Fractions

Irish has several ways to express fractions. For common values like a half, a third, and a quarter, there are special dedicated words. Other fractions are typically formed using ordinal numbers, or with a more mathematical structure for precision.

Special Fraction Words

The most common fractions have unique names rather than being formed from a general rule.

A Half (leath)

The word for “a half” is leath. A less common alternative is leathchuid. Leath can be used in several ways, either compounding with a noun or followed by the genitive case.

• leathúll - a half-apple (compounded)
• leath úill - a half of an apple (genitive)
• leath d’úll - a half of an apple (with de)

When referring to a specific item, use the definite article:

• leath an úill - a half of the apple
• leath na n-úll - a half of the apples
• leath den úll - a half of the apple (using den for de + an)
• an leath den úll - the half of the apple

For multiple halves, such as “five halves” (5/2), you can say cúig leath or cúig cinn de leatha.

• cúig leathúll - five half-apples

A Third (trian)

The most common word for “a third” is trian. The ordinal number tríú is also used, often with the word cuid (part/share). A less common alternative is treaschuid.

• trian úill - a third of an apple
• trian d’úll - a third of an apple
• trian an úill - a third of the apple
• tríú cuid an úill - a third (part) of the apple

For multiples, trian is used, and its plural is trianta or treana.

• dhá thrian den úll - two thirds of the apple
• trí treana den úll - three thirds of the apple
• dhá cheann de thrianta - two (items) of thirds

A Quarter (ceathrú)

The word for “a quarter” or “a fourth” is ceathrú. Like tríú, it is often used with cuid.

• an cheathrú den úll - the quarter of the apple
• an ceathrú cuid den úll - the quarter (part) of the apple

For multiples, you can use ceathrú or the plural ceathrúna.

• trí cheathrú den úll - three quarters of the apple
• trí ceathrúna den úll - three quarters of the apple
• trí cinn de cheathruithe - three (items) of quarters

General Fractions

Most other fractions are formed systematically from numbers.

Using Ordinal Numbers

For most fractions, the system is based on ordinal numbers. The basic fractional unit (e.g., “a fifth”, “a sixth”) is simply the ordinal number itself.

To express a fraction of something, you can add cuid (part) and use the preposition de.

• (an) cúigiú cuid den úll - (the) fifth part of the apple

For numerators greater than one, place the cardinal number before the fractional noun. This often causes a mutation.

• ceithre chúigiú (cuid) den úll - four fifths of the apple
• cúig shéú (cuid) den úll - five sixths of the apple
• seacht ndeichiú (cuid) den úll - seven tenths of the apple
• naoi n-ochtú (cuid) den úll - nine eighths of the apple

Fractions from 11 to 19

Fractions from one eleventh to one nineteenth have two common forms. One is a single compound word, and the other uses the phrase cuid déag (“teen part”).

When the numerator is greater than one, the compound form is typically used.

• sé aondéagú - six elevenths (6/11)
• deich ndódhéagú - ten twelfths (10/12)
• dhá thrídéagú - two thirteenths (2/13)

Fractions for Tens

Fractions based on tens (twentieth, thirtieth, etc.) also follow a regular pattern based on the cardinal number.

These forms behave like other fractional nouns when used with numerators greater than one.

• dhá fichiú cuid den úll - two twentieths of the apple
• trí dhaicheadú den úll - three fortieths of the apple
• naoi gcéadú den úll - nine hundredths of the apple

Alternative Constructions

Two other constructions are common, one used for counting fractions as items and another for mathematical contexts.

Counting with cinn de

To count fractions as discrete units, you can use the structure [number] cinn de [plural fractional noun].

• ceithre cinn de chúigithe - four (items) of fifths (4/5)
• ocht gcinn de sheachtuithe - eight (items) of sevenths (8/7)
• naoi gcinn d’ochtuithe - nine (items) of eighths (9/8)
• a cúig déag de shédéaguithe - fifteen (items) of sixteenths (15/16)

Mathematical Style (X ar Y)

A more formal or mathematical way to state a fraction is to say “X over Y”, using the formula a <numerator> ar a <denominator>. For numbers over 19, the second a is often dropped.

• a haon ar a dó - one over two (1/2)
• a cúig ar a sé - five over six (5/6)
• a hocht ar a seacht - eight over seven (8/7)
• a trí déag ar fiche - thirteen over twenty (13/20)
• a dó dhéag ar fiche a ceathair - twelve over twenty-four (12/24)

Mixed Numbers

Mixed numbers like “one and a half” are formed using go leith for halves, go dtrian for thirds, and is (and) for most other fractions.