GCD method: Find the greatest common divisor (GCD) of numerator and denominator, then divide both by it.
Sign rule: Keep the minus sign in the numerator (denominator positive) for a standard form.
Zero cases: If numerator is 0 (and denominator ≠ 0), the simplified result is 0/1.
Improper → Mixed: For |n| ≥ d, convert to a mixed number: w = ⌊|n| / d⌋, remainder r = |n| mod d.
Decimal/Percent:n/d as decimal, then multiply by 100 for percent; limit precision to avoid long repeats.
Prime factors (optional): GCD can be found via prime factorization, but Euclid’s algorithm is faster.
Common pitfalls
Do not leave a negative sign in the denominator; normalize it to the numerator.
Denominator must not be zero.
If GCD is 1, the fraction is already in simplest form.
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