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等价变换法就是将一个较复杂的问题变换成等价的、较简单的新问题,通过探索新问题的答案,使原问题获解。有许多数学题目用常规思路、方法求解,或是实施繁难,或是思路受阻。而灵活运用等价变换法,可使解答由繁变简,思路由受阻变畅通。下面举例浅析等价变换法在解题中的作用。 一、等价变换使解答简便 例1:81 18/19÷6.3×0.7 解题浅析:此题若按照四则运算顺序进行计算,第一步算“81 18/19÷6.3”时,首先把带分数、小数都化为假分数,然后根据分数除法的法则计算,解题过程繁琐,一不细心还会出错。事实上,只要认真分析、细致观察该题的结构特点,就会发现:把6.3等价变换成“9×0.7”后,再根据有关运算性质、定律使原题计算简便。 解:原式=81 18/19÷(9×0.7)×0.7
Equivalent transformation method is to transform a more complex problem into equivalent, simpler and new problem, and solve the original problem by exploring the answer to the new problem. There are many math problems with conventional ideas, methods to solve, or the implementation of complex, or blocked ideas. The flexible use of equivalent transformation method, can simplify the solution from the complex, ideas blocked by the change becomes unblocked. The following example illustrates the role of equivalent transformation method in solving problems. First, the equivalent transform to make the solution simple Example 1:81 18/19 ÷ 6.3 × 0.7 Problem Analysis: If the problem is calculated according to the four arithmetic sequence, the first step is “81 18/19 ÷ 6.3”, the first With fractional, fractionalized into fake scores, and then calculated according to the rules of fractional division, the problem-solving process cumbersome, not careful will make mistakes. In fact, as long as careful analysis and careful observation of the structural features of the title, we will find that: After transforming the equivalent of 6.3 to “9 × 0.7”, the original title is calculated according to the nature of the operation and the law. Solution: Original = 81 18/19 ÷ (9 × 0.7) × 0.7