Esperanto forms fractions with the official suffix -on-. The number before -on- names the denominator—the number of equal parts into which a whole is divided: duono is one of two equal parts, triono one of three, and centono one of one hundred. Ordinary grammatical endings then show whether the fraction is being used as a noun, adjective, or adverb.
The denominator takes -on-
The basic fraction words are nouns in -o:
| Fraction | Esperanto | Structure |
|---|---|---|
| 1/2 | duono | du + on + o |
| 1/3 | triono | tri + on + o |
| 1/4 | kvarono | kvar + on + o |
| 1/10 | dekono | dek + on + o |
| 1/100 | centono | cent + on + o |
The logic differs from English terminology. In triono, tri does not state that there are three pieces in the expression; it states that the whole was divided into three equal pieces.
Mi manĝis duonon de la sandviĉo kaj konservis la reston por poste.
I ate half of the sandwich and saved the rest for later.
Nur triono de la dungitoj laboras en la oficejo hodiaŭ.
Only one third of the employees are working in the office today.
The whole commonly follows with de, especially when it is definite: duono de la kuko, triono de la buĝeto, kvarono de la loĝantoj. The fraction noun is the head of the phrase.
Numerators greater than one
Put a cardinal before the fraction noun to give the numerator. Make the fraction noun plural because there is more than one fractional part:
Ni jam finis du trionojn de la vojaĝo.
We have already completed two thirds of the journey.
Tri kvaronoj de la ĉeestantoj voĉdonis por la propono.
Three quarters of those present voted for the proposal.
La baterio perdis kvin centonojn de sia kapacito dum la testo.
The battery lost five hundredths of its capacity during the test.
The cardinal itself remains invariant: du trionoj, not duj trionoj. Case appears on the fraction noun when the phrase's role requires it. In Ni jam finis du trionojn de la vojaĝo, the accusative marks the direct object of finis; in Tri kvaronoj ... voĉdonis, the fraction phrase is the subject.
The word unuono is theoretically “one whole divided by one,” but it is very rare because plain unu expresses the result more naturally. This is an honest lexical fact rather than an irregular grammatical prohibition.
Multiword denominators and spelling
When the denominator is a multiword cardinal, combine it before -on-. Hyphens can preserve the original boundaries:
Unu minuto estas sesdekono de horo.
One minute is one sixtieth of an hour.
Unu tago estas tricent-sesdek-kvinono de ordinara jaro.
One day is one three-hundred-and-sixty-fifth of an ordinary year.
For 1/12, both dekduono and the more visibly segmented dek-duono occur. A space would break the single derived word: dek duono would invite the reading “ten halves,” not “one twelfth.” For long denominators, hyphens are a practical clarity device: mil-ducentono is easier to parse than a dense unbroken form.
This spelling differs from an ordinary cardinal, where dek du is written as two words. Derivation with -on- turns the whole number into one word.
Adjective forms: duona, triona, kvarona
Replace the noun ending -o with -a when the fraction directly describes a noun:
Ni faru duonhoran paŭzon antaŭ la sekva kunsido.
Let's take a half-hour break before the next session.
La recepto bezonas kvaronan litron da lakto.
The recipe needs a quarter of a liter of milk.
Ŝi finis nur trionan parton de la raporto.
She finished only a one-third part of the report.
The adjective agrees normally. In kvaronan litron, both words are accusative because the measured amount is the object of bezonas. Common compounds such as duonhoro and kvaronlitro package the same meaning into one noun; transparent phrases duona horo and kvarona litro are equally grammatical.
Do not confuse fractional -on- with ordinal -a. Dua parto means the second part in a sequence; duona parto means a part equal to one half:
Mi legis la duan parton de la romano, sed nur duonon de ĝi.
I read the second part of the novel, but only half of it.
That minimal contrast is especially important for English speakers, because English uses similar-looking phrases such as “a second part” and “one second,” while Esperanto assigns each derivation a stable function.
Mixed numbers and units
A whole number plus a fraction can be expressed with kaj. Before a unit noun, the fractional adjective describes an understood single unit:
La riparo daŭris du kaj duonan horojn.
The repair lasted two and a half hours.
This expands conceptually to du horojn kaj duonan horon. That is why duonan is singular, while the final horojn presents the complete measurement as plural. The accusative -n marks duration.
Mi aĉetis unu kaj kvaronan kilogramojn da tomatoj.
I bought one and a quarter kilograms of tomatoes.
This compact pattern is normative but can feel structurally unusual to English speakers. A completely explicit alternative is often easier in conversation:
Mi aĉetis unu kilogramon kaj ducent kvindek gramojn da tomatoj.
I bought one kilogram and two hundred fifty grams of tomatoes.
For a value below one unit, use a fractional adjective or compound: duona litro, tri kvaronoj de litro, kvaronlitro. Units are not automatically plural merely because a written fraction has two numbers.
Adverb forms: extent and partial completion
With -e, a fraction describes the extent or manner of a state or action:
La glaso estas duone plena.
The glass is half full.
Mi nur duone komprenis la lastan demandon.
I only half understood the last question.
La panelo estas trione el korko, trione el ligno kaj trione el reciklita plasto.
The panel is one third cork, one third wood, and one third recycled plastic.
The three adverbs divide the panel's composition into equal shares. When the shares have different numerators, explicit noun phrases such as unu triono ... kaj du trionoj ... are clearest in technical writing; ordinary duone remains natural for “half/partly.”
Duone can also mean “partly” rather than an exactly measured 50 percent in everyday (informal) use: duone ŝerce means “half jokingly.” The context indicates whether the fraction is exact or figurative.
Fractions in clock time and written notation
Everyday time expressions often use duono and kvarono relative to an ordinal hour:
— Kioma horo estas? — Estas kvarono post la naŭa.
— What time is it? — It is a quarter past nine.
La trajno foriros je la sesa kaj duono.
The train will leave at half past six.
Digital notation such as 9:15 and fraction symbols such as ½ are concise writing conventions, not new grammar. In running text, pronounce or expand them according to the meaning: duono, tri kvaronoj, la naŭa kaj dek kvin minutoj. The dedicated pages on clock time and decimals, percentages, and mathematical reading cover those conventions fully.
Common Mistakes
Using an ordinal as a fraction
❌ Mi manĝis duan de la kuko.
Incorrect — dua means second in a sequence, not one half.
✅ Mi manĝis duonon de la kuko.
I ate half of the cake.
Forgetting plural fractional parts
❌ Tri kvarono de la grupo jam alvenis.
Incorrect — three separate quarter-parts require kvaronoj.
✅ Tri kvaronoj de la grupo jam alvenis.
Three quarters of the group have already arrived.
Separating a derived denominator incorrectly
❌ La rabato estas unu dek duono de la prezo.
Incorrect spacing — this obscures the intended fraction 1/12.
✅ La rabato estas unu dek-duono de la prezo.
The discount is one twelfth of the price.
Losing accusative marking on measured duration
❌ Ni atendis unu kaj duona horoj.
Incorrect — the duration needs accusative marking, and duona describes an understood singular horo.
✅ Ni atendis unu kaj duonan horojn.
We waited one and a half hours.
Using da for a definite whole
❌ Duono da la kuko restis.
Incorrect in the intended ‘half of that cake’ meaning — the definite whole takes de.
✅ Duono de la kuko restis.
Half of the cake remained.
Key Takeaways
Attach -on- to the denominator: triono is one of three equal parts. Put a cardinal before the noun and pluralize it for a larger numerator: du trionoj. Use -a to describe a fractional unit and -e for fractional extent, preserve normal case marking in measurements, and distinguish duona “half” from ordinal dua “second.”
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