Enter Fraction Values
Example Data Table
| Input | Simplified | Mixed Number | Decimal | Percentage |
|---|---|---|---|---|
| 24/36 | 2/3 | 2/3 | 0.666667 | 66.666667% |
| 45/15 | 3/1 | 3 | 3 | 300% |
| 3 9/12 | 15/4 | 3 3/4 | 3.75 | 375% |
| -18/30 | -3/5 | -3/5 | -0.6 | -60% |
| 7 14/21 | 23/3 | 7 2/3 | 7.666667 | 766.666667% |
Formula Used
The calculator reduces a fraction by dividing the numerator and denominator by their greatest common divisor. For mixed numbers, it converts the value to an improper fraction first, then simplifies the result.
Improper numerator for mixed numbers: (whole × denominator) + numerator
Greatest common divisor: gcd(|numerator|, |denominator|)
Simplified fraction: (numerator ÷ gcd) / (denominator ÷ gcd)
Decimal value: simplified numerator ÷ simplified denominator
Percentage: decimal × 100
How to Use This Calculator
- Select whether you are simplifying a simple fraction or a mixed number.
- Enter the numerator and denominator. Add the whole number only when using mixed mode.
- Choose how many decimal places and equivalent fractions you want displayed.
- Press Simplify Fraction to show the result above the form.
- Review the simplified fraction, mixed form, GCD steps, decimal value, percentage, and reciprocal.
- Use the CSV or PDF buttons to export the displayed result.
Frequently Asked Questions
1. What does simplifying a fraction mean?
It means rewriting a fraction in lowest terms so the numerator and denominator share no common factor except 1. The value stays exactly the same.
2. How does the calculator handle mixed numbers?
It first converts the mixed number into an improper fraction. After that, it reduces the improper fraction using the greatest common divisor and shows the mixed result again.
3. Why is the greatest common divisor important?
The greatest common divisor is the largest whole number that divides both fraction terms exactly. Dividing both terms by it produces the simplest equivalent fraction.
4. Can this tool simplify negative fractions?
Yes. The calculator normalizes the sign and places it in the numerator for standard display. Negative mixed numbers are also converted and simplified correctly.
5. What happens if the denominator is zero?
A denominator of zero is undefined in fraction arithmetic. The calculator blocks that entry and asks you to provide a nonzero denominator.
6. Does simplifying change the fraction value?
No. Simplifying only changes the appearance of the fraction. The reduced fraction, decimal value, and percentage all represent the same exact quantity.
7. What are equivalent fractions in the results?
Equivalent fractions are created by multiplying the simplified numerator and denominator by the same whole number. They look different but keep the same value.
8. When should I use the decimal and percentage outputs?
Use decimals for calculations, graphing, or comparisons. Use percentages when the fraction represents part of a whole, rate, score, probability, or completion level.