Why does the calculator use absolute values for the GCD?
The GCD measures shared size, not sign. The sign is handled after reduction so the denominator can stay positive.
Fraction Simplifier
Simplify fractions into lowest terms by finding the GCD of the numerator and denominator, preserving the equivalent value, and normalizing signs.
Lowest terms mean no shared factor remains
Simplification changes the form, not the value. The greatest common divisor is computed from absolute values, then the sign is normalized so the denominator stays positive.
Reduce a fraction
- Read numerator and denominator.
- Reject a denominator of zero.
- Find gcd(|n|, |d|).
- Divide both parts by the GCD.
- Move any negative sign to the numerator.
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Reduction, equivalence, and sign rules
Lowest-term form keeps the same value with the smallest whole-number parts.
Shared factor
Reduction
Lowest terms
Equivalent fractions
Sign rule
Zero numerator
Edge cases
- If the GCD is 1, the fraction is already simplified.
- A negative denominator is moved to the numerator.
- A zero numerator reduces to 0/1 when the denominator is not zero.
- Two negative signs make a positive fraction.
FAQ
Can a simplified fraction have a negative denominator?
It can represent the same value, but standard lowest-term form moves the negative sign to the numerator: 3/-4 becomes -3/4.
