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Spanish Grammar: Numbers & Math
Numbers Defined
Cardinal Numbers
Cardinal numbers, or simply cardinals, are those numbers (one, two, three, four, etc.) that are used to indicate the quantity of things in a group or set. The cardinal numbers answer the question How much? or How many?
I have owned four cars. (cardinal)
Ordinal Numbers
Ordinal numbers, or simply ordinals, are those numbers (1st, 2nd, 3rd, 4th, etc.) that indicate the order or position of something in a group or set. The ordinal numbers answer the question Which one? English and Spanish both have cardinal and ordinal numbers.This is the fourth car I have owned. (ordinal)
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CARDINAL NUMBERS
Uno and ciento and its multiples are the only cardinal numbers that change form.
1. Uno and numbers ending in uno (veinte y uno, treinta y uno, etc.) drop the final -o before a masculine noun.
María compra un libro.
Maria buys a book.
Compare:
Tengo una hermana.
I have a sister.
Tengo veinte y un (veintiún) sombreros.
I have twenty-one hats.
Note: The form uno is used after or in place of a masculine noun.
Voy a estudiar Capítulo Veinte y Uno.
I am going to study Chapter Twenty-one.
Él tiene muchos amigos, pero yo tengo solamente uno.
He has many friends, but I have only one.
(a) Ciento changes to cien before nouns, and before mil and millones.
Ciento setenta y seis
176
but:
Cien libros
100 books
Cien mil habitantes
100,000 inhabitants
Cien millones de dólares
100,000,000 dollars
(b) Multiples of ciento (doscientos, trescientos) agree in gender with the nouns they modify.
Compra doscientos libros.
He buys 200 books.
Hay doscientas muchachas en nuestra escuela.
There are 200 girls in our school.
El libro tiene cuatrocientas cuarenta y seis páginas.
The book has 446 pages.
2. Un is omitted before cien(to) and mil.
ciento
one hundred
cien alumnos
one hundred students
mil hombres
one thousand men
However, un is used with millón. De follows millón when a noun is used with it.
un millón
one million
un millón de personas
one million people
dos millones de habitantes
two million inhabitants
3. Numbers over 100 use y only if they end in a number which takes
y when it stands alone (16, 19, 27, 41, etc.).
ciento tres
103
ciento quince
115
ciento treinta
130
but:
ciento diez y seis (dieciséis)
116
doscientos setenta y nueve
279
4. The use of the decimal and comma with Arabic numbers (1, 2, 3, 4, etc.) is just the reverse of English.
| Spanish | English |
| $1.000 | $1,000 |
| $9.500.000 | $9,500,000 |
| $2,25 | $2.25 |
To designate volumes, chapters, pages, etc., either cardinal or ordinal numbers are used through tenth; above ten, cardinal numbers are used.
La séptima página (la página siete)
Page seven
But:
Falta la cuarta página.
The fourth page is missing.
Falta la página cuarenta y siete.
Page 47 is missing.
Note: The definite article el is used before the numeral and de before the name of the month.
Note: When referring to days of the month, the ordinal primero translates as first.
el dos de mayo
May 2
Nací el tres de mayo.
I was born on the third of May.
El cinco de mayo es día de fiesta en México.
The fifth of May is a holiday in Mexico.
But:
el primero de enero
January 1
El sábado es el primero de mayo.
Saturday is the first of May.
The numbers from 16 through 29 may be written as one word: dieciséis (16), diecisiete (17), dieciocho (18), veintiuno or veintiún (21), veintidós (22), etc.
Note: The change from -y to -i, and -z to -e, and the need for a written accent on dieciséis, veintiún, veintidós, veintitrés, and veintiséis, when the one-word form is used.
Ciento is not generally used when referring collectively to a group. Instead centenar is used. The same holds true for mil. Millar or miles is used in its place.
Note: Centenar and millar are usually followed by the preposition de (of).
Te lo he dicho centenares de veces.
I've told you hundreds of times.
Había centenares de ciclistas.
There were hundreds of cyclists.
Tenía centenares de soldados a su mando.
He had hundreds of soldiers under his command.
millares (miles) de visitantes
thousands of visitors
La gente huía del país a millares (miles).
People were fleeing the country by the thousands.
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TABLE OF CARDINAL NUMBERS
0 through 10
| cero | 0 |
seis | 6 |
| uno, -a | 1 |
siete | 7 |
| dos | 2 |
ocho | 8 |
| tres | 3 |
nueve | 9 |
| cuatro | 4 |
diez | 10 |
| cinco | 5 |
11 through 21
| once | 11 |
diez y seis, dieciséis | 16 |
| doce | 12 |
diez y siete, diecisiete | 17 |
| trece | 13 |
diez y ocho, dieciocho | 18 |
| catorce | 14 |
diez y nueve, diecinueve | 19 |
| quince | 15 |
veinte | 20 |
| veinte y uno, veintidós | 21 etc. |
Multiples of 10
| treinta | 30 |
setenta | 70 |
| cuarenta | 40 |
ochenta | 80 |
| cincuenta | 50 |
noventa | 90 |
| sesenta | 60 |
cien(to) | 100 |
| ciento (y) uno, etc. | 101 etc. |
Multiples of 100
Note: As adjectives, the numbers 200 to 900 adjectives are made feminine by dropping the -os and adding -as.
| doscientos | 200 |
ochocientos | 800 |
| trescientos | 300 |
novecientos | 900 |
| cuatrocientos | 400 |
mil | 1,000 |
| quinientos | 500 |
dos mil | 2,000 |
| seiscientos | 600 |
un millón | 1,000,000 |
| setecientos | 700 |
un billón | 1,000,000,000,000 |
Note: Un billón is the equivalent of one trillion.
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ORDINAL NUMBERS
The ordinal numbers have feminine forms ending in -a. Primero and tercero lose the final -o before a masculine singular noun. Above ten, the cardinal numbers generally replace the ordinals in Spanish. Note that as adjectives, ordinals must also agree in number (singular, plural) with the nouns they modify.
el primer hombre
the first man
la primera visita
the first visit
el tercer día
the third day
la tercera palabra
the third word
la segunda frase
the second sentence
Enrique Cuarto
Henry IV
Ordinal numbers are generally used only through décimo. To
express ordinal numbers above tenth, the cardinal numbers are usually
used. With titles of royalty and popes the definite article is not
used before the numeral and the ordinal must follow the names.
la calle veintidós
twenty-second street
lección quince
the fifteenth lesson (lesson fifteen)
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TABLE OF ORDINAL NUMBERS
1st through 10th
| primero | 1st |
sexto | 6th |
| segundo | 2nd |
séptimo | 7th |
| tercero | 3rd |
octavo | 8th |
| cuarto | 4th |
noveno (or nono) | 9th |
| quinto | 5th |
décimo | 10th |
11th through 20th
| undécimo | 11th |
décimo sexto | 16th |
| duodécimo | 12th |
décimo séptimo | 17th |
| décimo tercero | 13th |
décimo octavo | 18th |
| décimo cuarto | 14th |
décimo noveno | 19th |
| décimo quinto | 15th |
vigésimo | 20th |
21st through 1,000,000th
| vigésimo primero | 21st |
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| vigésimo segundo | 22nd |
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| trigésimo | 30th |
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| cuadragésimo | 40th |
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| quincuagésimo | 50th |
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| sexagésimo | 60th |
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| septuagésimo | 70th |
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| octogésimo | 80th |
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| nonagésimo | 90th |
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| centésimo | 100th |
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| milésimo | 1,000th |
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| millonésimo | 1,000,000th |
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MATHEMATICAL SIGNS
| más (or y) | + plus |
| menos | — minus |
| por | x times |
| dividido por | ÷ divided by |
| es, son | = is/are |
Dos y dos son cuatro.
Two plus two is four.
2 + 2 = 4
Tres menos uno son dos.
Three minus one is two.
3 - 1 = 2
Cuatro por dos son ocho.
Four times two is eight.
4 X 2 = 8
Diez dividido por dos son cinco.
Ten divided by two is five.
10 ÷ 2 = 5
Veces (times), multiplicado por (multiplied by), and es igual a (equals) are alternative uses.
Tres multiplicado por dos son seis.
Three multiplied by two is six.
35 dividido por 5 son 7.
35 divided by 5 is 7.
Dos más dos es igual a cuatro.
Two plus two is four.
4 veces 5 son 20.
4 times 5 is 20.
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FRACTIONS
Fractions through tenth are expressed by cardinals in the numerator and ordinals in the denominator, as in English. Two forms are irregular. Half is expressed by medio as an adjective and by la mitad as a noun. Third is expressed by tercio.
Los cinco octavos de la tierra
Five-eighths of the earth
Un año y medio
A year and a half
Media libra
Half a pound
La mitad de los estudiantes
Half the students
Dos y tres décimos
Two and three-tenths
The noun half is represented in Spanish by mitad and half, the adjective, is translated as medio, -a.
Cortó la manzana por la mitad.
She cut the apple in half.
Llegó a mitad de la película.
He arrived halfway through the film.
Añadir medio vaso de vino blanco.
Add half a glass of white wine.
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Table of Fractions
| un medio | 1/2 |
un séptimo | 1/7 |
| un tercio | 1/3 |
un octavo | 1/8 |
| un cuarto | 1/4 |
un noveno | 1/9 |
| un quinto | 1/5 |
un décimo | 1/10 |
| un sexto | 1/6 |