1, positive number: a number greater than 0.

2. Negative number: a number less than 0.

3. Positive numbers are greater than 0, negative numbers are less than 0, and positive numbers are greater than negative numbers.

Note: 0 is neither positive nor negative; -a is not necessarily negative, and +a is not necessarily positive; P is not a rational number;

Second, rational numbers.

1, rational number: a number consisting of integers and fractions. Include positive integer, 0, negative integer, positive fraction and negative fraction. Can be written as the ratio of two integers. Irrational numbers cannot be written as the ratio of two integers. It is written in decimal form, and the numbers after the decimal point are infinite. Such as: π)

Third, the number axis

1, number axis: Numbers are represented by points on a straight line, which is called number axis. Draw a straight line and take any point on the straight line to represent the number 0. This zero point is called the origin, which specifies that the right or upward direction of the straight line is positive; Select the appropriate length as the unit length, so as to take points on the number axis. )

2. Three elements of the number axis: origin, positive direction and unit length.

3. Antiquities: Only two numbers with different symbols are called reciprocal. The antonym of 0 is still 0.

Is the sum of opposites 0? a+b=0？ A and b are reciprocal.

Fourth, addition and subtraction of rational numbers.

1, sign first, then calculate the absolute value.

2. Addition algorithm: the same sign is added, and the absolute value is added. For the addition of different symbols, take the sign of the addend with large absolute value, and subtract the sign with small absolute value from the sign with large absolute value. Two opposite numbers add up to 0. Add and subtract a number with 0, and you still get this number.

Five, rational number multiplication (first determine the sign of the product, and then determine the size of the product)

1, the same sign is positive, the different sign is negative, and the absolute value is multiplied. Any number multiplied by 0 is 0.

2. Two numbers whose product is 1 are reciprocal.