Fractional splitting method
Fraction splitting includes the following aspects: splitting 1 into the sum of several different fractional units; For example,1= ... In my years of communication with students, I found that there is no systematic mathematical method for students to encounter this kind of problem except being in a hurry. I have long wanted to write a related teaching experience and introduce several methods to answer such questions. Recently, I am free. After writing these words, I asked the party for the methods of splitting scores, such as splitting items, formulas, direct splitting, and the three-step method of "expanding and reducing scores". The following specific examples, respectively, introduce in detail the splitting of fractions by splitting term elimination method. Splitting term elimination method is a method of series summation, in which another number (splitting term) is subtracted or added, and the same number (elimination term) is added or subtracted, so that the original number is split into the sum or difference of two numbers 1, and++is known, and A= () is found. (The answer is not the only analysis and solution: this question is to split 1 into the sum of four different decimal units. By using the first splitting term elimination method, 1 can be converted into the sum of two decimal units,1=1-+= (1-)+=+; After three consecutive uses, 1 can be changed into the sum of four different decimal units.1=1-+++= (1-+-)+-++Compared with the original formula, A = 2, B = 6 and c = 650. (2) After using the split term several times in succession, it is necessary to group it reasonably, so that the calculation result of each group is a score with a molecule of 1.