Property of the Neutral Element in The Multiplication of Fractions

It is likely that the most appropriate way to approach the definition of the Neutral Element Property in Fractional Multiplication is to initiate by a theoretical review, which allows to take into account certain notions, indispensable to understand this Law within of its precise mathematical context.


Fundamental definitions

Consequently, it will also be necessary to focus this review on two specific notions: the first, the very concept of Fractions, as this will help to know the nature of the expressions around which the operation takes place and the ownership of the neutral element. It will also be important to review the concept of Fraction Multiplication, to know what is the operation in which this Mathematical Law is given. Here’s each one:

Fractions

In this way, one can begin by saying that Mathematics has defined fractions as one of two possible expressions with which fractional numbers count, which then makes fractions can be interpreted as a form of representation of fractional numbers, i.e. those consisting of non-exact or non-whole quantities.

Likewise, the mathematical discipline has indicated that fractions may be understood as expressions consisting of two elements, each of which has its own definition and task, as can be seen below:

  • Numerator: First, you will find the numerator, consisting of a numerical element, which chooses to be placed at the top of the fraction, in order to indicate what part of the whole it represents.
  • Denominator: Likewise, the Denominator will occupy the bottom of the fraction, and it will be tasked with indicating how many parts the whole is divided into, from which the numerator indicates some parts.

Multiplication of fractions

Mathematics has also been given to the task of defining fraction multiplication as the operation by which it is a matter of determining what is the product of two or more fractions, or also what result is obtained once it adds to itself a determinad fraction, as many times as a second expression tells you, because as some authors point out, all multiplication can be understood as an abbreviated sum.

With regard to the correct form in which such an operation should be resolved, i.e. a multiplication between two or more fractions, the different sources agree that the right way to obtain the proceeds of the multiplication of the numerators, in order to find the numerator of the final result, while the denominators will proceed equally, which must be multiplied with each other. This procedure may be expressed mathematically as follows:

Property of the Neutral Element in Fraction Multiplication

Once each of these definitions have been revised, it may be much easier to approach a definition of the Neutral Element Property in Fraction multiplication, which is understood as the Mathematical Law that dictates than every time a fraction, whatever it is, it is multiplied by the unit, it is obtained as a result or product the same fraction, hence the unit is then considered the Neutral Element of Multiplication, since no fraction undergoes changes in its quantities or elements multiplying by him. This Law can be expressed mathematically as follows:

Example of the Neutral Element Property in Fraction Multiplication

However, the most efficient way to conclude an explanation of this specific mathematical property, present in Fraction Multiplication, may be to present some examples that allow us to see in practice how ever and in any case that a fraction multiplied by the unit will result in the fraction itself, as can be seen in the operations below:

Picture: pixabay.com

Property of the Neutral Element in The Multiplication of Fractions
Source: Education  
September 26, 2019


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