Real number:

Rational numbers and irrational numbers are collectively called real numbers.

Rational number:

Integers and fractions are collectively called rational numbers.

Irrational number:

Irrational numbers refer to infinite cyclic decimals.

Natural number:

The number of representative objects 0, 1, 2, 3, 4 ~ (including 0) is called natural number.

Number axis:

The straight line that defines the point, the positive direction and the unit length is called the number axis.

Countdown:

Two numbers with different symbols are opposite.

Countdown:

Two numbers whose product is 1 are reciprocal.

Absolute value:

The distance between the point representing the number A and the point on the number axis is called the absolute value of A, the absolute value of a positive number is itself, the absolute value of a negative number is its inverse, and the absolute value of 0 is 0.

Mathematical theorem formula

Rational number arithmetic

(1) addition rule: add two numbers with the same symbol, take the same symbol, and add the absolute values; Add two numbers with different signs, take the sign of the addend with larger absolute value, subtract the smaller absolute value from the larger absolute value, and add two numbers with opposite numbers to get 0.

Law of subtraction: subtracting a number is equal to adding the reciprocal of this number.

(3) Multiplication rule: two numbers are multiplied, the same sign is positive and the different sign is negative, and the multiplication takes the absolute value; Any number multiplied by 0 is 0.

(4) Division rule: dividing by a number is equal to multiplying the reciprocal of this number; Divide two numbers, the same sign is positive and the different sign is negative, and divide by the absolute value; Divide 0 by any number that is not equal to 0 to get 0.