Ratio Simplifier: Reduce Any Ratio to Lowest Terms

Every term is parsed to an exact fraction in arbitrary-precision integers. Fractions and decimals are cleared by multiplying through by the least common multiple of their denominators, which turns the whole ratio into whole numbers. The tool then divides every term by the greatest common factor found with the Euclidean algorithm, using the standard convention gcd(x, 0) = |x|. Lowest terms is reached exactly when that factor is 1.

Decimal example: 2.5 : 5 clears to 25 : 50, whose GCF is 25, giving 1 : 2. Units example: 200 g : 1.5 kg converts to a common base of milligrams, then reduces to 2 : 15.

Conventions this tool names and uses:

• Decimals are cleared lexically by counting the typed fractional digits and shifting into exact integers, never by floating-point multiplication, so 0.1 : 0.3 reduces to 1 : 3 rather than a corrupted value.
• A single zero term reduces normally under gcd(0, n) = n, so 0 : 5 becomes 0 : 1. Only an all-zero ratio has no simplest form.
• Negatives reduce on magnitude with each term's sign preserved, so -4 : 8 becomes -1 : 2. The tool never normalizes a global sign and never reorders terms.
• Different-units mode stays inside one dimension (time, length, mass, or volume) with the smallest metric unit as the exact-integer base. It rejects a mix such as mass with length.

Formula: simplified terms = cleared integers / gcd(all cleared terms)

See Sources below