The concept of number axis: the straight line defining the origin, positive direction and unit length is called number axis. Three elements of the number axis: origin, unit length and positive direction. Points on the number axis: All rational numbers can be represented by points on the number axis, but not all points on the number axis represent rational numbers. Generally, the right direction is the positive direction, and the points on the number axis correspond to any real number, including irrational numbers.

The concept of inverse number: Only two numbers with different signs are called inverse numbers. The significance of anti-numbers: grasp that anti-numbers appear in pairs and cannot exist alone. From the number axis, except 0, all the two numbers are inverse numbers, both on both sides of the origin, and the distance from the origin is equal.

The size of a rational number can be compared with that of a rational number. They are in the order from left to right, that is, from big to small (two rational numbers represented on the number axis, the number on the right is always greater than the number on the left); You can also use the nature of numbers to compare the sizes of two numbers with different symbols and 0, and use absolute values to compare the sizes of two negative numbers.

Rational number multiplication rule: two numbers are multiplied, the same sign is positive, the different sign is negative, and the absolute value is multiplied. Any number multiplied by zero equals zero. Multiplication law of multiple rational numbers: multiply several numbers that are not equal to 0. The sign of the product is determined by the number of negative factors. When there are odd negative factors, the product is negative.