2. The function of the number axis: ① indicates numbers; ② Comparative size; ③ indicates the distance.
3. Compare the sizes with the number axis: the numbers marked on the number axis are large on the right and small on the left, and the total number on the right is greater than that on the left. Positive numbers are greater than 0, negative numbers are less than 0, and positive numbers are greater than negative numbers.
4. The number axis is the basis of the combination of numbers and shapes, which vividly connects numbers with points on a straight line. The number axis can extend to both ends indefinitely, and the selection of origin and the determination of unit length can be "specified" according to actual needs.
Second, the opposite number.
1, the definition of inverse number: there are only two numbers with different signs. In particular, the inverse of 0 is 0.
2. Characteristics of enantiomers: If A and B are enantiomers, then A+B = 0; Conversely, if a+b=0, then a and b are reciprocal.
3. Geometrical meaning of opposites: On the number axis, the points corresponding to two opposites are on both sides of the origin, and the distance to the origin is equal; On the other hand, on both sides of the origin on the number axis, two points with the same distance from the origin represent opposite numbers.
Third, absolute value.
1. Definition of absolute value: On the number axis, the distance between the point corresponding to a number and the origin is called the absolute value of this number. Since the distance can only be positive or zero, the absolute value is non-negative, that is, the absolute value of any real number is non-negative: |a|≥0.
2, the absolute law:
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. Letters indicate:
Junior Middle School Mathematics: Number Axis, Reciprocal and Absolute Value (Summary)
3. The absolute values of two numbers are the same positive number, and they are opposite. For example, if |x|=5, then x = 5.
4. The absolute values of two mutually opposite numbers are equal, and the two numbers with equal absolute values are equal or opposite. For example, if |a|=|b|, then a=b or a =-B.
5. To find the absolute value of a number, we must follow the principle of "judge first, then remove the absolute value sign". When the number in the absolute value sign is uncertain, it should be classified and discussed, that is, it is divided into three categories: greater than 0, less than 0 and equal to 0.