Algebra (elementary mathematics)
The elementary algebra east is a branch of the Mathématiques whose object is the study of the laws which govern the numerical quantities. The qualifier of elementary appears at the same time as the modern algebra in order to differentiate it from this one. Today, it is the first approach of the algebra in the school course.
The algebra is different from the arithmetic by the introduction of letters (, , ,…, , , ,…, , , ,…) indifferently representing all the numbers and to which are applied same the rules of calculations that if it were about numbers.
It is thus possible to establish laws depending only on the nature of the operations, independently of the numbers.
The resolutions of equations and inequations, the study of the polynomials are applications of the algebra.
An algebraical expression consists of numbers, letters and operational signs:
- the sign is used to mark the Addition.
- the sign is used to mark the Soustraction.
- the signs or are used to mark the Multiplication. When the multiplication relates to two letters, it possible to write instead of .
- the sign is used to mark the Division, also being able to be written .
- the product of a number increased of 3 by itself is written .
- the difference of the squares of two numbers and is written
Évaluer an algebraical expression consists in allotting a value to each unknown factor, then to carry out arithmetic calculation obtained.
For example to evaluate the expression for consists in carrying out calculation .
Properties of the addition
Properties of the multiplication
Factorization and development
To factorize an algebraical expression, , consists in transforming of it the writing in the shape of a product of two or several expressions (, ,…) :
To develop an algebraical expression, , consists in transforming of it the writing in the form of a sum (or difference) of two or several expressions. (, ,…) :
Algebraic example of resolution of a problem
Simple problem: 2 tickets are worth 100 euros. What is worth a ticket? We can disregard nature of the ticket (euro, rouble, dollar,…), the resolution of the problem will be always the same one.
By noting the value of a ticket, the problem results in the equation .
By dividing each member by 2, one obtains .
In elementary the mathematics category
- Square (algebra)
- Divide check
- Equation (elementary mathematics)
- Simple equation
- Quadratic equation
- remarkable Identity (elementary mathematics)
- Inequality (mathematics)
- Inequation of the first degree
- Inequation of the second degree
- Inequation being solved by table of signs
- Power (elementary mathematics)
- System of equations (mathematical elementary)
Simple: Elementary will algebra
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