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同学们在解有理数的运算题时,由于弄不清有理数的概念、性质、运算顺序,经常出错.下面就大家在解题中经常出现的错误分类辨析如下.一、忽视符号例1计算:-1~6+8÷(-2)~2-(-4)×(-3).错解:-1~6+8÷(-2)~2-(-4)×(-3)=1+8÷4+12=1+2+12=15.辩析:错解中有两处错误:一是-1~6=1,这是由于不理解乘方的意义造成的;二是-(-4)×(-3)=12,这是由于没有掌握乘法的运算法则造成的.正解:-1~6+8÷(-2)~2-(-4)×(-3)=-1+8÷4-12=-1+2-12=-11.二、错用分配律例2计算:(-1/30)÷(2/3-1/10+1/6-2/5)错解:(-1/3)÷(2/3-1/10+1/6-2/5)=(-1/30)÷2/3-(-1/30)÷1/10+(-1/30)÷1/6-(-1/30)÷2/5
Students in the solution of rational numbers arithmetic problems, because they can not figure out the concept of rational numbers, nature, sequence of operations, often mistakes. Below we often in the problem-solving error classification as follows: First, ignoring the symbol Example 1 Calculation: 1 ~ 6 + 8 ÷ (-2) ~ 2 - (- 4) × (-3). Malposition: -1 ~ 6 + 8 ÷ (-2) ~ 2 - (- 4) × (-3) = 1 + 8 ÷ 4 + 12 = 1 + 2 + 12 = 15. Dispute: There are two mistakes in the wrong solution: one is -1 to 6 = 1, which is due to the meaning of the square caused by the failure to understand; the second is - (- 4) × (-3) = 12, which is due to the inability to grasp the multiplication algorithm. Positive Solutions: -1 ~ 6 + 8 ÷ (-2) ~ 2 - (- 4) × = -1 + 8 ÷ 4-12 = -1 + 2-12 = -11 Second, the misuse allocation law 2 calculation: (- 1/30) ÷ (2 / 3-1 / 10 +1 / 6- (1/1) ÷ (2 / 3-1 / 10 + 1 / 6-2 / 5) = (- 1/30) ÷ 2/3 - (- 1/30) ÷ 1/10 + (- 1/30) ÷ 1/6 - (- 1/30) ÷ 2/5