Why are fractions called proper, improper, and apparent?

We already know that:

  • Own fractions are those where the numerator is smaller than the denominator.
  • Improper Fractions are those where the numerator is greater than the denominator.
  • Apparent fractions are those where the numerator is multiple of the denominator.

But what is the reason they get these names? If you look in some dictionaries for the words "own," "inappropriate," and "apparent," you'll find definitions similar to the following:

Own: which is used for a right purpose; appropriate.

Improper: that does not exactly express the idea.

Apparent: supposed, similar, similar.

The term "own fraction" was first used in the English language in 1674 by Samuel Jeake and is included in his work. Arithmetic, published in 1701:

"Proper Fractions always have the Numerator less than the Denominator, so the meaningful parts are less than a Unit or Integer."

That is, he says that proper fractions always have the numerator smaller than the denominator, the parts being smaller than one unit or integer. Thus, a proper fraction corresponds to the intuitive idea of ​​fraction, in which some pieces of a divided integer are considered (which occurs when the numerator is smaller than the denominator).

In contrast, improper fractions are called this because they go beyond the intuitive idea of ​​fractions, since they result in more parts than those obtained by dividing the unit. For example, 5/2 is equal to 2.5, which is more than an integer.

Finally, apparent fractions are those where the numerator is a multiple of the denominator, that is, they represent an integer. That is why they are called apparent, since they appear to be a fraction, but actually result in an integer.

Text produced by Just math.