Property of the inverse element in the multiplication of fractions

Perhaps best, before moving forward on a definition of the Reverse Element Property in Fraction Multiplication, is to briefly review some notions, which allow us to understand this operation within its precise context.

Fundamental definitions

Consequently, it will be necessary to delimit this theoretical review to two specific notions: the first of them, the very definition of fractions, since this can help to understand the nature of the expressions involved in the operation that gives rise to the Property of the reverse element. Likewise, it will be necessary to throw lights on the concept of Fraction Multiplication because this is the operation on which this mathematical law is given. Here are each of these concepts:


In this way, it will begin by saying that the Mathematics has pointed out fractions as one of the two possible expressions with which you can account for a fractional number, which then converts the fractions into representations of numbers fractional, i.e. of non-exact or non-whole quantities.

Likewise, the mathematical discipline states that fractions may be considered as expressions consisting of two elements: first, the numerator will be found, which will constitute the element available at the top of the fraction, pointing out what the whole part of the fraction is; on the other hand, in the fraction you will also find the denominator, which will be made up of the number at the bottom of the expression, while your mission will be to point out in how many parts the whole is divided.

Fraction multiplication

Continuing with the revision of concepts, it will also be necessary to dwell on the notion of Fraction Multiplication, which has been explained in general by Mathematics as an operation, aimed at determining what product can be obtained on the basis to the multiplication of two or more fractions, or what is equal: get the sum total of a fraction by itself as many times as a second fraction indicates, since Multiplication is nothing but an abbreviated sum.

With regard to the correct way in which this operation must be solved, the different authors also agree that the product of the multiplication of all the elements that it serves as a numerator must first be obtained, and the result of which will be understood as the numerator of the expression. Likewise, denominators can be multiplied with each other, in order to obtain the denominator of the final result. This procedure may be expressed mathematically as follows:

Property of the reverse element in Fraction Multiplication

Once these definitions have been taken into account, it may then certainly be much easier to delve into the concept of Reverse Element Property, which is seen by Mathematics as a Law that states that always and in any case a fraction establish a multiplication operation with its inverse, the result or product will be equivalent to the unit.

It is also necessary to note that the inverse of a fraction will be understood as the same fraction but with its elements – numerator and denominator – inverted. This mathematical property can be expressed mathematically as follows:

Examples of The Property of the Reverse Element in The Multiplication of Fractions

However, it may still be necessary, before concluding with the explanation of this Mathematical Law, to present some examples that allow us to see in a practical way how and why whenever a fraction is multiplied with its inverse will yield as a product the unity , as shown below:


Property of the inverse element in the multiplication of fractions
Source: Education  
September 26, 2019

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