1 December 2023

In the field of mathematics, there are different operations that are easy in their initial stage and that, unknowingly, become the basis when solving a problem. In this particular case, there is something called complex fractions. This applies perfectly for equations, trigonometric functions and so on. Of course, if we combine it with the theory of like terms, its implementation becomes easier.

In this article you will not only learn about what a complex fraction is, but also those characteristics that define this mathematical operation. And, as if that were not enough, we will show you step by step how or what you have to do to simplify these types of fractions.

Meaning and concept of a complex fraction

We have to start by saying that complex fractions are a type of division which isfind two fractions by dividing each other. That is to say, that there is a fraction over another fraction and it is, in essence, for this reason that it is called complex. With this we mean that, in said fraction, in a general way, there are two numerators and two denominators. By means of a multiplication or product, they can be solved without any complication.

Now, when it comes only to integers or real numbers, it is not a problem at all. The difficulty begins to become present once more complex terms appear. In the case of linear algebra, we find complex fractionsyes expressed with independent variables. As a result of this, more “complicated” terms to handle arise, such as square roots, powers of base two or greater, notable products, trigonometric functions, complex numbers and much more.

In other words, the complex fraction base can be perfectly applied to any mathematical, physical and/or chemical field. This is one of the reasons why it is essential to understand how this problem is resolved. type of mathematical operation. Without your domain, it would be impossible to come up with an exact result without errors.

What are the characteristics of a complex fraction?

The first characteristic that we must highlight is that it is a division, which is made up of two fractions. However, this is not only limited to this, since, in a certain way, it is its simplest form. What does this mean? That it can be a little more complex, to the point of having two or more complex fractions in the same fraction.

That is, let’s imagine for a moment that we have A/B|C/D. This would be the most basic representation of a complex fraction. Well, when we say that it can be more complicated, we mean that in the part of the numerator and/or denominator, there can be a complex fraction. In this type of situation, what is done is to first solve the secondary fraction in the numerator or denominator and then solve the general one.

Therefore, we can say that another of the characteristics of complex fractions is that they can accommodate more mathematical operations before proceeding to solve them in the usual way. On the other hand, its mathematical nature allows it to be applied to any field in which there are algebraic operations. Therefore, this is something that you will see both in physics, chemistry classes and even, in more advanced studieszados in the technological field.

How to simplify a complex fraction?

Something that we did not mention in the previous point is that, in order to apply resolution methods such as the greatest common divisor, it is necessary solve the complex fraction first. To achieve this, you can base yourself on the following points that will serve as a process to follow.

  • The first thing is to identify that a fraction exists over another fraction.

  • Now locate the heYocentral line that divides both fractions.

  • You’re going to take the numerator of the first fraction and multiply it by the denominator of the second fraction.

  • The result is placed on the right side of the equation.

  • Now go with the denominator of the first fraction and multiply it by the numerator of the second fraction.

  • The result you write it on the right side of the equality.

Now you have two results, what you have to do is write a new fraction that will be the result of the operation you just carried out. The first result will be your new numerator and the second will be your new denominator. In this way, you will have already solved the complex fraction. From here, what remains is to see if it can be further simplified, either by solving some power that is pendinga square root, or something as simple as dividing between the two numbers.

In case you have not fully understood this, what you should consider is the following:

  1. You have a fraction of type A/B|C/D.

  2. When you solve it, the new fraction should look like this: AD|BC

It is worth mentioning that the terms AD and BC are being multiplied.

Examples and exercises of a complex fraction

Taking into account the theory that we have provided, you can do your own exercises on your own. you can do this get by substituting the basic shape A/B|C/D with any number or algebraic expression. Either way, let’s look at some of the examples we’ve prepared for you.

  1. 3/4|9/10

  2. 1/5|2/5

  3. (x+1)|(x-1)

  4. (3/5 + 1/5)|(4/7 – 1/7)

  5. (1/x^2)|(4/x²)

We have provided you with 5 examples with different difficulties so that you can use the basic notions. It is important to mention that for exercise number 3, it is practical and easy to solve as long as you know the property of binomials or notable products. In the case of exercise 4, here is a main operation that you must do. Initially, what you should do is the sum of fraction both in numeratoras the denominator and the result, apply the solution of the compound fractions.

For exercise number 5, we recommend that you review the properties of power a bit. This will be very useful when multiply and simplify fractions that have the same base. If you master the properties and mathematical bases, you will be able to solve any problem that is presented to you in an exam or academic test.

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