When people have already formed some ideas about whole numbers, began to emerge in the concept of fractions. The oldest fraction is "half". It would seem half - one half part of something. However, this value was fixed for the ancient concept recently. The expression "more than half", "lower half", "half-alive", "bad" , etc. indicate that the word "half" originally meant simply one of the two parts (not necessarily equal to each other). It also indicates the fact that the words "half" and "two" have different roots (and in all languages!). Already in the following time of occurrence of the terms "third" and "quarter" things are changing.