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一、包含除的合理性大家知道:在算术中,被乘数与乘数所表达的意义是不相同的。比如,儿童分3组植树,每组5人,求参加人数?其算式是5×3=15(人)。被乘数5表示每组的人数,乘数3表示组数。并且算式不能列为:3×5=15(人)。由于除法是乘法的逆运算,因此,已知积和乘数求被乘数与已知积和被乘数求乘数,二者的意义也是不相同的。就是说,算式15÷3=5(人)与15+5=3(组)有不同的含义。前者表示:15个儿童分3组植树,求每组的人数;后者表示:15个儿童分组植树,每组5人,可分成几组?由此可见,在算术中,根据除法的定义,把已知积和乘数求被乘数这种情况的除法称为等分除,而把已知积和被乘数求乘数这种情况的除法叫做包含除,是合乎逻辑的,也是很自然的。
First, the inclusion of the plausibility We all know: in arithmetic, multiplicand multiplier expressed meaning is not the same. For example, children are divided into 3 groups of trees, each group of 5 people, seeking the number of participants? The formula is 5 × 3 = 15 (people). The multiplicand 5 indicates the number of people in each group, and the multiplier 3 indicates the number of groups. And the formula can not be listed as: 3 × 5 = 15 (people). Since division is the inverse of multiplication, the multiplication of the known multiplicand and multiplicand is known to be multiplied by the known multiplicand, and the significance of the two is not the same. That is, the formula 15 ÷ 3 = 5 (people) and 15 + 5 = 3 (group) have different meanings. The former said: 15 children in 3 groups of trees, seeking the number of each group; the latter said: 15 children in groups of trees, each group of 5, can be divided into several groups? Thus, in arithmetic, according to the definition of division, It is logical and very logical to call the division of the case where the known product and the multiplicand are multiplied by the division of the case of multiplying the known product and the multiplicand by the multiplicand Nature.