四则运算的定律和性质是四则运算法则和一些速算的根据。本讲中所涉及的运算定律和性质,都只在非负整数这个范围内讨论其正确性,实际上,对任意数域它们都是成立的。另外,文中没有给出证明的性质,留给读者自己练习。加法运算定律两个数相加,交换加数的位置,它们的和不变。这叫做加法交换律(第五册p.21)。即 The law and nature of the four operations are based on four algorithms and some quick calculations. The laws and nature of the operations involved in this lecture discuss their correctness only in the context of non-negative integers. In fact, they are valid for any number of fields. In addition, the article did not give the nature of the proof, leaving the reader to practice their own. The law of addition adds two numbers, exchanging the places of the sums, and their sum unchanged. This is called the law of addition and exchange (Book V, p. 21). which is