“The numerator is the 'counter' — Latin numerator, one who numbers. In a fraction, the numerator counts how many parts you have. The denominator names the kind of part. The fraction is a conversation between two Latin words.”
Numerator in Latin means one who counts or numbers, from numerare (to count, to number), from numerus (number). In a fraction like 3/4, the numerator (3) counts how many parts you are dealing with. The denominator (4) denominates — names — what kind of parts they are (fourths). The fraction is a two-word statement: 'three of those things called fourths.' The Latin terms were adopted in medieval mathematical texts.
The word numerare gave English both 'numerate' (able to work with numbers) and 'enumerate' (to count off one by one). The numerator's job is enumeration — counting the parts. The denominator's job is denomination — naming them. This division of labor between counting and naming mirrors a deeper distinction in mathematics: quantity versus kind.
Roman numeration (I, V, X, L, C, D, M) made the numerator's job difficult. Try expressing 7/12 in Roman numerals. Hindu-Arabic numerals (1, 2, 3...) made fractions practical by giving the numerator clean, manipulable symbols. The word 'numerator' predates the notation that made it useful. The concept was waiting for the right symbols.
In everyday English, 'numerous' (from the same root) means many — a large number. 'Innumerable' means too many to count. The family of words from numerus all revolve around the act of counting. The numerator is the family member who stayed closest to the original job: sitting on top of a fraction, counting parts.
Related Words
Today
The numerator and denominator are a partnership — one counts, the other names. In 3/4, the denominator says 'fourths.' The numerator says 'three of them.' The fraction is a complete thought only when both are present. A numerator without a denominator is just a number. A denominator without a numerator is just a category.
The Latin counter sits on top. The Latin namer sits on the bottom. Between them, they describe every part of every whole.
Explore more words