Simplifying a ratio
A : B = (A ÷ GCD) : (B ÷ GCD)
A ratio compares two quantities, and like a fraction it has a simplest form: divide both sides by their greatest common divisor. With the defaults, 12:18 has GCD 6, so it simplifies to 2:3 — for every 2 of the first thing there are 3 of the second. Decimals are handled by scaling both sides to whole numbers first (up to 4 decimal places), so 1.5:2.25 becomes 150:225 → 2:3.
Solving A:B = C:D
A × D = B × C (cross-multiplication)
A proportion says two ratios are equal. Leave exactly one of the four boxes empty and the calculator cross-multiplies to find it. If 12:18 = 30:D, then D = 18 × 30 ÷ 12 = 45. This is the classic recipe-scaling and map-reading calculation: keep the relationship, change the size.
Splitting a total in a ratio
share = total ÷ (A + B), parts = A × share and B × share
To divide 120 in the ratio 12:18, add the parts (12 + 18 = 30), so each "share" is 120 ÷ 30 = 4. The two portions are 12 × 4 = 48 and 18 × 4 = 72. This works for splitting bills, inheritance, paint mixes and anything else shared unevenly.
The 1:n form
Simplified ratios are easiest to compare when the first side is 1. The calculator also shows this form: 2:3 becomes 1:1.5 — instantly readable as "one and a half times as much".