Both positive and negative numbers are 1. Books that have been learned before and are preceded by a negative sign "-"are called negative numbers.
2. The numbers other than 0 that I learned before are called positive numbers.
3. The number 0 is neither positive nor negative, and 0 is the dividing line between positive and negative numbers.
4. In the same problem, positive numbers and negative numbers have opposite meanings.
Rational numbers Positive integers, 0 and negative integers are collectively called integers, and positive and negative fractions are collectively called fractions.
Integers and fractions are collectively called rational numbers.
The number axis is 1, and the straight line defining the origin, positive direction and unit length is called the number axis.
2. Function of the number axis: All rational numbers can be represented by points on the number axis.
Note: The origin, positive direction and unit length of (1) axis are indispensable.
(2) The unit length of the same shaft cannot be changed.
Generally speaking, if it is a positive number, the point representing a on the number axis is on the right side of the origin, and the distance from the origin is a unit length; The point representing the number -a is on the left of the origin, and the distance from the origin is one unit length.
The inverse number 1 and only two numbers with different signs are called the inverse number.
2. The two points representing the opposite number on the number axis are symmetrical about the origin.
3. Add "-"before any number, and the new number represents the opposite number of the original number.
Absolute value 1. Generally speaking, the distance between the point representing the number A on the number axis and the origin is called the absolute value of the number A. ..
2. The absolute value of a positive number is itself; The absolute value of a negative number is its reciprocal; The absolute value of 0 is 0.
3. Compare the size of rational numbers.
(1) Positive number is greater than 0, 0 is greater than negative number, and positive number is greater than negative number.
(2) Two negative numbers, the larger one has the smaller absolute value.
The operation of rational numbers? 1, rational number addition:
(1) rational number addition rule:
① Add two numbers with the same symbol, remove the same symbol and add the absolute values;
(2) Sum two numbers with different absolute values, take the symbol with larger absolute value, and subtract the one with smaller absolute value from the one with larger absolute value;
(3) The result of adding two opposite numbers is 0;
(4) A number with 0 still gets this number.
(2) Arithmetic of rational number addition:?
The commutative law of addition: A+B+C = A+(B+C);
The associative law of addition: (a+b)+c=a+(b+c)
The basic idea of simple operation of addition operation path is: first, add the numbers that are opposite to each other; First, add the scores of the same denominator; First add up the numbers that add up to integers. ?
2, subtraction of rational numbers:
(1) rational number subtraction rule: subtracting a number is equal to adding the reciprocal of this number.
(2) Common mistakes in rational number subtraction: paying attention to one thing and losing another, and not paying attention to the sign of the result; Still using the habit of primary school calculation not to change subtraction into addition; Only the sign of operation is changed, but the sign of subtraction is not changed, and subtraction does not become reciprocal. ?
(3) Mixed operation steps of rational number addition: first, the subtraction is changed into addition, and then the operation is carried out according to the rational number addition rule.
3. Rational number multiplication
(1) rational number multiplication rule: two rational numbers are multiplied, the same sign is positive, the different sign is negative, and the absolute value is multiplied; Multiply any number by 0 to get 0.
(2) Arithmetic of rational number multiplication: exchange law: AB = BA associative law: (AB) C = A (BC); Commutation law: a(b+c)=ab+ac.
(3) Definition of reciprocal: If two rational numbers whose product is 1 are reciprocal, that is, ab= 1, then A and B are reciprocal; The reciprocal can also be seen as the inversion of the numerator and denominator. ?
4. Division of rational numbers
Rational number division rule: dividing by a number is equal to multiplying the reciprocal of this number, and 0 cannot be divided. This rule can convert division into multiplication; The law of division can also be regarded as: divide two numbers, the same sign is positive, the different sign is negative, and divide by the absolute value. Dividing 0 by any number that is not equal to 0 equals 0.5.
These are the math knowledge points I have compiled. I hope I can help you.