Calculator form
Use the optional whole part for mixed numbers. Leave it blank for a simple fraction.
Formula used
Simplified Fraction = (Numerator ÷ GCD) / (Denominator ÷ GCD)
GCD means the greatest common divisor shared by the numerator and denominator.
For mixed numbers: Improper Numerator = (|Whole Part| × |Denominator|) + |Numerator|
Decimal = Simplified Numerator ÷ Simplified Denominator. Percent = Decimal × 100
How to use this calculator
- Enter an optional whole part if your value is mixed.
- Enter the numerator and denominator.
- Choose the decimal and percent precision.
- Click Simplify Fraction to calculate.
- Review the simplified fraction, mixed number, decimal, percent, factors, and chart.
- Use the CSV or PDF buttons to save the result.
Example data table
| Input | Improper Fraction | GCD | Simplified Fraction | Mixed Number | Decimal | Percent |
|---|---|---|---|---|---|---|
| 0 18/24 | 18/24 | 6 | 3/4 | 3/4 | 0.75 | 75% |
| 2 12/18 | 48/18 | 6 | 8/3 | 2 2/3 | 2.666667 | 266.67% |
| -1 8/12 | -20/12 | 4 | -5/3 | -1 2/3 | -1.666667 | -166.67% |
| 0 45/60 | 45/60 | 15 | 3/4 | 3/4 | 0.75 | 75% |
| 0 120/200 | 120/200 | 40 | 3/5 | 3/5 | 0.6 | 60% |
Frequently asked questions
1. What does simplifying a fraction mean?
It means reducing a fraction to its smallest equivalent form. You divide the numerator and denominator by their greatest common divisor, without changing the value.
2. Can this calculator handle improper fractions?
Yes. It simplifies improper fractions directly and also converts the result into a mixed number when appropriate. That makes the answer easier to read and compare.
3. Can I enter mixed numbers here?
Yes. Add the whole part in the optional field, then enter the numerator and denominator. The calculator converts the mixed number into an improper fraction before simplifying it.
4. Why can the denominator never be zero?
A denominator of zero makes the fraction undefined. Division by zero is not valid in arithmetic, so the calculator blocks that input to protect the result.
5. Does simplification change the fraction’s value?
No. Simplification only changes the way the fraction is written. The value stays exactly the same because both parts are divided by the same common factor.
6. What happens with negative fractions?
The calculator normalizes the sign so the denominator becomes positive. It keeps the negative sign in the numerator or mixed-number front, which is the standard display style.
7. How is the greatest common divisor found?
It uses the Euclidean method, which repeatedly divides and checks remainders until the last nonzero remainder is found. That final value is the greatest common divisor.
8. Why show decimal and percent forms too?
Decimal and percent outputs help with grading, reports, finance, and comparisons. They let you understand the same fraction in formats people often use outside pure fraction notation.