为了发展学生的思维能力,有必要向学生提出一些需要思考的问题,这些问题应该是学生们经过努力能够解决,但需用不同寻常的方法。例如,我们提出如下的问题:在下列各分数中,把分子和分母中相同的数字约去,就得到: 这样的“约分法”显然是错误的,但意外的是结果确是正确的。我们自然要问: (a)这里得到的结果为什么是正确的? (b)这种约分法是否可用于其他分数? 下面我们向读者介绍求解这些问题的一种方法,先看十进位的两位数的情形,再看n位数的情形。对于两位数的“约分”,实际上是求丢番都方程的解。令 In order to develop the students’ thinking ability, it is necessary to ask the students some questions that need to be considered. These problems should be solved by the students through hard work, but they need to use unusual methods. For example, we ask the following question: In the following scores, the same numbers in the numerator and the denominator are subtracted to obtain: Such an “approximation method” is obviously wrong, but unexpectedly the result is indeed correct. We naturally ask: (a) Why are the results obtained here correct? (b) Can this kind of score be used for other scores? Below we introduce the reader to a method for solving these problems. Let’s look at the decimal two In the case of digits, look at the n-digit case again. For the “about division” of two digits, it is actually a solution to the Difan equation. make