How do you convert a percent to a fraction?

Write the percent as a fraction over 100, then simplify by dividing both numerator and denominator by their GCD. For 75%: write 75/100, GCD is 25, divide both: 3/4. For decimal percents like 12.5%, multiply numerator and denominator by 10 to get 125/1000, then simplify to 1/8.

What is 25% as a fraction?

25% as a fraction is 1/4. Write 25/100, find GCD(25,100)=25, divide: 25/25=1, 100/25=4. Result: 1/4.

What is 12.5% as a fraction?

12.5% as a fraction is 1/8. Write 12.5/100, multiply by 10/10 to get 125/1000, GCD(125,1000)=125, divide: 1/8. Verify: 1/8 = 0.125 = 12.5%.

What is 50% as a fraction?

50% as a fraction is 1/2. Write 50/100, GCD(50,100)=50, divide: 50/50=1, 100/50=2. Result: 1/2.

What is 150% as a fraction?

150% as a fraction is 3/2 (or 1 1/2 as a mixed number). Write 150/100, GCD(150,100)=50, divide: 3/2. As a mixed number: 1 and 1/2.

What is 33.33% as a fraction?

33.33% approximates 1/3. The exact repeating decimal 33.333...% equals exactly 1/3. The rounded value 33.33% gives 3333/10000 which does not simplify to a neat fraction. Use 1/3 for the repeating version.

Percent to Fraction Calculator

Sources & Methodology

✓Fraction simplification uses the Euclidean GCD algorithm as defined in NCTM grade 6-8 standards for number and operations with fractions.

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Khan Academy — Fractions, Decimals and Percents

Mathematical foundation for percent-to-fraction conversion and simplification methodology

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National Council of Teachers of Mathematics (NCTM)

Grade 6-8 fractions and ratios standards — equivalence and simplification methods used in this calculator

Methodology: Step 1: Write percent as p/100. Step 2: If percent has decimal places, multiply numerator and denominator by 10^(decimal places) to get integers. Step 3: Find GCD using Euclidean algorithm. Step 4: Divide both by GCD to get fully simplified fraction. Step 5: If numerator > denominator, express as mixed number.

⏱ Last reviewed: April 2026

How to Convert a Percent to a Fraction

Converting a percentage to a fraction follows a clear three-step process: write the percent as a fraction over 100, eliminate any decimal from the numerator, then simplify using the Greatest Common Divisor (GCD). The key challenge is handling decimal percentages like 12.5% — these require scaling before simplification.

Step-by-Step Method

Fraction = percent / 100 → simplify by GCD

Example: 75%
Step 1: 75/100 Step 2: No decimal Step 3: GCD(75,100) = 25
Divide: 75/25 = 3 and 100/25 = 4 → 3/4

Example: 12.5%
Step 1: 12.5/100 Step 2: ×10/10 = 125/1000 Step 3: GCD(125,1000) = 125
Divide: 125/125 = 1 and 1000/125 = 8 → 1/8

Common Percent to Fraction Reference Table

Percent	Unsimplified	GCD	Simplified	Decimal
10%	10/100	10	1/10	0.1
20%	20/100	20	1/5	0.2
25%	25/100	25	1/4	0.25
40%	40/100	20	2/5	0.4
50%	50/100	50	1/2	0.5
60%	60/100	20	3/5	0.6
75%	75/100	25	3/4	0.75
80%	80/100	20	4/5	0.8

The Euclidean Algorithm for GCD

The Euclidean algorithm finds GCD by repeated division. For GCD(75, 100): divide 100 by 75 to get remainder 25. Then divide 75 by 25 to get remainder 0. When remainder is 0, the last divisor (25) is the GCD. Both 75 and 100 divided by 25 gives 3/4.

Improper Fractions and Mixed Numbers

When the percent exceeds 100%, the result is an improper fraction (numerator greater than denominator). For 150% = 3/2. As a mixed number: 1 whole and 1/2. Improper fractions are standard in algebra; mixed numbers are more intuitive for everyday use. Both forms represent the same value.

💡 Quick Verify: After converting, divide numerator by denominator and multiply by 100 — it should equal your original percent. For 3/4: 3 ÷ 4 = 0.75 × 100 = 75%. A fully simplified fraction has GCD = 1, meaning no common factor remains between numerator and denominator.

Frequently Asked Questions

Write the percent as a fraction over 100, then simplify by dividing both numerator and denominator by their GCD. For 75%: 75/100, GCD is 25, divide both: 3/4. For decimal percents like 12.5%, multiply by 10/10 to eliminate the decimal, getting 125/1000, then simplify to 1/8.

25% as a fraction is 1/4. Write 25/100, find GCD(25,100)=25, divide both by 25: 25/25=1 and 100/25=4. Result: 1/4. This is the quarter fraction and one of the most common percent-to-fraction conversions.

75% as a fraction is 3/4. Write 75/100, GCD(75,100)=25, divide: 75/25=3, 100/25=4. Result: 3/4. Three-quarters is one of the most frequently used fractions in everyday calculations.

12.5% as a fraction is 1/8. Write 12.5/100, multiply by 10/10 to clear the decimal: 125/1000. GCD(125,1000)=125, divide: 1/8. Verify: 1/8 = 0.125 = 12.5%. The eighths are common in measurement — especially in US customary units.

33.33% approximates 1/3. The exact repeating decimal 33.333...% (one-third) equals exactly 1/3. For the rounded 33.33%, the exact fraction is 3333/10000 which does not simplify to a neat fraction. Use 1/3 when working with the repeating decimal version.

60% as a fraction is 3/5. Write 60/100, GCD(60,100)=20, divide: 60/20=3, 100/20=5. Result: 3/5. Verify: 3/5 = 0.6 = 60%.

150% as a fraction is 3/2 (improper fraction) or 1 1/2 (mixed number). Write 150/100, GCD(150,100)=50, divide: 150/50=3, 100/50=2. Result: 3/2. Percentages above 100% always produce improper fractions greater than 1.

Find the GCD of numerator and denominator using the Euclidean algorithm, then divide both by GCD. For 40/100: GCD(40,100)=20, divide: 40/20=2, 100/20=5. Simplified: 2/5. A fraction is fully simplified when GCD=1, meaning no common factor remains.

50% as a fraction is 1/2. Write 50/100, GCD(50,100)=50, divide: 1/2. One half is the simplest and most common fraction. 50% always equals exactly 1/2 regardless of context.

66.67% approximates 2/3. The exact repeating 66.666...% equals exactly 2/3. The rounded 66.67% gives 6667/10000, very close to but not exactly 2/3 (since 2/3 = 66.666...%). Always use 2/3 when working with the repeating decimal version.

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