Mathematical reasoning


Everyday life makes people face various problems that very possibly require their attention . These problems are something that require reasoning to be solved, especially if they have a certain degree of complexity. Among them, we have, of course, those of a mathematical type .


What is mathematical reasoning?

The mathematical reasoning is a type of reasoning designed to solve problems requiring a mathematical language and basic operations interrelate the symbols of this language (numbers). Its usefulness lies in that it allows the thinker to solve problems that require quantitative and spatial measurement , this competence being an element that makes sense in this context.

  • Definition of mathematical reasoning
  • features
  • What is it for
  • Elements
  • How to improve mathematical reasoning
  • Four operations of mathematical reasoning
  • Importance
  • Mathematical reasoning problems
  • Other examples

Definition of mathematical reasoning

It can be understood from psychic competences as well as from philosophical logic. Ultimately, mathematical reasoning is that type of reasoning that uses mathematical language and its most essential operations to solve problems that give rise to some concern. So usual , treated reality problems involving some aspect quantitative (ie numerical quantities) and spatial (distances, dimensions, locations in space).



It would be a skill that takes into account the reading and interpretation of numerical data . Numbers are, above all, symbols that, like letters, would try to make sense of an aspect of reality. Mathematical reasoning is a skill that starts from these elements to interpret the data, arguments and information that are expressed in this language.

It is a skill or skill that takes into account quantitative and spatial aspects of reality. This implies, somehow, the integration of knowledge cutting mathematics with other areas of knowledge. It is then about making a link between numerical and non-numerical aspects of reality, in order to see possible application channels.

It is also a form of reasoning that seeks its application in order to solve problems in everyday life. This implies that the data obtained from reality can be read from a numerical language , and that, with the symbols of this language, algorithmic and / or logical operations can be reached that are capable of responding to the problems presented by reality. .

What is it for

In short, we can find its usefulness where reality presents a problem that non-mathematical logical reasoning cannot solve. Very unlike other forms of reasoning , the mathematician uses symbols that represent numerical quantities. It is used to solve problems that express quantities and distances, which are, after all, a specialty of number language.



We refer here to any object or property to which, later, the symbols they try to represent will refer. In mathematical reasoning, the content could be the spatial quantities and dimensions of some aspect of reality.


It refers, on the other hand, to the symbols that come to represent the contents previously exposed. In this case, these symbols would be numbers, signs, algebraic or logical formulas.

How to improve mathematical reasoning

Some recommendations that we can make to improve mathematical reasoning are:

  • Keep in mind that a comfortable and pleasant environment helps the reasoning flow more easily.
  • Get in touch with challenging situations that require mathematical solution. Usually, counting bills and doing activities where the most basic operations help a lot to get started in this way of reasoning.
  • Use some apps that help in these types of activities. With the advancement of technology, it is easier to access mathematical knowledge. One of the most used games or applications for this purpose is, precisely, Sudoku.
  • Little by little, it makes activities more complex. Instead of just adding and subtracting, get in touch with estimating proportions (or percentages) of some product (for example, the percentage of your annual profits).

Four operations of mathematical reasoning

For the solution of some situations that require mathematical reasoning, we can find some operations that serve as a shortcut to the resolution of this problem. Here are some of these operations:

Crab method

It is named for its tendency to go back and forth throughout the mathematical operation like a crab. It is used in mathematics to solve problems where there is data that is conspicuous by its absence. In an operation, it is a matter of going in the reverse direction to which it was originally undertaken.

Rhombus method

It is a mathematical operation that seeks to solve problems that, under normal conditions, would require equations to be solved. It starts with a total of units that is multiplied by a unit value, which will be subtracted from the total collection. To all these, in turn, the sum will be divided between the unit value and the requested unit value.

Equivalence method

This method tries to start from equivalences that, later, will be simplified. This means that, to know the result of a problem where equivalences are raised, the data of each sector are simplified and these, in turn, are multiplied to know the final result.

Rectangle method

It is a method that starts from what is missing and what is left over in a problem. Either in distribution or in collection, the missing or surplus aspects of a problem are compared, and they are confronted in such a way that the measure of something that one wants to know can be known.


It is no secret that mathematical reasoning becomes of transcendental importance for humanity. Whether in economics , finance, technology or medicine , calculations and measurements are essential elements for the proper development of man. They are, in turn, elements that allow solving complex problems through operations brimming with simplicity.

Mathematical reasoning problems

  • Adelaida is older than Beatriz
  • Cecil is younger than Diane
  • Helen is younger than Cecil
  • Beatriz is older than Diane

Which of all is the greatest

The age of Rose is multiplied by 6, and to this result is added 4. If dividing this last sum by 3 gives 20. What is Rose’s age?

Other examples

We can find examples of mathematical reasoning in problems of:

  • Finance management within a business.
  • Estimates of the economic growth or development of a country.
  • Calculation of the distances necessary for the execution of a job.

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