The Ancient Romans preferred concrete, tangible concepts over abstraction. They always attached numbers to things, which explains why they ignored the concept of zero.
Familiar with the abacus for calculation, the Romans conceived numbers as sets or groups of objects. For example, the abstract equation 3 × 4 = 12 was understood as “three times a set of four objects gives twelve,” in Latin: ter quaterna duodecim sunt. Similarly, a division like 100 ÷ 5 = 20 was seen as “one hundred items divided into groups of five gives twenty parts,” or si centum in quinos partimur, fiunt eorum viginti partes.
This idea of grouping remained central in Latin. You do not say “in couple” but bini, not “in threes” but terni, not “in single file” but singuli. Romans did not think in terms of abstract numbers as we do today. To express multiplication or division, they used three categories: number adjectives (the result), number adverbs (iterations of a set), and number distributives (the set itself). [See: http://www.informalmusic.com/latinsoc/latnum.html]
Some Roman Fractions
Although lacking a zero, the Romans had a sophisticated fraction system, derived from weights and measures of land. Romans used symbols such as S for ½ and dot patterns like the quincunx for fractions. Most fraction names came from the as—a bronze coin or pound—divided into twelve parts (unciae):
- deunx (11/12)
- decunx (10/12)
- nonuncium / dodrans (9/12)
- bes / bessis (2/3)
- septunx (7/12)
- semis (1/2)
- quincunx (5/12)
- triens (1/3)
- quadrans / teruncius (1/4)
- sextans (1/6)
- sesuncia (1/8)
- uncia (1/12)
- semiuncia (1/24)
- binae sextulae / duella (1/36)
- siculus (1/48)
- sextula (1/72)
- dimidia sextula (1/144)
- scripulum (1/288)
Curiosity: The abacus lives on. In Japan, the soroban is still taught in primary schools, not only as a historical tool but as a means to develop rapid mental calculation. With the visual imagery of a soroban, one can sometimes calculate as quickly—or faster—than with a calculator.
☞ Discover the fascinating history of numerals,