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数学思想是数学基础知识、基本技能的本质体现,是形成数学能力、数学意识的桥梁.下面对数学思想在有理数中的应用举例加以说明,供同学们学习时参考,一、分类讨论思想例1若||a|=5,|b|=6,且a与b的乘积小于0,求a与b的和.解析:由|a|=5,|b|=6,得a=±5,b=±6.因为a与b的乘积小于0,所以a、b异号.当a=5时,b=-6;当a=-5时,b=6.所以a与b的和为-1或1.点评:当被研究的问题含多种情况,不能一概而论时,必须将可能出现的所有情况分类讨论,得出各种情况下相应的结论.注意分类要做到不重复、不遗漏.
Mathematical thinking is the basic knowledge of mathematics, the essence of the basic skills embodied, is the formation of mathematical ability, mathematical awareness of the bridge.The following mathematical examples of rational numbers in the application of examples to illustrate, for students to learn reference, a classification of ideas 1 If || a | = 5, | b | = 6, and the product of a and b is less than 0, find the sum of a and b. 5, b = ± 6. Since the product of a and b is less than 0, a and b have the same sign, b = -6 when a = 5 and b = 6 when a = -5. And is -1 or 1. Comment: When the problem being studied contains a variety of situations and can not be generalized, all situations that may arise must be discussed in a classification and the corresponding conclusions in all cases are drawn. Note that the classification should be non-repetitive , Do not miss out.