Italian fractions, decimals, and arithmetic come together as a small ecosystem with a few features that consistently surprise English speakers: the comma, not the period, marks decimals; mezzo and mezza are full-fledged adjectives, not just "half"; fractions reuse the ordinals you've already learned; and the language has a beautiful system of approximate quantities — una decina, un centinaio, migliaia — that English handles only awkwardly.
This page covers the four mathematical zones — fractions, decimals, percentages, arithmetic — plus the approximation system that lives in the same conceptual neighbourhood.
Fractions: cardinal numerator + ordinal-style denominator
The Italian fraction is built on a simple pattern: a cardinal number for the numerator, an ordinal for the denominator. One third is un terzo, one quarter is un quarto, one fifth is un quinto — the second word in each pair is the masculine singular ordinal you already know.
| Fraction | Italian | Construction |
|---|---|---|
| 1/2 | un mezzo (or mezzo) | special — see below |
| 1/3 | un terzo | cardinal 1 + ordinal 3rd |
| 1/4 | un quarto | cardinal 1 + ordinal 4th |
| 1/5 | un quinto | cardinal 1 + ordinal 5th |
| 1/6 | un sesto | cardinal 1 + ordinal 6th |
| 1/8 | un ottavo | cardinal 1 + ordinal 8th |
| 1/10 | un decimo | cardinal 1 + ordinal 10th |
| 1/12 | un dodicesimo | cardinal 1 + ordinal 12th |
| 1/100 | un centesimo | cardinal 1 + ordinal 100th |
For numerators greater than one, the denominator pluralises — it's still an ordinal, and ordinals are full adjectives that agree in number.
- 2/3 → due terzi
- 3/4 → tre quarti
- 5/8 → cinque ottavi
- 7/12 → sette dodicesimi
- 99/100 → novantanove centesimi
Ho mangiato tre quarti della pizza, scusami.
I ate three-quarters of the pizza, sorry.
Due terzi degli italiani vivono in città.
Two-thirds of Italians live in cities.
Cinque ottavi sono più di mezzo.
Five-eighths is more than half.
Halves: mezzo / mezza — adjective vs. noun
Half is the one fraction that breaks the pattern, because Italian inherits two distinct words for it.
As an adjective, mezzo agrees in gender and number with the noun it modifies. It typically goes before the noun.
- mezza ora — half an hour (feminine ora → feminine mezza)
- mezzo bicchiere — half a glass (masculine bicchiere → masculine mezzo)
- mezza giornata — half a day
- mezzo chilo — half a kilo
- mezza bottiglia — half a bottle
Ti aspetto da mezz'ora.
I've been waiting for you for half an hour.
Bevo solo mezzo bicchiere di vino a cena.
I only drink half a glass of wine at dinner.
Posso prendere mezza giornata di ferie?
Can I take half a day off?
As a noun (the abstract fraction 1/2), mezzo is masculine: un mezzo. This form is rare in everyday speech but appears in mathematical contexts.
Un mezzo più un mezzo fa uno.
One half plus one half makes one.
Tre quarti meno un mezzo fa un quarto.
Three-quarters minus a half makes a quarter.
In conversation, "half" of something is usually expressed with metà, a feminine noun, rather than un mezzo: la metà della classe (half the class), la metà della torta (half the cake). Mezzo as a freestanding noun belongs to arithmetic; metà belongs to ordinary description.
Solo la metà della classe ha superato l'esame.
Only half the class passed the exam.
Mi dai la metà del tuo panino?
Will you give me half your sandwich?
Decimals: the comma is the separator
This is the single most important typographic difference between Italian and English numbers: Italian uses a comma where English uses a period, and vice versa.
- English 3.14 → Italian 3,14
- English 0.5 → Italian 0,5
- English 1,000.50 → Italian 1.000,50
The comma marks decimals; the period (or, more often, a thin space) marks thousands. This is the European standard — French, German, Spanish, and most other European languages share it. Reading 3,14 aloud, you say tre virgola quattordici ("three comma fourteen") — virgola is the spoken word for the decimal separator.
Pi greco è circa tre virgola quattordici.
Pi is about 3.14.
La temperatura è scesa a meno cinque virgola due gradi.
The temperature dropped to minus 5.2 degrees.
L'inflazione è dello zero virgola otto per cento.
Inflation is at 0.8 percent.
Currency: euros and cents
Italian prices follow the decimal-comma rule. €10,50 is dieci euro e cinquanta in conversation, where cinquanta is read as "fifty cents" by inference. The full form dieci virgola cinquanta euro exists but is rare in everyday speech — Italians read prices the way English speakers read dollars and cents.
- €2,50 → due euro e cinquanta
- €5,99 → cinque euro e novantanove
- €100,00 → cento euro
- €1.000,00 → mille euro (note: the period separates thousands)
Quanto costa? Tre euro e cinquanta.
How much is it? Three fifty.
Il pranzo è venuto venticinque euro e settanta in due.
Lunch came to twenty-five seventy for two.
The plural of euro in Italian is, officially, euro — invariable. Dieci euro, not dieci euri. (The form euri is an informal variant heard occasionally and grates on careful speakers; stick with euro.) Centesimo (cent) does pluralise normally: cinquanta centesimi.
Percentages: per cento
Italian percentages use the construction cardinal + per cento, written either 50% or 50 per cento (with a thin space).
Il cinquanta per cento degli studenti ha approvato la proposta.
Fifty percent of the students approved the proposal.
L'IVA in Italia è del ventidue per cento.
VAT in Italy is 22%.
Lo sconto è del trenta per cento.
The discount is 30%.
The percentage takes the same definite article construction with prepositions: del ventidue per cento, al cinquanta per cento, con il dieci per cento. The number itself is read as an ordinary cardinal — trentatré per cento, cinquantacinque virgola cinque per cento (with decimals).
Arithmetic: the four operations
Italian arithmetic uses four small words for the operations and either fa or uguale for the equals sign.
| Symbol | Italian | Equation | Read aloud |
|---|---|---|---|
| + | più | 2 + 2 = 4 | due più due fa quattro |
| − | meno | 5 − 3 = 2 | cinque meno tre fa due |
| × | per | 3 × 4 = 12 | tre per quattro fa dodici |
| ÷ | diviso (per) | 10 ÷ 2 = 5 | dieci diviso (per) due fa cinque |
| = | fa / uguale | — | fa, uguale a, è uguale a |
The verb at the end is most often fa ("makes") in casual arithmetic — the form children use at school and adults use when calculating aloud. Uguale ("equal to") is more formal and shows up in classrooms, mathematical exposition, and writing.
Quattro più cinque fa nove.
Four plus five is nine.
Tre per sette fa ventuno.
Three times seven is twenty-one.
Cento diviso quattro fa venticinque.
One hundred divided by four is twenty-five.
Otto meno tre uguale cinque.
Eight minus three equals five (more formal register).
For division, the per in diviso per is optional: dieci diviso due or dieci diviso per due — both are correct, with the shorter form slightly more common in casual speech.
Squares, cubes, and powers
For exponents, Italian uses alla + ordinal:
- 3² → tre alla seconda (three squared, or "three to the second")
- 5³ → cinque alla terza (five cubed, or "five to the third")
- 2¹⁰ → due alla decima (two to the tenth)
You'll also hear al quadrato for squares and al cubo for cubes, in everyday speech and physics class.
Tre alla seconda fa nove.
Three squared is nine.
Due al cubo è otto.
Two cubed is eight.
For square roots, radice quadrata di: la radice quadrata di nove fa tre.
Approximate quantities: una decina, un centinaio, migliaia
Here is one of Italian's quiet treasures: a complete set of nouns that mean "about X." English approximates with "around" or "roughly"; Italian builds the approximation into the number itself.
| Italian | Meaning | Example |
|---|---|---|
| una decina | about ten | una decina di persone |
| una dozzina | a dozen (twelve, exactly) | una dozzina di uova |
| una quindicina | about fifteen | una quindicina di giorni (a fortnight) |
| una ventina | about twenty | una ventina di euro |
| una trentina | about thirty | una trentina di anni |
| una quarantina | about forty | una quarantina di chilometri |
| una cinquantina | about fifty | una cinquantina di pagine |
| un centinaio | about a hundred | un centinaio di persone |
| un migliaio | about a thousand | un migliaio di euro |
Alla festa c'erano una ventina di persone.
There were about twenty people at the party.
Ci vediamo tra una decina di minuti.
See you in about ten minutes.
Ho una quarantina d'anni.
I'm about forty (in my forties).
These nouns take the partitive di before the noun being counted: una decina di persone, una ventina di euro. The construction is invariant — you don't say una decina persone or una decina i persone.
The plural forms: centinaia, migliaia
The two big approximators have irregular plural forms that end in -a (a feminine plural inherited from the Latin neuter plural — the same pattern that gives us uovo / uova and ginocchio / ginocchia).
- un centinaio (about a hundred) → centinaia (hundreds)
- un migliaio (about a thousand) → migliaia (thousands)
Centinaia di tifosi sono andati allo stadio.
Hundreds of fans went to the stadium.
Migliaia di persone hanno firmato la petizione.
Thousands of people signed the petition.
Migliaia di anni fa, qui c'era il mare.
Thousands of years ago, there was sea here.
Una dozzina: the exception
Dozzina — a dozen — is exact, not approximate. Una dozzina di uova is exactly twelve eggs, the way it's sold at the market. The -ina ending is misleading here: quindicina, ventina, trentina are all approximate, but dozzina alone is the exact dozen.
Una dozzina di uova, per favore.
A dozen eggs, please.
Mezza dozzina di rose rosse.
Half a dozen red roses.
Ordinal numbers as fractions in everyday speech
One quiet Italian habit: native speakers often use the ordinal alone to imply a fraction. Un terzo literally means "one third" but in context can mean "the third part" of something previously mentioned. The article changes the meaning subtly — il terzo is "the third [thing]" while un terzo is the fraction.
Un quinto degli studenti era assente.
A fifth of the students were absent.
Riserviamo un decimo del bilancio per la pubblicità.
We reserve a tenth of the budget for advertising.
Common Mistakes
❌ Pi greco è 3.14.
Wrong notation — Italian uses a comma for decimals: 3,14.
✅ Pi greco è 3,14 (tre virgola quattordici).
Pi is 3.14 (three point fourteen).
❌ Mille euri.
Wrong — euro is invariable in standard Italian, not 'euri'.
✅ Mille euro.
A thousand euros.
❌ Tre alla due fa nove.
Wrong — exponents use the feminine ordinal: alla seconda, alla terza, alla decima.
✅ Tre alla seconda fa nove.
Three squared is nine.
❌ Un mezzo bicchiere di vino.
Wrong — as an adjective before a noun, half is just mezzo (no article): mezzo bicchiere.
✅ Mezzo bicchiere di vino.
Half a glass of wine.
❌ Una decina persone.
Wrong — approximators take the partitive di before the noun.
✅ Una decina di persone.
About ten people.
❌ Lo sconto è del cinquanta percento.
Wrong — Italian writes per cento as two words, not the anglicised single-word percento.
✅ Lo sconto è del cinquanta per cento.
The discount is fifty percent.
Key takeaways
Fractions use cardinal + ordinal: un terzo, due terzi, cinque ottavi. The ordinal pluralises with the numerator.
Halves have three forms: mezzo / mezza as an agreeing adjective (mezza ora), un mezzo as the abstract fraction in math, metà as the feminine noun for "half of" (la metà della classe).
The decimal separator is a comma: 3,14 is tre virgola quattordici. The period separates thousands: 1.000,50.
Arithmetic uses più / meno / per / diviso (per) with fa (casual) or uguale (formal) as "equals."
Italian has dedicated nouns for approximate quantities: una decina, una ventina, un centinaio, migliaia. They take the partitive di before the counted noun.
Dozzina is exact (twelve); the other -ina forms are approximate.
For the cardinals fractions are built from, see cardinals 0–20. For the ordinals that supply the denominators, see ordinals. For half-hour times, see telling time.
Now practice Italian
Reading grammar gets you part of the way. The exercises are where it sticks — free, no signup needed.
Open the Italian course →Related Topics
- Italian Numbers: OverviewA1 — An introduction to the Italian number system: cardinals (uno, due, tre), ordinals (primo, secondo, terzo), dates, time, measurements, fractions, and Italian's reversed punctuation conventions (decimal comma, thousands period).
- Italian Ordinal NumbersA1 — How to form and use Italian ordinals — primo through decimo, the productive -esimo suffix from undicesimo onward, full agreement in gender and number, and the special roles ordinals play in dates, centuries, popes, and rankings.
- Cardinal Numbers 0–20A1 — The Italian numbers from zero to twenty, with full pronunciation, stress patterns, the inflection of uno (un/uno/una/un'), the invariable status of due and tre, the accent on -tré in compounds, and the irregular forms diciassette and diciannove.
- Cardinal Numbers 100+A2 — Italian large numbers: cento and its compounds (duecento, trecento), mille and its plural mila (duemila, tremila), milione and miliardo (which DO inflect), the one-word concatenation rule up to a million, year notation, and Italian's reversed punctuation conventions for big numbers.
- Time ExpressionsA1 — How Italians talk about time — clock time, parts of the day, days and weeks and years past and future, frequency, speed, and the duration construction with present + da.
- Telling Time in ItalianA1 — How to ask and tell the time in Italian — the singular È l'una for 1:00 and plural Sono le tre for 3:00, the use of mezzo, mezza, and un quarto, the special words mezzogiorno and mezzanotte, the 24-hour clock for trains and TV schedules, and the prepositions a / alle for appointments.