# Chapter 9 | The Number

The main versions of the number in Irish are the Bare Number, the Cardinal Number, the Personal Number, the Ordinal Number, the Fraction and the Decimal Number.

1. The Bare Number

   A number that is not directly followed by a noun is called a bare number. The bare number is used in counting, e.g., a haon (EN: one); a cúig (EN: five); a deich (EN: ten) (see 9.2).

2. The Cardinal Number

   A number that is placed before a noun to express a number of things is called a cardinal number, e.g., trí leabhar (EN: three books); seacht gcupán (EN: seven cups); naoi mbád (EN: nine boats) (see 9.3).

3. The Personal Number

   A number that is used to count people is called a personal number, e.g., beirt bhan (EN: two women); ceathrar daltaí (EN: four students); ochtar feirmeoirí (EN: eight farmers) (see 9.4).

4. The Ordinal Number

   A number indicating the position of an object in a series of objects is called an ordinal number, e.g., an chéad teach (EN: the first house); an dara bean (EN: the second woman); an fichiú haois (EN: the twentieth century) (see 9.5).

5. The Fraction

   A fraction is a numerical quantity that is not an integer (whole number), e.g., ceathrú (1/4); ceithre chúigiú (4/5); cúig shéú (5/6) (see 9.6).

6. The Decimal Number

   The decimal number is another way of expressing a non-integer numerical quantity, using the decimal point, e.g., 3.1; 7.5; 18.49; 34.023 (see 9.7).

A choice is given between two systems for dealing with cardinal numbers and personal numbers in writing: the Established System and the Simplified System. The Established System is always used with numbers from 1–19. Either the Established System or the Simplified System may be used with numbers from 20 onwards.

1. The particle a is placed before numbers from 1–19, e.g., a haon (EN: one); a dó (EN: two); a trí (EN: three); bus a ceathair (EN: bus four); a hocht déag (EN: eighteen); and for 20–99 (other than the tens), it is placed before the last number, e.g., fiche a haon (EN: twenty-one); daichead a sé (EN: forty-six); seachtó a hocht (EN: seventy-eight).

2. The words ceathracha and daichead have a similar status. (TL Note: Both of these mean "forty.")

This is how the bare numbers from 0–19 are written.

Note that the bare number is used for times of day, e.g., a haon a chlog (EN: one o’clock); a seacht a chlog (EN: seven o’clock); a fiche tar éis a cúig (EN: twenty past five). This is how time is written in the form of figures: 5.30 p.m.; 4.26 p.m.; 13:00; 16:47.

This is how the bare numbers from 20–99 are written. The entire system between 20 and 29 is given in the table and examples are given for the other tens.

1. The numbers céad (EN: hundred), míle (EN: thousand), milliún (EN: million), billiún (EN: billion), etc. are nouns. Therefore, the cardinal number system is used if the numbers 2–19 are followed by a series of zeros corresponding to céad, míle, milliún, billiún, etc., e.g., ceithre chéad (EN: four hundred); dhá chéad míle (EN: two hundred thousand); naoi milliún déag (EN: nineteen million); dhá bhilliún (EN: two billion); ocht mbilliún (EN: eight billion) (see 9.3 The Cardinal Number).
2. No initial mutation is made to the noun after the tens, e.g., fiche míle (EN: twenty thousand); tríocha milliún (EN: thirty million); etc.

1. There are two systems for expressing odd numbers beyond 10,000 — the cardinal number system and the bare number system.
2. In the cardinal number system the word order follows the cardinal number rules, e.g., 24,000 — ceithre mhíle is fiche (see table 9N). Under the bare number system, the bare number plus the bare noun is used (céad, míle, etc.) without transformation, e.g., 24,000 — fiche a ceathair míle.

Note that is is used in the cardinal number system above 10,000 but not in the other bare numbers.

This is how the bare numbers over 10,000 are written.

1. The number added to a noun to express the number of things is called a cardinal number.
2. The noun comes after aon, dhá, trí, ceithre, cúig, sé, seacht, ocht, naoi, deich. (EN: 1–10 respectively).
3. Note that the cardinal numbers dhá and ceithre are used rather than the bare forms dó and ceathair (EN: two and four respectively).
4. The word amháin must be mentioned after the original aon and the noun. It is not, however, always necessary to mention aon, e.g., aon chapall amháin (EN: one horse only); capall amháin (EN: one horse).
5. d, t or s is not lenited after aon, e.g., aon doras amháin (EN: one door only); aon teach amháin (EN: one house only).

6. After the noun comes the word déag, e.g., ceithre leabhar déag (EN: fourteen books). The word déag is lenited if the word directly before it ends in a vowel (but see 9.3.2(e)), except after euro.

   Note that if the noun and the qualifier are a separate unit of meaning, e.g., madra rua (EN: fox); cat crainn (EN: pine marten); teach tábhairne (EN: pub); láthair champála (EN: campsite) (rather than an ordinary noun and qualifier, e.g., leabhar dearg) déag is placed after the noun and the qualifier, e.g., ceithre mhadra rua dhéag (EN: fourteen foxes); cúig theach tábhairne dhéag (EN: fifteen pubs); sé chat crainn déag (EN: sixteen pine martens); seacht n‑iora ghlasa dhéag (EN: seventeen gray squirrels). Any other qualifier is added after déag, e.g., sé chat crainn déag mhóra (EN: sixteen large pine martens); seacht n‑iora ghlasa dhéag fhiáine (EN: seventeen gray squirrels).

7. two is not lenited after the article, aon or céad, e.g., an dá leabhar (EN: the two books); an chéad dá leabhar (EN: the first two books); aon dá leabhar (EN: one of the two books).
8. The cardinal numbers aon, dhá (but see 8.3.3), trí, ceithre, cúig and sé lenite the following singular noun, e.g., trí bhád (EN: three boats); but the word cent is not lenited, e.g., trí cent (EN: three cents).
9. The cardinal numbers seacht (EN: seven), ocht (EN: eight), naoi (EN: nine) and deich (EN: ten) eclipse the following singular and plural nouns, e.g., seacht gcnámh (EN: seven bones); deich gcinn (EN: ten heads); but the word euro is not eclipsed, e.g., ocht euro (EN: eight euros); naoi euro (EN: nine euros), and neither is cent, e.g., ocht cent (EN: eight cents); deich cent (EN: ten cents).

There are a number of nouns whose nominative plural form, or a distinct plural form, is used after the cardinal numbers 3–10 and after numbers ending in 3–9. Those nouns are shown in the table below. Although é fichid is not a plural version, that version is included in this class.

1. The nominative singular form of nouns used with the cardinal numbers 1–2 and after numbers ending in 1–2, e.g., aon phingin amháin (EN: one penny); dhá bhliain (EN: two years); aon uair déag (EN: eleven times); dhá cheann is tríocha (EN: thirty-two).
2. The plural form is not lenited after 3–6 or after numbers ending in 3–6, e.g., trí seachtaine (EN: three weeks); ceithre cinn déag (EN: fourteen heads).
3. After 3–6 and after numbers ending in 3–6 h is placed before the plural form uaire, e.g., cúig huaire (EN: five times).
4. The numbers 7–10 and numbers ending in 7–9 eclipse the plural form, e.g., seacht mbliana (EN: seven years); ocht bpingine déag (EN: eighteen pennies).
5. déag is not lenited after the plural form, even if it ends in a vowel, e.g., trí bliana déag (EN: thirteen years); ocht n‑uaire déag (EN: eighteen times).
6. The nominative singular form is used after the tens (other than deich), e.g., fiche bliain (EN: twenty years); tríocha pingin (EN: thirty pennies); ochtó troigh (EN: eighty feet).

1. Following for the cardinal number 1, the adjective accompanying the noun is in the singular and is of the same gender as the noun.
2. Following the other numbers (2–19), the adjective is in the plural and is omitted.
3. The word déag is placed before an adjective or adjectives accompanying the noun (but see 9.3.1(f)).

1. Following the cardinal number 1, the adjective accompanying the noun is in the singular, and is of the same gender as the noun.
2. The adjective in the plural is placed after the plural form but the adjective is not lenited if that plural form ends in a vowel. The adjective is lenited after cinn and fichid.

1. Singular form of the article
   1. The singular form of the article is placed before the cardinal number 1, before numbers ending in 1, and before plurals of 10 from 20 onwards.
   2. t‑ is placed before the cardinal number aon after the article, e.g., an t‑aon leabhar amháin (EN: the one book); an t‑aon bhileog amháin (EN: the one sheet). The t‑ is removed after a preposition, e.g., san aon leabhar amháin (EN: in the one book); tríd an aon fhuinneog amháin (EN: through the one window).
   3. The singular form of the article placed before the cardinal number dhá also but the cardinal number becomes dá, e.g., an dá chapall (EN: the two horses).
2. Plural form of the article
   1. It is the plural form of the article that is placed before the cardinal numbers 3–9 and 13–19.
   2. h is placed before a cardinal number beginning with a vowel after the plural form of the article, e.g., na hocht gcapall (EN: the eight horses).
3. The article does not affect adjectives following cardinal numbers and nouns, e.g., an dá chapall mhóra (EN: the two big horses).

1. Nouns and adjectives change form in the genitive after aon, e.g., ualach aon chapaill mhóir amháin (EN: one big horse’s load); fráma aon fhuinneoige báine amháin (EN: one white window frame); except when déag follows, e.g., ualach aon chapall déag mhóra (EN: eighteen big horses’ load); fráma aon fhuinneog déag bhána (EN: eighteen white window frames).
2. For 2–19, the form of the noun or the cardinal number in the genitive does not change, e.g., fad dhá mhéadar (EN: two meters long); costas trí fhuinneog (EN: cost of three windows); úinéir seacht ngabhar (EN: owner of seven goats); tréimhse naoi n‑oíche (EN: period of nine nights); tiománaithe trí thacsaí dhéag (EN: drivers of thirteen taxis); but the adjective is put in the plural, and it is lenited, e.g., costas trí fhuinneog dheasa (EN: cost of three nice windows); úinéir seacht ngabhar chrosta (EN: owner of seven cross goats); tiománaithe trí thacsaí dhéag chostasacha (EN: drivers of thirteen costly taxis); unless it is a distinct plural form ending in a vowel or a broad consonant, e.g., trí bliana crua (EN: three hard years).

1. aon

   A change of form on a noun and an adjective in the genitive after any place where the article is there is subject to the following points.

   1. Subject to the gender of the noun, use an or na in the genitive case before the ordinal number aon when déag does not follow it, e.g., ualach an aon chapaill amháin (EN: the load of the one horse); costas na haon fhuinneoige amháin (EN: the cost of the one window); but ábhar an aon chuntas déag amháin (EN: the content of the one account of ten); ag ceartú an aon aiste dhéag shuimiúla (EN: correcting the one essay of ten significant).
   2. If the noun is feminine, an h must be placed before the cardinal number aon, e.g., i gcaitheamh na haon oíche amháin sin (EN: in the course of that one night).
   3. If the noun is masculine, the t‑ is removed before the cardinal number aon, e.g., ar feadh an aon lae amháin sin (EN: over the course of that one day).
2. Change dhá to dá after the singular article (an, don, sa, etc.).
3. For the cardinal numbers trí to deich, the cardinal numbers (trí, ceithre, cúig, ocht, deich) are eclipsed in the genitive case after the article (na).
4. The same rules apply to nouns with a particular plural form and the adjectives accompanying them (see 9.3.4) as applied in the nominative case, e.g., tréimhse na sé bliana fada (EN: the period of six long years); deireadh na naoi seachtaine déag fada (EN: the end of the nineteen long weeks); Cogadh na Naoi mBliana (EN: the Nine Years’ War); costas na dtrí troithe cearnacha eile (EN: the cost of the three other square feet); úinéir an dá cheann bhána (EN: the owner of the two white ones); praghas na dtrí cinn mhóra (EN: the price of the three big ones).

The rules for writing the cardinal numbers 1–19 in figures are the same as those for writing them in words, e.g., 1 chapall mór (EN: 1 big horse); 3 bhád bheaga (EN: 3 small boats); 7 n‑oíche dhorcha (EN: 7 dark nights); 13 seachtaine fuara (EN: 13 cold weeks); 17 ngluaisteán shaora (EN: 17 free cars); 19 mbliana fada (EN: 19 long years).

1. The nominative singular form of the noun is placed after the tens. No initial mutation is made to the noun.
2. If there is an adjective, it agrees with the gender of the noun.
3. The singular form of the article is placed before the tens, e.g., an fiche teach nua (EN: the twenty new houses); an seasca duine cáiliúil (EN: the sixty famous people).
4. In the genitive case, if the article is not present, no change of form is made to the noun or to the cardinal number.
5. If the article is present in the genitive case, the article affects the initial mutation of the number as it would on a masculine noun, but no initial mutation is made on f or s.

1. There are two systems for the cardinal numbers above 20 (other than the tens mentioned earlier, see 9.3.9): the Established System and the Simplified System. Both systems apply to the cardinal numbers whether written in words or in figures. Both systems are equivalent and acceptable.

2. The Established System

   1. The noun is in the singular form or in its particular plural form and the appropriate initial mutation is made to the noun.
   2. After numbers ending in 1, the adjective agrees with the gender of the noun. For numbers ending in 2–9, the adjective is in the plural and is lenited (but see 9.3.4).

3. The Simplified System

   1. The noun is always in the singular, even if it is a noun that has a particular plural form, and no initial mutation is made to it. The adjective is always in the singular and is lenited according to the gender of the noun.
   2. For numbers ending in 2 or 4, the bare numbers dó and ceathair are used instead of dhá and ceithre.
4. If multiples of 10 are involved, there is only one form, e.g., céad is fiche bád (EN: one hundred and twenty boats).
5. Regarding the article, the pattern used with the numbers 1–19 is followed with the numbers above 20, e.g., an t‑aon leabhar is fiche (EN: the twenty-one books); an dá bhord is tríocha (EN: the thirty-two tables); na cúig pheann is seasca (EN: the sixty-five pens) (see 9.3.5).

In the Established System, the reverse order is used below 100 for numbers above 100, e.g., céad fiche is aon chapall amháin (EN: one hundred and twenty-one horses); dhá mhíle, trí chéad is ceithre chapall (EN: two thousand, three hundred and four horses); etc.

The other rules are the same as the rules for the cardinal numbers mentioned in 9.3.10.

The rules of the Established System and the Simplified System, respectively, (see 9.3.10) are applied when numbers above 20 are written in figures.

1. The personal numbers (2–10 and 12) are used to count people.
2. The usual system of numbers is used to count aon duine dhéag or a number of people greater than dháréag (EN: twelve), e.g., aon duine dhéag (EN: eleven people); trí dhuine dhéag (EN: thirteen people); ceithre dhuine is daichead (EN: forty-four people).

1. The bare personal number
   1. The personal number can be used bare (without a noun following) to count the number of people, e.g., An bhfaca tú an bheirt? (EN: Did you see the two of them?); Gabhadh seachtar (EN: Seven were captured).
   2. The bare personal number in the genitive is treated as a common noun, e.g., cor beirte (EN: a pair of); col ceathrair (EN: a group of four); col seisir (EN: a group of six).
2. The article before the bare personal number
   1. All personal numbers except beirt are masculine nouns, e.g., an bheirt (EN: the two); an ceathrar (EN: the four); an t‑ochtar (EN: the eight).
   2. Dháréag is not lenited after the article, aon or céad, e.g., bhí an dáréag ann (EN: there were twelve); gach aon dáréag acu (EN: each of them had twelve); an chéad dáréag a cháiligh (EN: the first twelve qualified).
   3. The bare personal number in the genitive is treated as a common noun when preceded by the article, e.g., cótaí an tseisir (EN: the coats of the six); ticéid an ochtair (EN: the tickets of the eight); gluaisteán na beirte (EN: the car of the two).

   Table 9RThe Bare Personal Numbers — The Nominative and Genitive Cases with the Article

   Number	Nominative Case	Genitive Case
   1	an t‑aon duine amháin	ainm an aon duine amháin
   2	an bheirt	tuairimí na beirte
   3	an triúr	éadaí an triúir
   4	an ceathrar	táillí an cheathrair
   5	an cúigear	bád an chúigir
   6	an seisear	teach an tseisir
   7	an seachtar	scoil an tseachtair
   8	an t‑ochtar	meitheal an ochtair
   9	an naonúr	foireann an naonúir
   10	an deichniúr	tithe an deichniúir
   11	an t‑aon duine dhéag	foireann an aon duine dhéag
   12	an dáréag	airgead an dáréag

3. The adjective with the bare personal number — Beirt (EN: two (people))
   1. If an adjective qualifies the word beirt and it is in the nominative*, the adjective is in the nominative plural and lenited, e.g., an bheirt cháiliúla (EN: the two famous); beirt mhisniúla (EN: two brave); don bheirt óga (EN: to the two young).
   2. If the word beirt, when following the article and in the genitive, is qualified by an adjective that follows it, the adjective is in the feminine singular genitive, e.g., tuairimí na beirte díograisí (EN: the opinions of the two enthusiastic); nótaí na beirte misniúla (EN: the notes of the two brave); iarrachtaí na beirte cróga (EN: the efforts of the two courageous).
   3. If the word beirt, when in the genitive but without the article preceding it, is qualified by an adjective that follows it, and it is following and subject to another noun, the adjective is in the plural following beirt and lenited (and the genitive change does not apply to the word beirt but it is lenited), e.g., moltaí bheirt mhisniúla (EN: the praises of two brave); tuairimí bheirt cháiliúla (EN: the opinions of two famous); obair bheirt acadúla (EN: the work of two academic).
   4. If the word beirt, when in the genitive but without the article preceding it, is qualified by an adjective that follows it, and it is subject to a compound preposition or a verbal noun, the adjective is in the plural following beirt and lenited (and no change is made to the word beirt either), e.g., le haghaidh beirt inniúla (EN: for two capable); ag moladh beirt mhaithe (EN: praising two good).
4. The adjective with the bare personal number — Triúr to dháréag
   1. If the personal numbers triúr to dháréag (but see 9.4.1(b)), and they are in the nominative*, are being qualified by an adjective that follows them, the adjective is in the nominative singular without any lenition, e.g., triúr mór (EN: three big); ceathrar ard (EN: four tall); an cúigear saibhir (EN: the five rich); don dáréag clúiteach (EN: to the twelve famous).
   2. If the personal numbers triúr to dháréag (but see 9.4.1(b)), and they are in the genitive, are being qualified by an adjective that follows them, the usual rules regarding adjectives in the genitive case that apply to nouns are applied to the adjectives accompanying them, e.g., éadaí an cheathrair bhig (EN: the clothes of the four small); meitheal ochtair dhíograisigh (EN: the effort of the eight diligent); airgead an dáréag chlúitigh (EN: the money of the twelve famous) (see Chapter 4).

* Or in the vocative, dative or accusative.

1. The form of the personal number and the form of the noun following it
   1. If the word beirt, when in the nominative*, is being qualified by a noun that follows it, the noun is in the genitive plural and lenited (except for a noun beginning with d, t or s), e.g., beirt chaptaen (EN: two captains); beirt chumadóirí (EN: two composers); beirt drumadóirí (EN: two drummers); ag beirt bhan (EN: with two women).
   2. If the word beirt, when in the genitive without the article, is being qualified by a noun that follows it, and it is following and subject to another noun, the genitive change does not apply to the word beirt but it is lenited and the noun is in the genitive plural and lenited (except for a noun beginning with d, t or s), e.g., moltaí bheirt chumadóirí (EN: the praises of two composers); tuairimí bheirt chaptaen (EN: the opinions of two captains); obair bheirt saineolaithe (EN: the work of two experts).
   3. If the word beirt, when in the genitive but without the article preceding it, is being qualified by a noun that follows it, and it is following and subject to a compound preposition or a verbal noun, no change is made to the word beirt and the noun is in the genitive plural and lenited (except for a noun beginning with d, t or s), e.g., le haghaidh beirt mholtóirí (EN: for two evaluators); ag moladh beirt saighdiúirí (EN: praising two soldiers).
   4. The genitive plural of the noun follows the personal numbers from triúr to dháréag (but see 9.4.1(b)) when counting people, e.g., triúr bádóirí (EN: three boatmen); ceathrar múinteoirí (EN: four teachers).
   5. The genitive change does not apply to the personal numbers from triúr to dháréag (but see 9.4.1(b)) if there is a noun following, e.g., athair ceathrar mac (EN: father of four sons); máthair cúigear iníonacha (EN: mother of five daughters); geansaithe dháréag peileadóirí (EN: sweaters of twelve footballers).

   * Or in the vocative, dative or accusative.

   Table 9SThe Personal Numbers — The Form of the Noun following the Personal Number

   Number	Nominative Case	Genitive Case
   1	fear amháin/aon fhear amháin bean amháin/aon bhean amháin	hata aon fhir amháin + hata aon mhná amháin
   2	beirt bhan	páistí bheirt bhan
   3	triúr bádóirí	báid triúr bádóirí
   4	ceathrar scoláirí	torthaí ceathrar scoláirí
   5	cúigear fear	gaolta cúigear fear
   6	seisear ban	páistí seisear ban
   7	seachtar bádóirí	long seachtar bádóirí
   8	ochtar báicéirí	cístí ochtar báicéirí
   9	naonúr fear	talamh naonúr fear
   10	deichniúr girseach	airgead deichniúr girseach
   11*	aon imreoir déag	cultacha aon imreoir déag
   12	dháréag bádóirí	soitheach dháréag bádóirí

   * Note that 11 is treated as it is in the cardinal number system, and that the noun is not put in the genitive (see 9.3.6(a)).

2. The article before a personal number with a following noun
   1. The singular form of the article is used before the personal numbers. They are all masculine except for beirt.
   2. Dháréag is not lenited after the article, aon or céad, e.g., an Dáréag Aspal (EN: the twelve apostles); gach aon dáréag scoláirí (EN: each of the twelve students); an chéad dáréag múinteoirí a cháiligh (EN: the first twelve teachers who qualified).
   3. If the word beirt, when in the genitive following the article, is being qualified by a noun that follows it, the noun is in the genitive plural and is not lenited (but the genitive change does apply to the word beirt), e.g., tuairimí na beirte múinteoirí (EN: opinions of the two teachers); nótaí na beirte saineolaithe (EN: notes of the two experts); tuairiscí na beirte comhfhreagraithe (EN: reports of the two correspondents); tithe na beirte deartháireacha (EN: houses of the two brothers).
   4. The genitive form change does not apply to the personal numbers from triúr to dháréag nor to the noun following, but the article affects the initial mutations of the personal numbers as it would affect the genitive of any other singular noun, e.g., cótaí an cheathrar daltaí (EN: coats of the four students); oifig an tseachtar tréidlianna (EN: office of the seven treasurers); Scoil an tSeachtar Laoch (EN: School of the Seven Heroes).

   Table 9TThe Personal Numbers — The Article before a Personal Number with a following Noun

   Number	Nominative Case	Genitive Case
   1	an t‑aon fhear amháin an t‑aon bhean amháin	hata an aon fhir amháin hata na haon mhná amháin
   2	an bheirt bhan	páistí na beirte ban
   3	an triúr bádóirí	báid an triúr bádóirí
   4	an ceathrar scoláirí	torthaí an cheathrar scoláirí
   5	an cúigear fear	gaolta an chúigear fear
   6	an seisear ban	páistí an tseisear ban
   7	an seachtar bádóirí	long an tseachtar bádóirí
   8	an t‑ochtar báicéirí	cístí an ochtar báicéirí
   9	an naonúr fear	talamh an naonúr fear
   10	an deichniúr girseach	airgead an deichniúr girseach
   11*	an t‑aon imreoir déag	cluiche an aon imreoir déag
   12	an dáréag bádóirí	soitheach an dáréag bádóirí

   * Note that 11 is treated as it is in the cardinal number system, and that the noun is not put in the genitive (see 9.3.7(a)(i)).

3. The adjective with a noun following a personal number
   1. Following the personal number beirt, the adjective is in the nominative plural and lenited, e.g., beirt bhan cháiliúla (EN: two famous women); beirt ghirseach chruthaitheacha (EN: two creative girls); beirt amhránaithe cháiliúla (EN: two famous singers); beirt mhúinteoirí shealadacha (EN: two temporary teachers).
   2. If the word beirt, when in the genitive but without the article preceding it, is being qualified by a noun + adjective that follows it, and it is following and subject to another noun, the adjective being qualified is in the plural and lenited, e.g., moltaí bheirt léachtóirí acadúla (EN: recommendations of two academic lecturers); tuairimí bheirt iriseoirí sheanbhunaithe (EN: opinions of two established journalists); saothar bheirt ghramadóirí chliste (EN: work of two clever grammarians).
   3. If the word beirt, when in the genitive but without the article preceding it, is being qualified by a noun + adjective that follows it, and it is following and subject to a compound preposition or a verbal noun, the adjective being qualified is in the plural and lenited, e.g., le haghaidh beirt mholtóirí dheasa (EN: for two nice reviewers); ag moladh beirt chumadóirí shamhlaíocha (EN: praising two imaginative composers).
   4. Following the personal numbers triúr to dháréag (but see 9.4.1(b)), the adjective accompanying the noun is in the genitive plural, e.g., triúr scoláirí díograiseacha (EN: three diligent students); ceathrar girseach éirimiúil (EN: four clever girls); bád an triúr bádóirí tuirseacha (EN: the boat of the three tired boatmen); airgead an deichniúr ban bríomhar (EN: the money of the ten lively women). Examples with and without the article are shown in the table below.

   Table 9UThe Personal Numbers — The Adjective with a Noun following a Personal Number

   Number	Nominative Case	Genitive Case
   1	fear ciallmhar amháin bean shaibhir amháin an t‑aon fhear cineálta amháin an t‑aon bhean dheas amháin	cóta aon fhir chiallmhair amháin geansaí aon mhná saibhre amháin cóta an aon fhir chineálta amháin geansaí na haon mhná deise amháin
   2	beirt bhan mhisniúla beirt fhear chróga beirt scoláirí chumasacha an bheirt bhan mhisniúla an bheirt fhear chróga	an bheirt scoláirí chumasacha oifig bheirt bhan mhisniúla páistí bheirt fhear chróga cóipleabhair bheirt scoláirí chumasacha oifig na beirte ban mhisniúla páistí na beirte fear chróga cóipleabhair na beirte scoláirí chumasacha
   3	triúr fear mór triúr girseach galánta an triúr bádóirí tuirseacha	hataí triúr fear mór gúnaí triúr girseach galánta báid an triúr bádóirí tuirseacha
   4	ceathrar (an ceathrar) scoláirí maithe	scrúduithe ceathrar (an cheathrar) scoláirí maithe
   5	cúigear (an cúigear) fear inniúil	gaolta cúigear (an chúigear) fear inniúil
   6	seisear (an seisear) ban cumasach	páistí seisear (an tseisear) ban cumasach
   7	seachtar (an seachtar) bádóirí óga	long seachtar (an tseachtar) bádóirí óga
   8	ochtar (an t‑ochtar) báicéirí díograiseacha	cístí ochtar (an ochtar) báicéirí díograiseacha
   9	naonúr (an naonúr) fear ocrach	talamh naonúr (an naonúr) fear ocrach
   10	deichniúr (an deichniúr) girseach bríomhar	airgead deichniúr (an deichniúr) girseach bríomhar
   11*	aon (an t‑aon) imreoir déag thapa	cultacha aon (an aon) imreoir déag thapa
   12	dháréag (an dáréag) scoláirí borba	leabhair dháréag (an dáréag) scoláirí borba

   * Note that 11 is treated as it is in the cardinal number system, and that the noun is not put in the genitive (see 9.3.6(a) and 9.3.7(a)(i)).

1. It is recommended to write the personal numbers from 1–12 in words rather than figures. If they are written in figures, they are treated as cardinal numbers, e.g., 2 bhean bheaga (EN: 2 small women), 4 bhádóir cháiliúla (EN: 4 famous boatmen), 7 bhfeirmeoir shaibhre (EN: 7 wealthy farmers) (see 9.3.8).
2. The cardinal number system is used to count numbers of people above dháréag. See 9.3.1 for a description of the cardinal number system from 1–19, e.g., trí bhean déag (EN: thirteen women); ceithre ghirseach déag ghalánta (EN: fourteen elegant girls); 17 mbádóir (EN: 17 boatmen); 19 bhfear ocracha (EN: 19 old men); and see 9.3.10 for a description of the cardinal number system over 20, e.g., trí bhean arda is caoga (EN: fifty-three tall women); 49 ngirseach ghalánta (EN: 49 elegant girls).

A simplified system can be used with the cardinal numbers and the personal numbers above twenty. See 9.3.10(c) for a description of that Simplified System, e.g., fiche a cúig fear mór (EN: twenty-five big men); tríocha a sé bean shaibhir (EN: thirty-six wealthy women); 46 bádóir cumasach (EN: 46 talented boatmen); 56 girseach chróga (EN: 56 brave girls).

1. The ordinal number céad (an chéad) (EN: first, (the first)) can be used with a singular or plural noun. The singular article is used when a singular noun is following, e.g., an chéad chaibidil (EN: the first chapter), and the plural article when a plural noun is following, e.g., na chéad chaibidlí (EN: the first chapters).

2. The ordinal number céad is lenited after the article, e.g., an chéad leabhar (EN: the first book); na chéad rialacha (EN: the first rules), but it is not lenited:

   1. in the contexts mentioned in Chapter 1 where there is eclipsis after the article in the dative case, e.g., ar an gcéad duine (EN: on the first person); leis an gcéad cheadúnas (EN: with the first license);
   2. when céad is used as a prefix in a masculine noun or in a plural noun, e.g., céadainm, an céadainm (EN: first name, the first name); Céad-Aire, an Céad-Aire (EN: First Minister, the First Minister); céadonóracha, na céadonóracha (EN: first honors, the first honors); (but céadghairm, an chéadghairm (EN: first call, the first call); céadsearc, an chéadsearc (EN: first love, the first love); according to the usual rules of the feminine noun); or as a prefix in a verb, e.g., céadbhlaisim (EN: I taste first), céadbhlaisfidh sé (EN: he will taste first) (but ón uair a chéadbhlais mé é (EN: from the time I first tasted it), according to the usual rules of verbs in the past tense, indicative mood);
   3. following the possessive adjectives (feminine, third person singular), e.g., a céad cheolchoirm (EN: her first concert) and ár, bhur, a (third person plural), e.g., ár gcéad teach (EN: our first house); bhur gcéad charr (EN: your first car); a gcéad mhac (EN: their first son).
3. The ordinal number céad causes lenition of the noun or adjective it governs in all cases, e.g., an chéad fhear (EN: the first man); an chéad bhean (EN: the first woman); na chéad cheithre ghloine (EN: the first four glasses); na chéad bhlianta (EN: the first years); clann an chéad fhir (EN: the children of the first man); mac na chéad mhná (EN: the son of the first woman); lucht na chéad bhliana (EN: the people of the first year); unless the initial letter is d, t or s, e.g., na chéad daoine (EN: the first people), an chéad saighdiúir (EN: the first soldier); an chéad turas (EN: the first journey); ceadúnas an chéad tógálaí (EN: the license of the first builder). (See 9.5.4 for more information on ordinal numbers in the genitive case.)
4. The ordinal number céad is used in the for 1, but for other ordinals ending in 1, the word aonú is used. In the nominative case, t‑ is prefixed to aonú after the article, e.g., an t‑aonú lá is tríocha (EN: the thirty-first day).

1. The singular form of the article precedes the ordinal numbers (except for the ordinal number 1, see 9.5.1), e.g., an dara bean (EN: the second woman); an dóú teach (EN: the second house); an tríú tuarascáil (EN: the third report); an ceathrú bean is fiche (EN: the twenty-fourth woman); an cúigiú comhartha is seasca (EN: the sixty-fifth sign).
2. After the ordinal number dara and all ordinal numbers ending in -ú, h is prefixed to a noun beginning with a vowel, e.g., an dara hoíche (EN: the second night); an tríú hurlár (EN: the third floor); an séú hóstán déag (EN: the sixteenth hotel); an t‑ochtú hurlár is tríocha (EN: the thirty-eighth floor).
3. The article usually precedes the first number in the ordinal number, unless a possessive adjective or gach precedes it, e.g., an tríú lá ach gach dara bliain (EN: the third day but every second year); a tríú bliain (EN: his third year).
4. A system that follows the rules of the cardinal numbers (The Established System) is used to indicate the position of a thing in a series below 100, e.g., an dara hábhar is tríocha (EN: the thirty-second item); an ceathrú cathaoir is caoga (EN: the fifty-fourth chair); an seachtú hoíche is seachtó (EN: the seventy-seventh night); an t‑ochtú madra is nócha (EN: the ninety-eighth dog).
5. No lenition is added to the word déag in the ordinal number, e.g., an tríú duine déag (EN: the thirteenth person); an t‑ochtú bosca déag (EN: the eighteenth box); an naoú leabhar déag (EN: the nineteenth book).

1. A system based on the multiplicative number system is used to indicate the position of a thing in a series above 100, e.g., céad a ceathair — an céad is ceathrú feirmeoir (EN: the one hundred and fourth farmer); cúig chéad seasca a ceathair — an cúig chéad seasca is ceathrú heitleán (EN: the five hundred and sixty-fourth airplane); seacht míle, ceithre chéad a naoi déag — an seacht míle, ceithre chéad is naoú hóstán déag (EN: the seven thousand, four hundred and nineteenth hotel).
2. Lenition is added to the word déag after the number míle, e.g., an trí mhíle dhéag is ceathrú hoileán (EN: the three thousand and fourteenth island).

1. For the ordinal number céad, the noun following it is declined and the article agrees with the number and gender of the noun, e.g., an chéad fhear, clann an chéad fhir (EN: the first man, the family of the first man); an chéad bhean, clann na chéad mhná (EN: the first woman, the family of the first woman); na chéad cheithre bliana, tús na chéad cheithre bliana (EN: the first four years, the beginning of the first four years); na chéad chúig charr, plátaí clárúcháin na chéad chúig charr (EN: the first five cars, the registration plates of the first five cars); na chéad taiscéalaithe, eachtraí na chéad taiscéalaithe (EN: the first explorers, the adventures of the first explorers).
2. For all other ordinal numbers, the noun is never declined, e.g., mac an dara bean (EN: the son of the second woman); mac an dara fear (EN: the son of the second man); eagraíocht tríú tír (EN: the organization of the third country); oideachas tríú leibhéal (EN: the third level of education); clúdach an cheathrú tuarascáil (EN: the cover of the fourth report); deireadh an fichiú haois (EN: the end of the twentieth century); tús an aonú haois is fiche (EN: the beginning of the twenty-first century).
3. The t‑ is dropped before aonú, ochtú, ochtódú, etc., e.g., an t‑aonú bliain déag, tús an aonú bliain déag (EN: the eleventh year, the beginning of the eleventh year); an t‑ochtú haois déag, tús an ochtú haois déag (EN: the eighteenth century, the beginning of the eighteenth century); an t‑ochtódú cruinniú, miontuairiscí an ochtódú cruinniú (EN: the eighteenth meeting, the minutes of the eighteenth meeting).
4. The article affects the initial mutations of the ordinal numbers as it would affect a masculine noun, e.g., bróga an chúigiú girseach (EN: the shoes of the fifth girl); seoladh an cheathrú teach is daichead (EN: the launch of the forty-fourth house); but no initial mutation is made to f or s, e.g., lucht an seachtú hoifig (EN: the people of the seventh office); bonn an fichiú himreoir (EN: the base of the twentieth player); deireadh an seascadú comhdháil (EN: the end of the sixteenth conference).

The adjective is declined according to the noun, e.g., an chéad bhean mhór (EN: the first big woman); an chéad fhear mór (EN: the first big man); seol an chéad bháid ghoirm (EN: the launch of the first blue boat); deireadh na chéad tuarascála cuimsithí (EN: the end of the first comprehensive report); na chéad scoláirí maithe (EN: the first good students); eachtraí na chéad taiscéalaithe cáiliúla (EN: the adventures of the first famous explorers); an tríú fear mór is tríocha (EN: the thirty-third big man); cóta an daicheadú bean mhór (EN: the coat of the forty-first big woman).

1. Ordinal numbers are written in figures by adding ú (EN: st, nd, rd, th) after the figure, e.g., an 1ú, an 2ú, an 19ú, an 123ú.
2. The rules for writing ordinal numbers in figures are the same as the rules for writing ordinal numbers in words (see 9.5.1 to 9.5.5 above). Note that h is prefixed before a vowel and no lenition is added after 1ú since it is aonú (not céad).

1. A standard fraction has two parts: the numerator and the denominator. The numerator is placed above the line and the denominator below the line, e.g., for 6/7, 6 is the numerator and 7 is the denominator.

2. The ordinal numbers are used to indicate the denominator except for the words leath and trian.

   Note that a special plural form treana of the noun trian is used with the numbers 3–10. The noun is left unmodified after trí, ceithre, cúig, sé, e.g., 3/3 — trí treana; 4/3 — ceithre treana; and it is eclipsed after seacht, ocht, naoi, deich, e.g., 9/3 — naoi dtreana; 10/3 — deich dtreana.

3. When the denominator is a number between 11–19, a form derived from the ordinal number is used, e.g., 4/13 — ceithre thrídéagú; 6/15 — sé chúigdéagú.
4. When the denominator is a number over 20, the order of the words is the same as that of the bare numbers but an ordinal number is used instead of a bare number at the end, e.g., 1/30 — tríochadú; 4/97 — ceithre nócha seachtú.

5. Fractions are written in several different ways, as illustrated below. Option (i) is the structure most commonly used.

   1. It is possible to use two bare numbers with the preposition ar or the compound preposition os cionn between them to express any fraction, e.g., 1/11 — a haon ar a haon déag; a haon os cionn a haon déag; 7/8 — a seacht ar a hocht; a seacht os cionn a hocht; 4/15 — a ceathair ar a cúig déag; a ceathair os cionn a cúig déag; 33/57 — tríocha a trí ar chaoga a seacht; tríocha a trí os cionn caoga a seacht; 136/82 — céad tríocha a sé ar ochtó dó; céad tríocha a sé os cionn ochtó dó. Fiche is not lenited in fractions, e.g., 3/24 — a trí ar fiche a ceathair.
   2. When the numerator is 1, the word cuid can be used with the ordinal numbers to express fractions, e.g., 1/2 — leath; an leathchuid; 1/3 — trian; an tríú cuid; 1/11 — aondéagú; an t‑aondéagú cuid. The form with cuid is usually used when the denominator is a number over 20, e.g., 1/27 — an fiche seachtú cuid; 1/156 — an céad caoga séú cuid. For the tens, however, one would rather say tríochadú, etc. ná an tríochadú cuid.
   3. When the numerator is between 2 and 10, the cardinal numbers and the ordinal form (see (b), (c) and (d) above) are used to express the fraction. Fractions are common nouns and the usual rules of the cardinal numbers are followed when counting them, e.g., 7/8 — seacht n‑ochtú; 4/15 — ceithre chúigdéagú; but fichiú is not lenited, e.g., 3/20 — trí fichiú.
   4. As an alternative to (iii) above, when the numerator is between 2 and 10 the noun ceann/cinn can be used with the preposition de and the plural form of the denominator, e.g., 7/8 — seacht gcinn d’ochtuithe; 4/15 — ceithre cinn de chúigdéaguithe;
   5. When the numerator is more than 10, bare numbers can be used as follows: the numerator (stated as a bare number) + de + the plural of the denominator, e.g., 33/57 — tríocha a trí de chaoga seachtuithe; 136/82 — céad tríocha a sé d’ochtó dóithe. This form is preferred when the numerator is more than 10 and when the denominator is more than 20.

1. The Denominator 2–19

   The following table shows two options for writing fractions with denominators from 2–19 and numerator 1.

   Table 9YThe Fractions — The Denominator 2–19

   Fraction	Denominator	Form with cuid	Fraction	Denominator	Form with cuid
   1/2	leath	an leathchuid	1/11	aondéagú	an t‑aondéagú cuid
   1/3	trian	an tríú cuid	1/12	dódhéagú	an dódhéagú cuid
   1/4	ceathrú	an ceathrú cuid	1/13	trídéagú	an trídéagú cuid
   1/5	cúigiú	an cúigiú cuid	1/14	ceathairdéagú	an ceathairdéagú cuid
   1/6	séú	an séú cuid	1/15	cúigdéagú	an cúigdéagú cuid
   1/7	seachtú	an seachtú cuid	1/16	sédéagú	an sédéagú cuid
   1/8	ochtú	an t‑ochtú cuid	1/17	seachtdéagú	an seachtdéagú cuid
   1/9	naoú	an naoú cuid	1/18	ochtdéagú	an t‑ochtdéagú cuid
   1/10	deichiú	an deichiú cuid	1/19	naoidéagú	an naoidéagú cuid

2. Denominator 20+

   The following table gives examples of how to deal with denominators above 20 (except the tens) when the numerator is 1. The form with cuid is usually used for such fractions. The order of that form is the same as that used in the cardinal numbers but an ordinal number is used instead of a bare number at the end and the numeral a is left in the middle.

   Table 9ZThe Fractions — The Denominator 20+

   Fraction	Form with cuid	Fraction	Form with cuid
   1/21	an fiche aonú cuid	1/87	an t‑ochtó seachtú cuid
   1/32	an tríocha dóú cuid	1/98	an nócha ochtú cuid
   1/43	an daichead tríú cuid	1/99	an nócha naoú cuid
   1/54	an caoga ceathrú cuid	1/156	an céad caoga séú cuid
   1/65	an seasca cúigiú cuid	1/2,987	an dá mhíle naoi gcéad ochtó seachtú cuid
   1/76	an seachtó séú cuid	1/3,234,567	an trí mhilliún, dhá chéad tríocha is ceithre mhíle, cúig chéad seasca seachtú cuid

   Note that an ordinal number is used for the tens, e.g., fichiú, céadú, míliú, etc., and that the form with cuid is not usually used with them, e.g., 1/30 — tríochadú; 1/50 — caogadú.

1. The Numerator 2–10
   1. The cardinal number system is followed when the numerator is more than 1 since the denominators are common nouns (exception: fichiú is not lenited, e.g., trí fichiú). The following table gives examples of fractions when the numerator is a number between 2 and 10.

      Table 9AAThe Fractions — The Numerator 2–10

      Fraction		Fraction		Fraction
      3/2	trí leath	2/11	dhá aondéagú	4/30	ceithre thríochadú
      2/3	dhá thrian	3/12	trí dhódhéagú	5/40	cúig dhaicheadú
      5/4	cúig cheathrú	4/13	ceithre thrídéagú	6/50	sé chaogadú
      4/7	ceithre sheachtú	7/16	seacht sédéagú	9/80	naoi n‑ochtódú
      8/9	ocht naoú	9/18	naoi n‑ochtdéagú	9/100	naoi gcéadú
      9/10	naoi ndeichiú	6/19	sé naoidéagú	3/1,000	trí mhíliú
      10/3	deich dtreana	3/20	trí fichiú	5/1,000,000	cúig mhilliúnú

   2. Alternatively, the noun ceann/cinn can be used with the preposition de and the plural form of the denominator.

      Table 9BBThe Fractions — The Numerator 2–10 — The Form with ceann/cinn and the Preposition de

      Fraction	ceann/cinn + de	Fraction	ceann/cinn + de
      2/21	dhá cheann de fiche aonuithe	10/156	deich gcinn de chéad caoga séithe
      3/32	trí cinn de thríocha dóithe	5/209	cúig cinn de dhá chéad naoithe
      4/43	ceithre cinn de dhaichead tríthe	2/2,987	dhá cheann de dhá mhíle, naoi gcéad ochtó seachtuithe
      5/54	cúig cinn de chaoga ceathruithe	3/3,234,567	trí cinn de thrí mhilliún, dhá chéad tríocha is ceithre mhíle, cúig chéad seasca seachtuithe

2. The Fractions when the Numerator is more than 10

   When the numerator is more than 10, bare numbers are used as follows: the numerator (stated as a bare number) + de + the plural of the denominator.

   Table 9CCWhen the numerator is more than 10, bare numbers are used as follows: the numerator (stated as a bare number) + de + the plural of the denominator.

   Fraction	Bare Number Modified by de	Fraction	Bare Number Modified by de
   11/2	a haon déag de leatha	19/12	a naoi déag de dhódhéaguithe
   12/3	a dó dhéag de thrianta	20/19	fiche de naoidéaguithe
   15/6	a cúig déag de shéithe	45/17	daichead a cúig de sheachtdéaguithe
   17/8	a seacht déag d’ochtuithe	87/13	ochtó a seacht de thrídéaguithe
   18/9	a hocht déag de naoithe	123/12	céad fiche a trí de dhódhéaguithe

#9.6.4 Large Numerators and Denominators