Perhaps the best thing, before advancing the explanation of the right ways to simplify fractions, in order to find the irreducible fraction, will be to revise some definitions, which will allow us to understand these methods in their precise context.
In this sense, it may also be prudent to focus this theoretical review on two specific notions: the first, the very concept of fractional numbers, because this will allow us to understand the nature of the numerical elements involved. It will also be necessary to revise the notion of fraction, since this will give the notion of the expression on the basis of which simplification will be made. Here’s each one:
In this way, it will be necessary to begin to say that fractional numbers will be those used to represent inaccurate numerical quantities, hence they are called fractionaries, which is precisely because they account for a fraction or portion of a number.
Also, the mathematical discipline has pointed out that fractional numbers can be considered – along with whole numbers – as one of the two elements by which the set of rational numbers is formed, also known as the Q set.
As for the expression of such numbers, Mathematics indicates that fractional numbers can be written both in the form of a decimal expression and through a fraction.
Concept of fractions
On the other hand, it will also be relevant to refer to the concept of fraction, which will be understood basically as a portion of a number or quantity, represented through the division raised between two natural numbers, each of which constitutes a part of the fraction, and which have been defined as follows:
- Numerator: This is the number that occupies the top of the fraction. Its function is to point out the part of the whole to which the fraction refers.
- Denominator: For its part, this number occupies the bottom of the fraction. You will be done with the task of pointing out the part of which this expression gives an account.
How to simplify fractions
Given these definitions, it is then likely to be much easier to understand the nature of the fraction simplification operation, which is basically defined as the mathematical procedure that is performed in order to obtain the irreducible fraction of a fraction, that is, that expression that cannot be reduced once again, and which is taken as the most simplified possible form of a fractional number expressed in the form of a fraction.
However, mathematics indicates that at least two possible methods can be seen in reference to fraction simplification, each of which has been explained as follows:
Through common dividers
First, you will have a method of dividing both the numerator and denominator by common dividers, until you find an expression where no more of these dividers common to both fraction terms can be found. An example of this type of simplification method would be the following:
When reaching this fraction, it is considered that the irreducible fraction has been achieved, since there is no possibility of finding a common divider for both numbers.
Through the maximum common divider
Secondly, mathematics indicates that a fraction can also be simplified through a procedure in which the prime factors of each element of the fraction are calculated, and then the least exponent elements are chosen.
Likewise, the product of these prime factors is determined, achieving the maximum common divider, number between which the numerator and denominator will be divided respectively, thus resulting in the irreducible fraction. An example of this method may be the following:
Reduce the following fraction:
It then proceeds to break down each of these integers that make up the fraction into its prime factors:
The lowest exponent prime factors are then chosen, and the product is calculated:
22 . 3 .5= 4. 3. 5 = 60
In doing so, the Maximum Common Divider is then achieved, the number by which both the numerator and the denominator of the fraction to be simplified will be divided.
September 21, 2019