Fractions in French
Un Demi, Un Tiers, Un Quart, and the Ordinal Rule

The Irregular Three: Demi, Tiers, Quart

Un demi is half. From Latin dimidium. Used as a fraction noun (boire un demi = to drink a half-pint of beer at a French café) and as a prefix adjective (une demi-heure, une demi-bouteille, un demi-tour). The prefix-adjective form is invariable in writing: une demi-heure (half an hour), not une demie-heure. The standalone fraction noun does have a feminine form (une demie) in some specific musical and time contexts.

Un tiers is a third. From Latin tertius. The form is invariable in spelling between singular and plural (un tiers, deux tiers) but takes a plural-s in some cases for grammatical balance: les deux tiers de la population. The s is silent in pronunciation. Common phrases: le tiers monde (the third world, dated geopolitical term), une tierce personne (a third party), le tiers payant (third-party payment, a French health-insurance billing system).

Un quart is a quarter. From Latin quartus. Pluralises regularly: trois quarts (three quarters, with audible plural-s in liaison contexts). Common phrases: un quart d’heure (a quarter of an hour, 15 minutes), les quarts de finale (the quarter-finals in sports), un quart d’avance (a quarter ahead, in nautical and racing contexts). The Latin counter quater (the fourth address suffix in addresses) shares the same root.

Reference Table

The Regular Pattern: Cardinal + Ième for 1/5 and Above

From 1/5 onward, the rule is consistent. Take the cardinal form of the denominator, add the ordinal suffix -ième, and you have the fraction. Cinq + ième = cinquième (1/5). Six + ième = sixième (1/6). Sept + ième = septième (1/7). Huit + ième = huitième (1/8). Neuf + ième = neuvième (1/9; note the f changes to v as in the ordinal). Dix + ième = dixième (1/10). Cent + ième = centième (1/100). Mille + ième = millième (1/1000).

For larger denominators, the pattern continues without surprise: un vingtième (1/20), un cinquantième (1/50), un soixante-dixième (1/70), un quatre-vingtième (1/80), un quatre-vingt-dixième (1/90). The vigesimal forms appear in 70-99 fractions exactly as they do in cardinals. Belgian and Swiss fractional forms use the regional cardinals: un septantième (1/70), un huitantième (1/80, in Vaud / Valais / Fribourg), un nonantième (1/90).

For pluralisation: when the numerator is greater than one, the fractional noun takes a plural-s. Deux cinquièmes (2/5), trois huitièmes (3/8), cinq dixièmes (5/10). The ordinal-derived fraction nouns are masculine (un dixième, les dixièmes) regardless of what they refer to; this is the convention of grammatical gender for fractional units in French.

Demi vs Moitié: The Two Words for Half

French has two words for the concept of one half, and they are not interchangeable. Demi functions primarily as an adjective and as a fraction noun. Moitié functions as an ordinary noun referring to the half-portion of something specific.

Use demi as a hyphenated adjective before a noun: une demi-heure (half an hour), une demi-bouteille (half a bottle), une demi-portion (half-portion), un demi-tour (a U-turn / half-turn), une demi-finale (semi-final). Demi in this position is invariable; the adjacent noun pluralises: deux demi-heures, trois demi-bouteilles.

Use demi as a noun for half a beer: un demi at a French café = a 25 cl draught beer (half of the standard 50 cl pre-metric measure). In time-telling, after a noun, demi agrees with gender: il est dix heures et demie (10:30, demie agrees with feminine heure), il est midi et demi (12:30, demi agrees with masculine midi). See telling time in French.

Use moitié as a noun for half of a specific thing: la moitié du gâteau (half the cake), la moitié des étudiants (half the students), la moitié de ma vie (half my life). Moitié is feminine. It always takes the article (la moitié, une moitié) and is followed by de + the thing being halved. À moitié as an adverb means “half-” or “halfway”: à moitié fini (half-finished), à moitié plein (half-full).

Where Fractions Naturally Appear

Cooking. French recipes use fractional measurements naturally. Un quart de litre de lait (250 ml of milk), la moitié d’un citron (half a lemon), trois quarts d’une tablette de chocolat (three quarters of a chocolate bar). For halving recipes: diviser la recette par deux. For sharing: partager en quatre (split into four), en six, etc.

Music. Note durations in French are explicitly fractional. La ronde = whole note (4 beats). La blanche = half note (2 beats). La noire = quarter note (1 beat). La croche = eighth note. La double croche = sixteenth note. La triple croche = thirty-second note. The fractional names are not used; the symbolic names (ronde, blanche, noire, croche) are. But musicians do say une mesure à quatre quarts (4/4 time), à trois quarts (3/4 time), à six huitièmes (6/8 time), all with the explicit fractional vocabulary.

Sports rankings. Les huitièmes de finale (round of 16), les quarts de finale (quarter-finals), les demi-finales (semi-finals), la finale (the final). The fractional-of-final structure is unique to sports, derived from old elimination-bracket terminology.

Pedagogical maths. Primary-school French maths teaches the ordinal-derived fraction names systematically. The fraction simple form is what every French primary-school child learns. Fraction décimale (decimal fraction, denominator a power of 10) and fraction irréductible (fully reduced fraction) are the technical terms for further classification.

Frequently Asked Questions