First, the concept of inverse number.
Reciprocal is a commonly used concept in mathematics, which describes the symmetrical relationship between two numbers on the number axis at zero. The definition of reciprocal is closely related to the addition of numbers. The definition of reciprocal will be explained in detail from three aspects: concept, nature and application.
Second, the inverse number represented by the number axis
The number axis is a graphical tool for representing real numbers, which corresponds to real numbers one by one through points on a straight line. On the number axis, every real number can find an opposite number, and they are symmetrical at zero. For any number a, its reciprocal -b represents the point on the axis of the number that is symmetric with A about zero.
Third, the nature of the inverse number
Uniqueness of inverse number: each real number has only one inverse number. The essence of opposites: the sum of opposites is equal to zero, that is, a+(-a)=0. Extension of inverse number property: If a+b=0, then B is the inverse number of A, and vice versa.
Fourth, the algorithm of reciprocal
Addition of antonyms: If A and B are antonyms of two real numbers, then a+b=0. Reciprocal multiplication: a real number multiplied by its reciprocal is equal to-1, that is, a * (a) =-a * a =-a 2.
Fifthly, the application of reciprocal in mathematics.
Equation solution: deformation and solution can be carried out by adding and subtracting the opposite number of a number on both sides of the equation. Mathematical reasoning: In mathematical proof, the concept of reciprocal is often used to deduce and prove conclusions. Arithmetic operation: In arithmetic operation, the nature of reciprocal is widely used, such as operation adjustment in addition and subtraction.
Summary:
Inverse number refers to a number that is symmetrical with a certain number on the number axis. Its definition is that if for a real number A, there is a real number B that makes a+b=0, then B is called the inverse of A. The inverse number satisfies the symmetry on the number axis, and has uniqueness and specific operation rules.
In mathematics, the concept of reciprocal is widely used in the fields of equation solving, mathematical reasoning and arithmetic operation, which is of great significance for deeply understanding the basic concepts and operation rules of mathematics.