2026-03-08
Learn to convert any percentage to a simplified fraction with the GCD method. Includes common conversion chart and worked examples.
The Basic Method
Converting a percentage to a fraction is a three-step process: 1) Write the percentage as a fraction with 100 as the denominator. 2) If the percentage has decimals, multiply top and bottom to remove them. 3) Simplify by dividing both by their Greatest Common Divisor (GCD).
Example: 75% → 75/100 → GCD(75, 100) = 25 → 75÷25 / 100÷25 = 3/4.
Handling Decimal Percentages
When a percentage contains decimals (like 12.5%), multiply both the numerator and denominator by 10 for each decimal place: 12.5% → 12.5/100 → multiply by 10 → 125/1000 → GCD(125, 1000) = 125 → 1/8.
For 33.33%: This is actually 33⅓%, which equals exactly 1/3. Repeating decimal percentages correspond to clean fractions — 66.67% = 2/3, 16.67% = 1/6, 8.33% = 1/12.
Finding the GCD (Greatest Common Divisor)
The Euclidean algorithm efficiently finds the GCD: repeatedly divide the larger number by the smaller and take the remainder until the remainder is 0. The last non-zero divisor is the GCD.
Example: GCD(375, 1000): 1000 ÷ 375 = 2 remainder 250. 375 ÷ 250 = 1 remainder 125. 250 ÷ 125 = 2 remainder 0. GCD = 125.
Percentages Over 100%
Percentages above 100% convert to improper fractions or mixed numbers. 150% = 150/100 = 3/2 = 1½. 225% = 225/100 = 9/4 = 2¼. These represent values greater than one whole.
Common Conversion Chart
Memorize these for speed: 10% = 1/10, 12.5% = 1/8, 20% = 1/5, 25% = 1/4, 33.3% = 1/3, 37.5% = 3/8, 40% = 2/5, 50% = 1/2, 60% = 3/5, 62.5% = 5/8, 66.7% = 2/3, 75% = 3/4, 80% = 4/5, 87.5% = 7/8.
Real-World Applications
Shopping: "30% off" means you pay 7/10 of the original price. "Buy one get one 50% off" means each item costs 3/4 price on average.
Statistics: Expressing probabilities as fractions (a 25% chance = 1/4) can make them more intuitive and easier to compare.
Cooking: Scaling recipes by percentages becomes easier when converted to fractions — reducing to 75% means making 3/4 of the recipe.
FAQ
Why do some percentages give messy fractions?
Percentages like 37% give 37/100 which can't be simplified because 37 is prime. Not every percentage corresponds to a "clean" fraction — only those whose numerator shares factors with 100 (factors: 2, 4, 5, 10, 20, 25, 50).
Is there a shortcut for common percentages?
Yes — divide by the obvious factor: 25% → ÷25 → 1/4. 50% → ÷50 → 1/2. 20% → ÷20 → 1/5. For others, find GCD(n, 100) mentally.