One of the biggest reasons for fear of students, is to find literal expressions or mathematical statements, perhaps many of them think that it is uphill to understand such expressions when they are presented, it is important to emphasize that through the use of literals, has been could base the general understanding of mathematics as well as other important sciences in different areas of our intellectual development, because many of the statements of these sciences are formulated through the algebraic language, sentences in the form of equations composed of words which name coefficients, unknowns and operations.
The use of literals using the algebraic language at first may seem difficult to learn, however once done is simple and very useful, only then will understand the importance of it because we can apply it in different cases of our lives if we wanted to, or in solving problems in the academic or scientific field, because through them, this wonderful language is well used to build powerful algebraic expressions to search for a specific solution.
We can say that mathematical writing through the use of literals allows us to express, the focus of a given statement in a much more reduced, concise and general, taking into account that for the beginning of understanding and deepening of that language we must consider the next:
- When we refer to any number, whose value is considered indeterminate, we use the letters:
A,b,c,d,e…….x,y,z
- If we wish to indicate the sum of two numbers, we must make use of the expressions:
a+b o e+f o x+y
But if instead we want to indicate the subtraction operation:
a-c ; g-h ; y-zFor the division we must do it with:
a/b ; h/i ; x/yProduct of the same literal:
a.a = a^2Para el Cuadrado de una suma:
(a+b)^2= a2+2ab+b2For the Square of a difference:
(a-b)^2= a2-2ab+b2For the Sum by difference:
(a+b)(a-b)= a2-b2
With these conditions and others of a similar nature, we can represent quantities in similar situations, where numbers, literals and operational symbols such as those described above intervene, with this we can give our initial steps to understanding the formulation of such versatile expressions. algebraic.
A simple but important contribution of this language is the fact of the hierarchy of operations, as we know in mathematics we must perform several consecutive and combined operations, so we can determine an appropriate order for the development or resolution of a mathematical approach or problem, we often use the parenthesis and the bracket, since these allow us to determine which operation we must carry out in the first place, therefore when we find a parenthesis this will indicate that the operation that is inside, will be the first to solve, while operable. By means of the hierarchy of operations within a given algebraic expression, we find that both multiplication and division have preference over addition and subtraction, making it clear that if in said algebraic expression we only find a combination of multiplication and division operations, the order will be indifferent in which these operations are resolved, the same will happen when we only have addition and subtraction combinations.
Example: 4. [7-6.(8+x)].
At the student or academic level, we frequently use one of the first rules or conditions of algebraic writing, the famous algebraic sum, which is more than the combination of addition and subtraction operations of numbers with or without literals, example:
- 8 - 9 + 12 – 4 + 6
- 2b + 3a + 5b – 6a – 7b + 4b
The above described, allows us to expand our knowledge of mathematics in a generalized manner, therefore we have until now clear that the use of literals represent any number, this will then allow us to describe the mathematical relationship that we can symbolize when we find algebraic expressions such as:
- 3.b
- 2.a
- y+z
- (m-n)/5
- b2+c2+d^2
With this the first thing we do is identify the literal or letter of that expression, because as we have mentioned, in this language literals represent any number, for our first case, the literal b represents any number, if we have to this is multiplied by 3, we say that this algebraic expression represents three times any number, in our second case, it would represent twice the number, for our third case, we find something more complex because we have two literals that add up , therefore, this algebraic expression represents the sum of any two numbers, our fourth case would represent 1/5 of the difference between any two numbers and our fifth case would be the sum of the squares of any three numbers.
We can also perform the opposite operation, that is, we find statements which could be transformed into some algebraic expression, which would facilitate the solution of the same; Thus:
- A rectangle whose base is 4 times its height.
As we know the area of a rectangle is given by the product of its base (b) by the height (h), represented by an algebraic expression A = bh (the literals to be used can be any), which allows us to calculate any rectangular area regardless of its dimensions.
For the case raised, first, we must use a literal to denote the height of said rectangle, for this exercise we will use the letter h, of the general formula before described, then we have that the product of 4 times the height, would be the value of the base, of the raised rectangle, that is, b = 4.h; therefore, if in this case we would like to calculate the area according to the conditions established for this rectangle we would have:
A = b.h; where b = 4h, we have then;
A = 4h.h, that is; A = 4h ^ 2, we conclude that:
A = b.h = 4h ^ 2
With this we can expand an already established algebraic formulation, as we did in the previous case, therefore, the algebraic expressions are formulated through the combination of one or several terms, when it is composed of a single term we call it monomial (3x ), which are formed by indeterminate numbers, represented by letters, by fixed numbers and letters, but if more than one term appears, we join them through the signs of addition or subtraction, giving expressions called polynomials (4x ^ 2 + 3x +2), where the constant part of a certain term we call coefficient, we have then for example in 7ax, the coefficient is 7, and the literal is (ax), therefore the numerical value of an algebraic expression is the number that is obtained when we substitute its letters, for particular values that are attributed to it, where afterwards it is only necessary to carry out the operations that are indicated.
It is important to emphasize that we must always be clear about the wide scope of the use of literals in the world of mathematics, starting with the understanding of its rules or norms, applying them to practical exercises of different kinds, with these in addition to deepening our skills at the moment to formulate such expressions, will allow us to break the fear that gives us to find a mixture of literals and numbers in a mathematical approach or another scientific branch.
The success of learning will undoubtedly always depend on the dedication and perseverance of each of us at the time of wanting to acquire and expand a certain knowledge, all the contributions underpinned for such purposes are channels through which we can help transit all people who so wishPodemos decir entonces, que las matemáticas es un infinito universo de conocimiento donde con la utilización de literales nos ha brindado un mayor desarrollo y expansión de nuestra intelectualidad.
Hoping that this contribution has been useful, with some recommendations for the acquisition of mathematical learning through the use of literals, which leads to the formation of algebraic expressions, both in the academic field and in any other, until the next delivery;
regards.
