分数加法法则与乘法法则的辨析——以两个算式的比较分析为例  

Comparison of Fractional Addition Rule and Fractional Multiplication Rule——Taking the Comparative Analysis of Two Formulas as an Example

作　　者：张锐 詹紫浪 ZHANG Rui;ZHAN Zi-lang(School of Information Engineering,Lanzhou City University,Lanzhou Gansu 730070;Journal Editorial Department,Lanzhou City University,Lanzhou Gansu 730070)

机构地区：[1]兰州城市学院信息工程学院,甘肃兰州730070 [2]兰州城市学院学报编辑部,甘肃兰州730070

出　　处：《甘肃高师学报》2023年第2期69-73,共5页Journal of Gansu Normal Colleges

基　　金：甘肃省教育科学“十三五”规划2019年度重点课题“新工科背景下地方应用型本科院校高等数学教学改革研究——以兰州城市学院为例”(GS[2019]GHBZ146).

摘　　要：文章在梳理小学阶段分数概念的基础上,对分数的加法和乘法运算法则进行比较,既有由浅入深合乎情理的认识,也有严密精准合乎逻辑的推理,使学生真正理解整数乘法可以看作是特殊的整数加法,但分数乘法并不是分数加法的特殊情况,分数加法和分数乘法有各自不同的运算法则.然后,结合分数的公理化定义,对分数加法和乘法运算法则作进一步验证.This paper makes a detailed analysis of the concept of fraction in primary school,on the basis of which the addition and multiplication of fractions are compared.Through simple to profound explanations and logical reasoning,students can truly understand that integer multiplication is a special form of integer addition,but fractional multiplication is not a special case of fractional addition.Fractional addition and multiplication have their own different algorithms.Then,combined with the axiomatic definition of fractions,the fractional addition and multiplication algorithms are further verified.

关 键 词：分数加法法则 分数乘法法则 比例加法 算理分析 公理化定义分析 

分 类 号：O121.1[理学—数学]