In order to know the meaning of the term improper fraction, it is necessary, first of all, to discover the etymological origin of the two words that give it its shape:
-Fraction, first of all, comes from Latin. Exactly it derives from “fractio, fractionis”, which can be translated as “broken piece” and which derives at the same time from the verb “frangere”, which is synonymous with “break”.
-Impropia, secondly, we have to emphasize that it also emanates from Latin. In his case, from “impropius”, which can be translated as “that does not belong to the characteristics that correspond to a person or thing”. A word that is the result of the sum of several lexical components, such as the following: the prefix “in-”, which means “not without”; the word “pro”, which is synonymous with “in favor”; the adjective “private”, which is equivalent to “private”; and the suffix “-io”, which is used to indicate “result” or “effect”.
A fraction is an expression that refers to a division. It is made up of two numbers separated by a dividing line: the numerator (located on this line) is the number to be divided, while the denominator (shown below the line) is the amount by which it is divided.
Let’s see a example. 5/8 is a fraction that has the number 5 as numerator and number 8 as a denominator. In this case, the fraction indicates the division of 5 on 8: 0.625.
According to their characteristics, we can classify fractions in different ways. A improper fraction is the one whose denominator is less than its numerator. Therefore, the fraction is greater than 1. On the other hand, when the denominator is greater than the numerator, we are facing a proper fraction, which represents a number greater than 0 but less than 1.
Taking into account this explanation, we can affirm that 4/3To cite one case, it is an improper fraction. Its numerator is 4 and its denominator, 3: As you can see, the numerator is greater than the denominator. If we solve the division, we will notice that the result is greater than 1: 1.33.
Sometimes the numerator is much larger than the denominator. That is the case of the fraction 5872/4. The numerator (5872) it is 1468 times higher that the denominator4), as we discovered when performing the division.
8/3, 54/7, 581/29, 892/431 Y 182530/51779 they are other improper fractions. The condition is always the same: that the numerator is greater than the denominator or, in other words, that the denominator is less than the numerator. When this property is fulfilled, the fraction is called improper.
In addition to everything indicated, we cannot ignore either that improper fractions have the particularity that they can be converted or represented by a mixed number, that is, as a natural number plus a proper fraction.
In order to be able to represent an improper fraction in that way, the process that must be followed is to divide the numerator by the denominator. The quotient that remains will be the natural number while what is the remainder will be the numerator of the proper fraction.