Fraction Simplifier Calculator
Reduce one integer fraction to lowest terms and see its mixed-number and decimal forms.
Content updated August 1, 2026
Numerator and denominator are divided by their greatest common divisor. The decimal display is truncated with an ellipsis after 12 places when it does not terminate.
A fraction is in lowest terms when its numerator and denominator have no common factor greater than one. Enter the two integers and the calculator divides both by their greatest common divisor.
The reduced denominator is always shown as positive, so any negative sign moves to the numerator. Mixed-number and decimal forms help check the magnitude without changing the exact reduced fraction.
The Fraction Simplifier formula
g = gcd(|a|, |b|); simplified fraction = (a ÷ g)/(b ÷ g)a = integer numerator · b = nonzero integer denominator · g = greatest common divisor. A negative denominator is normalized.
Worked example
For 42/56, gcd(42, 56) = 14. Dividing both terms by 14 gives the lowest-terms fraction 3/4, whose decimal value is 0.75.
Assumptions, rounding, and limitations
Assumptions
- Numerator and denominator are integers.
- The denominator is not zero.
- The fraction's unit, if any, is unchanged by reduction.
Rounding: Fraction reduction is exact. Non-terminating decimal previews are truncated after 12 places and marked with an ellipsis.
Limitations
- Each input may contain at most 50 digits.
- Does not accept decimal numerators, compound fractions, or symbolic algebraic expressions.
Why the greatest common divisor works
Dividing numerator and denominator by the same nonzero integer does not change a fraction's value. Using their greatest common divisor removes every shared factor in a single step.
For negative denominators, multiplying both numerator and denominator by −1 preserves the value and places the sign in the conventional numerator position.
Frequently asked questions
▶How do I simplify a fraction?
Find the greatest common divisor of the numerator and denominator, then divide both by it.
▶Can the numerator be zero?
Yes. Zero over any nonzero integer simplifies to 0/1.
▶Can the denominator be negative?
Yes. The calculator moves the sign to the numerator so the reduced denominator is positive.
▶Why does the decimal sometimes end with an ellipsis?
A non-terminating decimal is truncated after 12 places and marked with an ellipsis. The fraction remains exact.
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Open calculator →Disclaimer: Fraction Simplifier Calculator results are estimates for general information and education only, and are not financial, tax, legal or medical advice. Verify important decisions with a qualified professional.