We explain what the algebraic language is, its origins and functions. Also, examples of algebraic expressions and what types they can be.
What is an algebraic language?
The algebraic language is the language of the math. That is, to an expression system that uses symbols and numbers to express what we usually communicate through words, and that allow us to formulate theorems, solve problems and express proportions or formal relationships of a different nature.
The algebraic language was born, logically, together with the algebra, the branch of mathematics that studies the relationship and combination of abstract elements according to certain rules.These elements can be numbers or quantities, but they can also be unknown values or certain numerical ranges, for which letters are used (known as unknowns or variables).
Originally, this field of knowledge was called al-jabr wa l-muqabala, that is, "the science of reestablishing equilibrium", as formulated by one of his parents, the Persian astronomer, geographer and mathematician Al-Juarismi (ca. 780-ca. 850). The name came from studying how to move a term from one side of an equation to the other, or how to add one to both sides to preserve the proportion. Over time, al-jabr came to Latin as algeber or algebra.
Seen like this, then, the algebraic language is the language of algebra. The written forms that this language produces are known as algebraic expressions: any number, any equation are perfect examples of this. Using these kinds of expressions, then, we can "speak" the algebraic language, and communicate relationships and operations that go far beyond the scope of mere arithmetic.
What is an algebraic language for?
As we have said before, the algebraic language is used to construct algebraic expressions, that is, formulations in which numbers, symbols and letters are combined to express a logical and / or formal relationship, in which some quantities are known and others are unknown.
The algebraic expressions, then, are ordered chains of these signs, in which we will find numbers, letters and arithmetic operators. Depending on what they are, we can distinguish between, for example:
- Unknowns (expressing unknown values) or variables (expressing non-fixed values), the latter being dependent or independent.
- Arithmetic signs (expressing certain arithmetic operations).
- Superscripts or powers (which involve multiplying a number by itself a certain number of times).
- Roots or radicals (which involve dividing a number by itself a certain number of times).
- Features (that express a dependency relationship between two values of two or more expressions).
Examples of algebraic expressions
The following are examples of algebraic expressions:
- 19465 + 1
- 9x + 2
- 6x. 2 (4 + x)
- 2x3
- 8a + 4b = c
- y - 20 (x) = ½
- F (x) = 2 (A, B)
- 4 (a + b)
- 6A + 2B - C = 0
- 4½ = 2
- 2y = x - 2
- 1 / (y + x). 5
- x3 + 2y2 + 9
- [53. (a + b)] - 7
- 9 + 9 + 9 + 9
- 5 + (1 - y) = 3
- 84
- y - x + 1