Numerator
The numerator is the top number in a fraction, indicating how many parts of the whole are being counted.
Definition
The numerator is the top number of a fraction: it counts how many pieces you have. In a fraction $a/b$, the numerator is the value $a$, representing the count of equal parts being considered; when the fraction is read as a division, the numerator is the dividend. In the rational number $a/b$ (an equivalence class of pairs), $a$ is the numerator, and under the canonical representative (lowest terms) it is uniquely determined up to sign; in a polynomial fraction (rational function) $p(x)/q(x)$, the numerator is the polynomial $p(x)$.
Example
In the fraction $5/8$, the numerator is $5$: if a chocolate bar is broken into $8$ equal pieces and you have $5$ of them, the $5$ counts your pieces. In $7/12$, the numerator $7$ is the dividend when computing $7/12$ as a decimal ($0.5833\ldots$), divided by the denominator $12$. For the rational function $(x^2-1)/(x+3)$, the numerator $x^2-1$ factors as $(x-1)(x+1)$, revealing potential simplification with the denominator; partial fraction decomposition rewrites a rational function in terms of simpler numerators over linear or irreducible quadratic denominators.
Key Insight
The word "numerator" comes from the Latin word for "counter" or "numberer": it literally counts the pieces you are talking about. Changing only the numerator scales the fraction proportionally, doubling the numerator doubles the value ($2/5$ is twice $1/5$), which is why numerators and denominators play distinct roles in fraction arithmetic. In measure theory, a fraction $p/q$ as a ratio of measures generalizes the notion of numerator to continuous settings, underpinning definitions of probability and density.