🔢 Fraction to Decimal & Ratio Calculator
Convert any fraction to a decimal and percentage, simplify fractions to lowest terms, or simplify a ratio like 8:12 — with the math shown step by step.
Last Updated: July 10, 2026
Enter a Fraction
Result
📊 Common Fraction–Decimal–Percentage Table
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.3333 | 33.33% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 2/3 | 0.6667 | 66.67% |
| 3/8 | 0.375 | 37.5% |
| 5/6 | 0.8333 | 83.33% |
💡 Always Simplify With the GCD
To fully simplify a fraction, divide both numerator and denominator by their greatest common divisor (GCD), not just any shared factor. 18/24 shares a factor of 2 (giving 9/12), but the true GCD is 6, giving the fully simplified 3/4.
🔢 How to Convert Fractions and Simplify Ratios
Fraction to Decimal
Decimal = Numerator ÷ Denominator
Example: 18 ÷ 24 = 0.75
Fraction to Percentage
Percentage = Decimal × 100
Example: 0.75 × 100 = 75%
Simplifying With the Euclidean Algorithm (GCD)
To find GCD(18, 24): 24 = 1×18 + 6, then 18 = 3×6 + 0. The last non-zero remainder, 6, is the GCD. Divide both terms by 6: 18/6 = 3, 24/6 = 4, giving 3/4.
Simplifying a Ratio
Divide both terms of the ratio by their GCD. For 8:12, GCD(8,12) = 4, so 8÷4 : 12÷4 = 2:3.
💡 Real-World Examples & Use Cases
See how fraction-to-decimal conversion and simplification work with real numbers.
3/4 as a decimal and percentage
A recipe calls for 3/4 of a cup of flour.
Result: 3 ÷ 4 = 0.75, or 75% — already in simplest form (GCD = 1).
Simplifying 18/24
A test score is reported as 18 correct out of 24 questions.
Result: GCD(18,24) = 6, so 18/24 simplifies to 3/4, which is 0.75 or 75%.
Simplifying a ratio of 8:12
A recipe uses 8 parts water to 12 parts concentrate.
Result: GCD(8,12) = 4, so the ratio simplifies to 2:3, equivalent to a decimal of 0.6667.
⚠️ Common Mistakes & Pro Tips
- Stopping at a common factor, not the GCD: Dividing 18/24 by 2 gives 9/12 — correct but not fully simplified. Always find the greatest common divisor.
- Confusing ratio order: A ratio of 8:12 is not the same as 12:8 — order matters and changes the meaning.
- Rounding repeating decimals too early: 1/3 = 0.333... — round only at the final step to avoid compounding errors in longer calculations.
- Forgetting the percentage step: Percentage is decimal × 100, not the decimal value itself.
🔍 People Also Ask
How do you turn 3/4 into a decimal?
Divide 3 by 4: 3 ÷ 4 = 0.75.
What is the fastest way to simplify a fraction?
Find the GCD of the numerator and denominator using the Euclidean algorithm, then divide both by it.
Is 2:3 the same ratio as 8:12?
Yes — 8:12 simplifies to 2:3 because both terms share a GCD of 4.
❓ Frequently Asked Questions
What is the Euclidean algorithm used to find the GCD?
It repeatedly replaces the larger number with the remainder of dividing it by the smaller number until the remainder is zero; the last non-zero remainder is the GCD.
How do I simplify a ratio like 8:12?
Divide both terms by their GCD. GCD(8,12) = 4, so 8:12 simplifies to 2:3.
Is a ratio the same as a fraction?
A ratio compares two quantities (A:B) while a fraction represents a part of a whole (A/B); mathematically they simplify the same way using the GCD.
How do I convert a repeating decimal back to a fraction?
Set the repeating decimal equal to x, multiply by a power of 10 to shift the repeating part, subtract the original equation, and solve for x as a fraction.
What is 1/3 as a decimal?
1/3 = 0.3333... (repeating), commonly rounded to 0.33 or expressed as 33.3%.
Why does my simplified fraction look different from what I expected?
Always divide by the greatest common divisor, not just any common factor, to reach the fully simplified form.
Can this calculator handle improper fractions?
Yes. Improper fractions (where the numerator is larger than the denominator) convert to decimals greater than 1, such as 7/4 = 1.75.