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Fractions
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Fractions are numerical constructions such as 3/4, 5/8, or 3.234 indicating the quotient of two numbers. From a linguistic point of view, Dutch fractions are complex formations consisting of one ordinal and one or two cardinals, and optionally a coordinatingenand, such as drie-vierde3/4 and drie-en-vijf-achtstethree and five eighth3 5/8; there are special forms for the smallest numbers halfhalf1/2, derdethird1/3, kwartquarter1/4 and for one combination anderhalfotherhalf1 1/2. Decimal fractions such as drie komma tweevierendertigthree point two four and thirty3.234 have their own grammar.

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Vulgar fractions are built from one cardinal and one ordinal by means of a process that looks like compounding. The semantics is multiplicative: een zevendeone seventh, twee zesdetwo sixth2*(1/6). There are special forms for the smallest numbers (een) half(a) half1/2, (een) derde(one) third1/3 (the same irregular form as the ordinal) and (een) kwart(one) quarter1/4; the regular forms (een) tweedea two-th1/2 and een() vierdeone four-th1/4 are possible in certain genres (mathematics, very formal writing).

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Historically related (via umlaut) to half is the noun helfthalf (see Etymologiebank).

Complex fractions are built from a cardinal, an optional en, and a simple fraction. There is a special form for one combination anderhalfotherhalf1 1/2; the regular form een een tweedeone one two-th1 1/2 is possible in certain genres (mathematics, very formal writing). The semantics of complex fractions is a combination of addition and multiplication: twee twee zesdetwo two sixth2+(2*(1/6)), twee en twee zesdetwo and two sixth2+(2*(1/6)).

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The semantics of simple fractions is multiplicative. However, whereas multiplication in mathematics is commutative, it is not in Dutch and related languages. That is, in mathematics, the order of the elements multiplied is irrelevant: three times six is the same as six times three. But in natural language fractions, only one word order is possible, viz., cardinal before ordinal: een zevendeone seventh1/7 is fine, *zevende eenseventh one is ungrammatical as a fraction.

Decimal fractions have their own grammar, derived from spelling pronunciation, allowing for some variation: twee komma zeventwo point seven2.7, vierendertig komma honderdeenentachtigfour and thirty point hundred one and eighty34.181, vierendertig komma eenen acht eenfour and thirty point one eight one34.181. There is at least one idiom built on this construction schema: nul komma nulzero point zero0.0, zero, nada, zilch.

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Fractions thus have a construction-specific semantics: the ordinals have a different meaning when used to build fractions than when they are used as “real” ordinals.

German fractions are not identical to ordinal numbers, as they receive the ending -tel (ein Zwölf-tel) or -stel (ein Zwanzig-stel); they are declined like neuter nouns. Except for 1/2, they do not change in the plural: 1/2 ein Halb / die Hälfte, 1/3 ein Drittel, 1/4 ein Viertel, 1/5 ein Fünftel, 1/6 ein Sechstel, 1/7 ein Siebtel, 1/8 ein Achtel, 1/9 ein Neuntel, 1/10 ein Zehntel, 1/11 ein Elftel, 1/12 ein Zwölftel, 1/13 ein Dreizehntel, . . ., 1/20 ein Zwanzigstel, 1/73 ein Dreiundsiebzigstel, 1/100 ein Hundertstel, 1/5041 ein Fünftausendeinundvierzigstel, 3/4 drei Viertel, 52/89 zweiundfünfzig Neunundachtzigstel.

As the distribution of the two variants -tel and -stel parallels that of -te vs. -ste in the ordinals, it seems perhaps advisable to consider the German fractions to be built upon the German ordinals by means of a suffix -l. From that perspective, in German and English and in Dutch, denominators of fractions are built from ordinal numbers. There is only difference: German has an additional suffix -l. One might even be tempted to postulate, for parallel's sake, a corresponding suffix in Dutch and English as well, realized as zero.

Conclusion: Fractions have a construction-specific semantics, found nowhere else in the grammar of Dutch. The ordinals used to build fractions have a different semantics in fractions than they have when used as ordinals.

References:
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