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所谓“整体思想”是指将一个复杂的量(它可以是一个比,也可以是一个代数式等)看成一个整体,下面用一例说明如何利用这种思想解题。 例,把一个矩形剪去一个正方形,所剩矩形与原矩形相似,则原矩形的长边与短边的比值为___,(山西省1993年中考题) 解此题时,许多同学虽能依题意列出比例式,但由于头脑中没有“整体思想”,因此最终未能求出比值,此题求解的难点在于如何从比例式中求出比值,而运用整体思想是突破这一难点的有效办法。
The so-called “whole idea” refers to a complex quantity (it can be a ratio, it can also be an algebraic formula, etc.) as a whole. The following example shows how to use this idea to solve the problem. For example, if you cut a rectangle to a square, and the remaining rectangle is similar to the original rectangle, the ratio of the long side to the short side of the original rectangle is ___ (Shanxi Provincial Examination in 1993) When you solve this problem, many students can According to the question, the proportions are listed, but because there is no “whole idea” in the mind, the ratio cannot be found finally. The difficulty in solving this problem lies in how to find the ratio from the ratio, and using the whole idea is to break through this difficulty. The effective way.