Topics Mathematics

Question Is 0 really a fraction? Because some do not agree that it is not a fraction. But I have a thought Fraction=no. of equal parts considered/total no. of parts So if I divide a chocolate in 4 parts and eat no parts then I can associate with no part the no. zero and so 0/4 a fraction. Am I right?

Accepted:
June 13, 2013

Comments

I don't know anybody who claims that 0 is not a fraction. But I suppose it depends on what you mean by "fraction". If you mean a numeral (that is, a name or description of a number) that is normally written in the format: (integer numeral)/(integer numeral), e.g., 3/4, then, I suppose, strictly speaking, "0" is not a fraction. But you are correct to point out that "0/4" is a fraction. It is then common to identify integer numerals like 0,1,2, ...with fractions 0/1, 1/1, 2/1,... (and, of course, fractions like 2/1 are identified with fractions 4/2, 6/3, etc., just as 1/2 is identified with 2/4, 3/6, etc.). What's really going on here is that a single number, say 4, can be written as lots of different fractions: 4/1, 8/2, 16/4, etc., and these different numerals are then "identified" as naming or describing the same number.

So, fractions are numerals. Perhaps what you have in mind are rational numbers, which are typically written as fractions. And, of course, 0 is a perfectly good rational number, no matter how you choose to write it. One way of characterizing the rational numbers is as those that are the quotients of two integers (which, of course, can be written as fractions, which, in turn, are really just shorthand for a division problem). The other typical way of characterizing the rational numbers is as those whose decimal parts repeat; thus 1/2 = 0.50000...(with the "0"s repeating), 1/3 = 0.3333... (with the "3"s repeating), and 1/7 = 0.142857142857... (with the "142857" repeating). On this view, 0 = 0/1 = 0.000... (with the "0"s repeating).