The first step we are going to take in order to understand the meaning of the term denominator is to make its etymological origin clear. In doing so, we discover that it comes from Latin, specifically, from the word “denominator”, which can be translated as “the smallest number that exists in a fraction”.
Denominator is that which names. A denomination, on the other hand, is the name or nickname that identifies a person or a thing and that allows to distinguish it from another.
The concept of denominator is used in mathematics to name, in fractions, the number that indicates the equal parts in which the unit is divided. The denominator is written below the numerator and is separated from the numerator by a horizontal dash or line known as the dividing line.
For example: “The teacher asked us to write five fractions with even denominators”, “The children still have trouble working with such large denominators”, “In the example above, 8 is the numerator and 26 is the denominator”.
It can therefore be said that the denominator is the number that appears at the bottom of a fraction. Above it is the dividing line and, at the top, the numerator appears. If we want to write, as a fraction, the expression of a third, we will have to specify: 1/3. The number 1 will be the numerator and 3, the denominator.
Likewise, within the area of algebra, we would have to establish that the term literal denominator is also often used. This is used to define what the divisor would be.
In the same way, it should be noted that one of the most common operations that are usually done in this area is to proceed to pass a negative denominator into a positive one. That is a task that is done by multiplying the numerator and denominator by the fraction -1/-1. Likewise, if necessary, the operation could be continued by reducing the fraction to its simple form.
On the other hand, it is necessary to establish that the denominator of a fraction can never be the number zero. And it is that if it were so, a notable problem would occur since the division by it would result in a limit with infinite value, which is indeterminate and that no electrical apparatus of mathematics can write.
In this sense, we must also clarify that dividing by zero is something that is not defined theoretically since infinity, which we have mentioned would be obtained, is not a number. Hence, it cannot establish that as the denominator because it would fall into a mathematical contradiction.
The common denominator is one that is the same in two or more fractions. This makes operations between fractions easier. The notion of least common denominator, on the other hand, refers to the result of calculating the least common multiple of the fractions with different denominators.
In everyday language, finally, the expression “common denominator” is used to refer to something that is shared by different things: “Defensive weakness is the common denominator of the Bolivian and Ecuadorian teams”.