# Fractions are not numbers

July 16, 2010 2 Comments

Yes, fraction isn’t a kind of number. It is misleading to put fraction alongside the sets of numbers – counting, whole, integers, rational, irrational and real. The diagram below which are in many Mathematics I (Year 7) textbooks is inviting misconceptions.

Fraction is not a number but a form for writing numbers just like the decimals, percents, and other notations that use exponents and radicals, etc. The fraction form of numbers is used to describe quantities that is 1) part of a whole, 2) part of a set, 3) ratio, and 4) as an indicated operation. Yes, it can also represent all the rational numbers but it doesn’t make fractions another kind of number or as another way of describing the rational numbers. Decimals can represent both the rational and the irrational numbers but it is not a separate set of numbers or used as another way of describing the real numbers!.

I prefer the Venn diagram to show the relationships among the different kinds of numbers like the one shown below:

The diagram clearly shows that the set of real numbers is composed of the rational and the irrational numbers. The integers are part of the set of rational numbers just like the counting numbers are members of the set of whole numbers and the whole numbers are members of the set of integers. The properties of each of these set of numbers can be investigated. We do not investigate if fraction is closed or is commutative under a certain operation for example, but we do it for the rational numbers.

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