Understanding French Fractions and Decimals
French fractions and decimals express parts of a whole and precise quantities. They are essential for:
Common uses:
- Cooking: une demi-tasse (half a cup)
- Time: une heure et demie (an hour and a half)
- Measurements: deux mètres et demi (2.5 meters)
- Statistics: un tiers des étudiants (one third of students)
- Prices: trois euros cinquante (3.50 euros)
Key differences from English:
- Decimal separator: virgule (comma) instead of point
- Fraction formation: different patterns for common fractions
- Agreement: fractions can agree like adjectives
Understanding French fractions and decimals is crucial for precise communication in academic, professional, and everyday contexts.
Examples
J'ai mangé la moitié du gâteau. (I ate half of the cake.)
Expressing parts - portion of a whole
Le prix est de quinze euros virgule quatre-vingt-dix. (The price is 15.90 euros.)
Decimal expression - precise amounts
Un quart des élèves sont absents. (A quarter of the students are absent.)
Statistical expression - proportional relationships
Common Fractions
The most frequently used fractions have special forms:
Basic French Fractions
| Pronoun | Conjugation | English |
|---|---|---|
| un demi | 1/2 | une demi-heure (half an hour) |
| un tiers | 1/3 | un tiers du temps (a third of the time) |
| un quart | 1/4 | un quart d'heure (a quarter hour) |
| trois quarts | 3/4 | trois quarts d'heure (three quarters of an hour) |
| un cinquième | 1/5 | un cinquième de la population (a fifth of the population) |
| un dixième | 1/10 | un dixième de seconde (a tenth of a second) |
Special Vocabulary
Alternative words for common fractions:
la moitié = un demi (half)
le tiers = un tiers (third)
le quart = un quart (quarter)
Used as nouns: La moitié est partie.
UN DEMI - Half
UN DEMI has several forms and uses:
Examples
Une demi-heure (half an hour) - hyphenated compound
Une heure et demie (an hour and a half) - separate word
Un demi-litre (half a liter)
Deux litres et demi (two and a half liters)
DEMI as Prefix
Hyphenated compounds with demi-:
une demi-bouteille (half bottle)
un demi-kilo (half kilo)
une demi-journée (half day)
un demi-siècle (half century)
ET DEMI after Numbers
Adding "and a half" to quantities:
trois heures et demie (three and a half hours)
cinq kilos et demi (five and a half kilos)
Agreement Rules
DEMI agreement patterns:
Before noun: invariable - une demi-heure
After noun: agrees - une heure et demie
Formation of Other Fractions
Most fractions are formed using ordinal numbers:
Fraction Formation Pattern
| Pronoun | Conjugation | English |
|---|---|---|
| un + ordinal | fraction | un cinquième (1/5), un sixième (1/6) |
| deux + ordinal | fraction | deux cinquièmes (2/5), trois sixièmes (3/6) |
| numerator + ordinal | fraction | sept dixièmes (7/10), neuf centièmes (9/100) |
Regular Pattern
Cardinal + ordinal formation:
2/7 = deux septièmes
5/8 = cinq huitièmes
3/10 = trois dixièmes
7/100 = sept centièmes
Decimal Numbers
French uses virgule (comma) as the decimal separator:
Examples
2,5 = deux virgule cinq (2.5)
15,75 = quinze virgule soixante-quinze (15.75)
0,25 = zéro virgule vingt-cinq (0.25)
3,14 = trois virgule quatorze (3.14)
Reading Decimals
How to pronounce decimal numbers:
1,2 = un virgule deux
10,05 = dix virgule zéro cinq
Writing Convention
French decimal notation:
French: 3,14 (comma)
English: 3.14 (period)
Percentages
French percentages use pour cent:
Examples
25% = vingt-cinq pour cent
50% = cinquante pour cent
100% = cent pour cent
0,5% = zéro virgule cinq pour cent
Percentage Expressions
Common percentage phrases:
Un pourcentage élevé (a high percentage)
Le taux de réussite (the success rate)
Time Expressions with Fractions
Fractions are commonly used with time:
Time Fractions
| Pronoun | Conjugation | English |
|---|---|---|
| un quart d'heure | 15 minutes | quarter hour |
| une demi-heure | 30 minutes | half hour |
| trois quarts d'heure | 45 minutes | three quarters hour |
| une heure et quart | 1:15 | quarter past one |
| une heure et demie | 1:30 | half past one |
| deux heures moins le quart | 1:45 | quarter to two |
Clock Time
Telling time with fractions:
Il est trois heures et quart. (It's quarter past three.)
Il est midi et demi. (It's half past noon.)
Cooking and Measurements
Fractions are essential in cooking and measurements:
Examples
Une demi-tasse de farine (half a cup of flour)
Un quart de litre de lait (a quarter liter of milk)
Deux kilos et demi de pommes (2.5 kilos of apples)
Un tiers de cuillère à café (a third of a teaspoon)
Recipe Language
Common cooking fractions:
une demi-cuillère (half spoon)
un quart de tasse (quarter cup)
Mathematical Operations
Expressing mathematical operations with fractions:
Examples
Un tiers plus un tiers égale deux tiers. (1/3 + 1/3 = 2/3)
La moitié de huit est quatre. (Half of eight is four.)
Mathematical Vocabulary
Key terms for fraction operations:
plus (plus), moins (minus), fois (times)
divisé par (divided by), égale (equals)
Money and Prices
Using decimals with currency:
Examples
Trois euros cinquante (3.50 euros)
Quinze euros quatre-vingt-dix (15.90 euros)
Un euro vingt-cinq (1.25 euros)
Cent euros pile (exactly 100 euros)
Price Expressions
Common ways to express prices:
Ça coûte deux euros cinquante. (It costs 2.50 euros.)
Le prix est de quinze euros. (The price is 15 euros.)
Statistics and Proportions
Using fractions in statistical contexts:
Examples
Un tiers des étudiants réussissent. (One third of students succeed.)
La moitié de la population vote. (Half the population votes.)
Deux cinquièmes du budget (two fifths of the budget)
Trois quarts du temps (three quarters of the time)
Common Mistakes with Fractions
Here are frequent errors students make:
1. Decimal separator: Using period instead of comma
2. DEMI agreement: Wrong agreement patterns with demi
3. Fraction formation: Incorrect ordinal number usage
4. Time expressions: Mixing up fraction time patterns
Examples
❌ 2.5 → ✅ 2,5
Wrong: French uses comma, not period for decimals
❌ une demie-heure → ✅ une demi-heure
Wrong: DEMI before noun doesn't agree
❌ deux heures et demi → ✅ deux heures et demie
Wrong: DEMI after feminine noun must agree
❌ un quatrième → ✅ un quart
Wrong: quarter has special form, not ordinal