Fractions, Percentages, and Arithmetic

Once you can count, the next everyday job is to cut things up and add them together: a third of the class, twenty-five percent off, two plus two. Icelandic does this with tools English does not have. Where English builds fractions out of ordinals ("one third, one quarter"), Icelandic reaches for a small family of dedicated nouns — helmingur "a half", þriðjungur "a third", fjórðungur "a quarter" — that behave like any other masculine noun and pull the thing being divided into the genitive. Percentages run through the neuter word prósent, and spoken arithmetic has its own little vocabulary (plús, mínus, sinnum, deilt með) where the answer is hooked on with er/eru. This page is about putting all of that to work. (The ordinals themselves — þriðji, fjórði — live on their own page; here we only borrow the idea of "third" and "quarter" as portions.)

Fractions are nouns: helmingur, þriðjungur, fjórðungur

This is the headline difference from English. English says "one third", "two thirds" — a numeral plus an ordinal. Icelandic has a set of fraction nouns ending in -ungur (plus the irregular helmingur for "half"), and they decline like ordinary masculine nouns. Þriðjungur is not "one third" assembled from parts; it is a single word that means "a third (of something)", the way English "a third" can be a noun ("I'll take a third").

The -ungur nouns are masculine and decline like -ur masculines: þriðjungur (nom.), þriðjung (acc.), þriðjungi (dat.), þriðjungs (gen.); plural þriðjungar. They are fully productive and idiomatic — when an Icelander means "a third of the cake" they say þriðjungur af kökunni or þriðjungur kökunnar, never a word-for-word einn þriðji. For fractions higher than a sixth or so the -ungur series thins out, and speakers switch to X hluti ("X-th part", with an ordinal) — tíundi hluti "a tenth part".

The fraction noun takes a genitive (or af + dative)

Because these are nouns, the thing being divided attaches to them like any other possessor: in the genitive. Þriðjungur nemenda is literally "a third of-students", with nemenda (genitive plural) doing the work English does with "of". This bare genitive is the crisp, written-feeling option. In everyday speech you will just as often hear the partitive af + dative: þriðjungur af nemendum, helmingur af kökunni. Both are correct; the bare genitive sounds a touch more formal.

hálfur — the adjective "half", for halving concrete things

Alongside the fraction noun helmingur, Icelandic has the adjective hálfur "half", which behaves like any adjective: it agrees in gender, number, and case with the noun it modifies. Use hálfur when you are describing a thing that is itself half — hálfur kassi "half a box", hálfur lítri "half a litre", hálf flaska "half a bottle". Use the noun helmingur when you mean "half of" some specific whole.

The rough division of labour: hálfur (adjective) for a thing that is half full or half size; helmingur (noun) for "half of" a named whole. "Half of the students" is helmingur nemenda, not *hálfir nemendur (which would mean "half-students", students who are somehow only half there).

Percentages: prósent

A percentage is read with the word prósent, a neuter noun that in practice stays invariant after a number: tíu prósent "ten percent", fimmtíu prósent "fifty percent". The number in front does not force the usual 1–4 agreement gymnastics the way króna does, because prósent sits there unchanged — you say eitt prósent (neuter "one") but then tvö prósent, þrjú prósent with the neuter numerals, and from five up the numeral is invariant anyway. So 25 % is read tuttugu og fimm prósent.

There is also the older, more literary phrasing X af hundraði — literally "X out of a hundred" — which you still meet in formal or legal prose and in set phrases, but in everyday and journalistic Icelandic prósent dominates.

Reading arithmetic aloud

Spoken sums have a small fixed vocabulary. The key thing for English speakers is the last word: the result is introduced by er (singular) or eru (plural), the verb "to be", and it agrees in number with the answer — so "two plus two are four" comes out tveir plús tveir *eru fjórir, with plural *eru because the answer (fjórir) is plural.

Note that sinnum ("times") is the multiplication word — literally an old genitive plural of sinn "time, occasion" — and deilt með ("divided by/with", með + dative) is the everyday division phrase: tólf deilt með þremur "twelve divided by three". (Careful, textbook Icelandic actually splits the two numbers across two prepositions — deilt í tólf með þremur, "divided into twelve with three" — because division is not symmetric and the two roles, dividend and divisor, need keeping apart; but in ordinary spoken sums X deilt með Y is what you hear.) The "=" is most often er/eru, but you will also hear gera ("makes") in shopkeeping contexts (það gera fimm hundruð krónur "that makes 500 krónur"). For a single-item answer use er; for a plural answer use eru.

English vs Icelandic, in brief

Three habits transfer wrongly. First, English makes fractions from ordinals ("one-third"), so learners build *einn þriðji — but Icelandic prefers the fraction noun þriðjungur and feeds it a genitive. Second, English keeps "of" everywhere ("a third of the class"); Icelandic uses a bare genitive (þriðjungur nemenda) or af + dative, never a stray *af with the bare-genitive version. Third, in spoken sums English says "two plus two equals four" with a singular verb; Icelandic uses er/eru and makes the verb agree with the answer — tveir plús tveir *eru fjórir*. None is hard, but each is a place the English reflex misfires.

Common Mistakes

The single most common error is calquing "one third / one quarter" literally. Reach for the noun: þriðjungur, fjórðungur, fimmtungur.

The thing being divided is genitive (or af + dative), never left in the nominative.

In the everyday "by X percent" frame, prósent sits unchanged.

The result verb agrees with the answer: plural answer → eru, singular answer → er.

Key Takeaways

• Fractions are nouns in Icelandic: helmingur (1/2), þriðjungur (1/3), fjórðungur (1/4), fimmtungur (1/5) — masculine -ur nouns that decline (þriðjungs in the genitive). Prefer them to a literal "one third".
• The divided thing follows in the genitive (þriðjungur nemenda) or as af + dative (þriðjungur af nemendum); the bare genitive is a touch more formal.
• hálfur is the adjective "half" and agrees (hálfur kassi, hálft kíló); use it for things that are themselves half, and the noun helmingur for "half of" a whole.
• Percentages use the neuter, largely invariant prósent (tuttugu og fimm prósent); the formal X af hundraði survives in elevated prose.
• Spoken sums: plús, mínus, sinnum, deilt með; the answer is joined by er/eru (or gera), and the verb agrees with the answer — tveir plús tveir *eru fjórir*.