Summary of knowledge points of mathematical theorems in junior high school of Beijing Normal University Edition [Grade 7]

First, rational numbers.

rational number

1, classification of rational numbers:

Classification according to the definition of rational numbers: classification according to the natural symbols of rational numbers;

1. Positive integer 1. positive integer

① Integer 2. Zero ① positive rational number

Rational number 3. Negative integer 2. Positive fraction

4. Positive fraction rational number ②0

② score

3. Negative integer

5. Negative integer ③ Negative rational number 4. negative score

2. Positive numbers and negative numbers are used to represent numbers with opposite meanings.

(2) Number axis

1, definition: the straight line defining the origin, positive direction and unit length is called the number axis.

2. The three elements of the number axis are: origin, positive direction and unit length.

(3) reciprocal

1. Definition: Only two numbers with different symbols are opposite to each other.

2. Geometric definition: The number represented by two points on both sides of the origin with the same distance from the origin on the number axis is called.

Do the opposite.

3. Algebraic definition: Only two numbers with different signs are called reciprocal, and the reciprocal of 0 is 0.

(4) Absolute value

1, definition: the distance from the point representing the number A on the number axis to the origin is called the absolute value of the number A.

2. Geometric definition: the absolute value of a number A is the distance between the point representing the number A on the number axis and the origin.

3. Algebraic definition: the absolute value of a positive number is itself, the absolute value of a negative number is its reciprocal, and the absolute value is 0.

It's 0.

a (a>0)，

That is, for any rational number A, there is | a | = 0 (a = 0).

–a(a < 0)

4, the calculation rule of absolute value:

(1) The absolute values of two opposite numbers are equal.

(2) If | a | = | b|, then a =-b or a =-b. 。

(3) If | a |+| b | = 0, then | a | = 0 and | b | = 0.

Related conclusions:

The inverse of (1)0 is itself.

(2) The absolute value of non-negative number is itself.

(3) The absolute value of a non-positive number is its reciprocal.