numerator

Numerator is a term in mathematics that denotes the top part of a common fraction. In a fraction such as a/b, a is the numerator and b is the denominator. The numerator indicates how many parts of the whole are being considered, while the denominator indicates how many equal parts make up the whole.

Examples: 3/4 has numerator 3; its decimal equivalent is 0.75. In a mixed number like 2 1/3, the fractional part 1/3 has numerator 1; the whole number part 2 is separate, but the concept of numerator applies to the fractional part.

In algebra and rational expressions, the numerator can be a polynomial or more complex expression, such as (x+2) in (x+2)/(x-5). Simplifying rational expressions often involves manipulating the numerator and denominator, including canceling common factors when allowed.

In probability and statistics, the numerator counts favorable outcomes, while the denominator counts total outcomes. The probability of an event is the ratio of the numerator to the denominator.

Etymology and related terms: the word numerator comes from Latin numerus meaning “number,” via Old French and other linguistic pathways. It is contrasted with the denominator, which represents the total number of parts into which the whole is divided.

See also: denominator, fraction, ratio, proportion, decimal.