Mathematical thinking method is the guiding ideology and basic strategy to deal with mathematical problems, and it is the soul of mathematics. Therefore, it is our important guarantee to understand and master the mathematical thinking method based on mathematical knowledge, improve our thinking level, truly understand the value of mathematics, and establish scientific mathematical concepts, so as to develop and apply mathematics. The chapter of algebra about multiplication and division contains many important mathematical thinking methods, which need us to explore, expand and apply. To sum up, there are mainly the following types: 1. An example of mathematical thinking of whole substitution: 1: a+b=2, the value to be found. Analysis: the algebraic expression to be solved is transformed into an expression of a+b, and then the whole substitution is evaluated. Solution: ∵a+b=2∴ Original formula: to find the known value ... It is not difficult to find that the problem can be solved by whole substitution. Solution: 2. Mathematical thought example 3 of classified discussion: if it is completely flat, find the value analysis of a: find the undetermined coefficient or a and b in the formula in a completely flat way. Solution: ∫ Polynomial is completely flat, ∴ 2 (a+4) x = 2 ×× 5. When 2(a+4)=-10, a= -9. Third, the mathematical idea of reducing to example 4: the value of the known solution. Analysis: The key to solve this problem is to find the relationship between the evaluation formula and the known, and the following two solutions can be adopted. Solution 1: Pass and you get it. By，So = 12。 Solution 2: = Description: Solution 1 According to the principle that both sides of the equation can be raised to the power of n at the same time, the correlation sum in the evaluation formula is constructed from the known ones, and then the evaluation formula is constructed according to same base powers's multiplication and division rules. The basic idea of this solution is to change from known to target, that is, "known target"; The second scheme uses the reversibility of the operation rules of power, that is, the power law of inverse power and same base powers's multiplication and division law, and the solution process is straightforward and in one go. The basic idea of this solution is to turn the target into the known, that is, "the target is known". Fourth, the thinking method of inverse thinking is 1, and the operational nature of inverse power Example 5: Calculation: Analysis: If the calculation is multiplied, it will. At this time, it will be much simpler if the nature of power operation is reversed. Solution: = 2. Reverse complete flattening law 6: calculation and analysis: there are many median factors, so it is difficult to calculate them directly. At this time, if we can grasp the structural characteristics of numbers and skillfully reverse the formula of complete square, we can simplify the calculation process. Solution: The original formula = = 5. Ideas and methods of constructing a formula model Example 7: Calculate11×10/×10001. Analysis: If you multiply directly, the amount of calculation is very large, but look carefully:101=100+,10001=10000+/