Inverse sign 1. The concept of inverse number: Only two numbers with different signs are called inverse numbers.

2. The meaning of opposites: Grasp that opposites appear in pairs and cannot exist alone. From the number axis, except 0, they are two opposite numbers, which are on both sides of the origin and have the same distance from the origin.

3. Simplification of multiple symbols: regardless of the number of "+",there are odd "﹣" and even "﹣", and the result is positive.

4. Summary of conventional methods: The way to find the reciprocal of a number is to add "﹣" before this number. For example, the reciprocal of A is ﹣a, and the reciprocal of m+n is ﹣(m+n). At this time, m+n is a whole. When you put a minus sign before an integer, use parentheses.

Absolute value 1. Concept: The distance between a number and the origin on the number axis is called the absolute value of this number.

(1) The absolute values of two opposite numbers are equal;

② There are two numbers whose absolute values are equal to positive numbers, one number whose absolute values are equal to 0, and no number whose absolute values are equal to negative numbers.

③ The absolute values of rational numbers are all non-negative.

2. If the letter A is used to represent rational numbers, then the absolute value of the number A should be determined by the value of the letter A itself:

(1) When a is a positive rational number, the absolute value of a is itself a;

(2) When A is a negative rational number, the absolute value of A is its inverse-A;

③ When a is zero, the absolute value of a is zero.

That is | a | = {a (a > 0) 0 (a = 0) | a (a < 0)

Comparison of rational number 1. Comparison of rational numbers:

The number axis can be used to compare the sizes of rational numbers, and their order is from left to right, that is, from big to small (the number on the right of two rational numbers represented on the number axis 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.

2. The rational number size comparison law:

① Positive numbers are all greater than 0;

② Negative numbers are all less than 0;

③ Positive numbers are greater than all negative numbers;

(4) Two negative numbers, the greater the absolute value, the smaller it is.

Three methods of comparing rational numbers;

1. Rule comparison: all positive numbers are greater than 0, all negative numbers are less than 0, and all positive numbers are greater than all negative numbers. Two negative numbers are bigger, but the absolute value is bigger.

2. Number axis comparison: the number represented by the right point on the number axis is greater than that represented by the left point.

3. Compare the differences:

If a-b > 0, then a > b；;

If a-b < 0, then a < b；;

If a-b = 0, then a-b = 0 b.

Algebraic evaluation 1. Algebra: replacing letters in algebraic expressions with numerical values, and the calculated results are called algebraic values.

2. Evaluation of algebraic expression: the value of algebraic expression can be directly substituted into calculation. If a given algebraic expression can be simplified, it should be simplified before evaluation.

The required questions briefly summarize the following three types:

① The known conditions are not simplified, but the given algebraic expression is simplified;

② given conditions are simplified, given algebraic expressions are not simplified;

③ The known conditions and given algebraic expressions should be simplified.