Glossary
ratio
A ratio compares two quantities by division, written with a colon or as a fraction — 2 to 3 means two parts of one thing for every three of another.
A ratio compares two quantities by division. The ratio 2:3 means two parts of the first quantity for every three parts of the second, and it can be written 2:3, 2/3 or "2 to 3". When a whole is divided in a given ratio, the key step is to count the total parts. A mix that is 2 parts concentrate to 3 parts water has 2 + 3 = 5 equal parts, so the concentrate is 2/5 of the mix and the water 3/5. In 25 L of that mix, the concentrate is 25 ÷ 5 × 2 = 10 L. The classic error is to read the ratio as a fraction of the second quantity only — taking 2/3 of the mix instead of 2/5, treating 2:3 as though it were 2-of-3 rather than two parts out of five. A rate, such as miles per hour, is a ratio of two different units.
Taught in
Related terms
- proportion — A proportion is an equation saying two ratios are equal. Solve it by keeping like units facing each other and cross-multiplying.
- percent change — A percent change is the amount of change divided by the value you started from, written as a percent: (new − old) ÷ old × 100.
Source: OpenStax Prealgebra, Elementary Algebra and College Algebra, first editions (CC BY 4.0); NIST SP 811 (units). Each definition restates the two Mathematics guides in this exam, which carry the per-source citations on their own pages. (OpenStax 1e and NIST SP 811 accessed 2026-10-07)