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2022年243有理数的加法 .pdf

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1、名师精编优秀教案第二十二课时第二十三课时一、课题2.4 有理数的减法二、教学目标1使学生掌握有理数减法法则并熟练地进行有理数减法运算；2培养学生观察、分析、归纳及运算能力三、教学重点和难点有理数减法法则四、教学手段现代课堂教学手段五、教学方法启发式教学六、教学过程（一）、从学生原有认知结构提出问题1计算：(1)(-2.6)+(-3.1)；(2)(-2)+3；(3)8+(-3)；(4)(-6.9)+02化简下列各式符号：(1)-(-6)；(2)-(+8)；(3)+(-7)；(4)+(+4)；(5)-(-9)；(6)-(+3)3填空：(1)_+6=20；(2)20+_=17；(3)_+(-2)=-

2、20；(4)(-20)+_=-6在第 3 题中，已知一个加数与和，求另一个加数，在小学里就是减法运算如_+6=20，就是求 20-6=14，所以 14+6=20那么(2)，(3)，(4)是怎样算出来的？这就是有理数的减法，减法是加法的逆运算（二）、师生共同研究有理数减法法则问题 1(1)(+10)-(+3)=_；(2)(+10)+(-3)=_教师引导学生发现：两式的结果相同，即(+10)-(+3)=(+10)+(-3)教师启发学生思考：减法可以转化成加法运算但是，这是否具有一般性？问题 2(1)(+10)-(-3)=_；(2)(+10)+(+3)=_名师精编优秀教案对于(1)，根据减法意义，这

3、就是要求一个数，使它与-3 相加等于+10，这个数是多少？(2)的结果是多少？于是，(+10)-(-3)=(+10)+(+3)至此，教师引导学生归纳出有理数减法法则：减去一个数，等于加上这个数的相反数教师强调运用此法则时注意“两变”：一是减法变为加法；二是减数变为其相反数（三）、运用举例变式练习例 1计算：(1)(-3)-(-5)；(2)0-7例 2计算：(1)18-(-3)；(2)(-3)-18；(3)(-18)-(-3)；(4)(-3)-(-18)通过计算上面一组有理数减法算式，引导学生发现：在小学里学习的减法，差总是小于被减数，在有理数减法中，差不一定小于被减数了，只要减去一个负数，其差

4、就大于被减数例 3计算：(1)(-3)-6-(-2)；(2)15-(6-9)例 4 15 比 5高多少？15 比-5 高多少？课堂练习1计算(口答)：(1)6-9；(2)(+4)-(-7)；(3)(-5)-(-8)；(4)(-4)-9；(5)0-(-5)；(6)0-52计算：(1)15-21；(2)(-17)-(-12)；(3)(-2.5)-5.9；（四）、小结1教师指导学生阅读教材后强调指出：由于把减数变为它的相反数，从而减法转化为加法有理数的加法和减法，当引进负数后就可以统一用加法来解决2不论减数是正数、负数或是零，都符合有理数减法法则在使用法则时，注意被减数是永不变的七、练习设计1计算：

5、(1)-8-8；(2)(-8)-(-8)；(3)8-(-8)；文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9

6、HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6

7、G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K

8、5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P

9、4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N

10、4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:

11、CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4名师精编优秀教案(4)8-8；(5)0-6；(6)6-0；(7)0-(-6)；(8)(-6)-02计算：(

12、1)16-47；(2)28-(-74)；(3)(-37)-(-85)；(4)(-54)-14；(5)123-190；(6)(-112)-98；(7)(-131)-(-129)；(8)341-2493计算：(1)1.6-(-2.5)；(2)0.4-1；(3)(-3.8)-7；(4)(-5.9)-(-6.1)；(5)(-2.3)-3.6；(6)4.2-5.7；(7)(-3.71)-(-1.45)；(8)6.18-(-2.93)5计算：(1)(3-10)-2；(2)3-(10-2)；(3)(2-7)-(3-9)；6当 a=11，b=-5，c=-3 时，求下列代数式的值：(1)a-c；(2)b-c；(

13、3)a-b-c；(4)c-a-b利用有理数减法解下列问题(第 79 题)：7世界最高峰是珠穆朗玛峰，海拔高度是8848m，陆上最低处是位于亚洲西部的死海湖，湖面海拔高度是-392m两处高度相差多少？8分别求出数轴上两点间的距离：(1)表示数 6 的点与表示数2 的点；(2)表示数 5 的点与表示数0 的点；(3)表示数 2 的点与表示数-5 的点；(4)表示数-1 的点与表示数-6 的点9某地一周内每天的最高气温与最低气温如下表，哪天的温差最大？哪天的温差最小？10*填空：(1)如果 a-b=c，那么 a=_；(2)如果 a+b=c，那么 a=_；(3)如果 a+(-b)=c，那么 a=_；(

14、4)如果 a-(-b)=c，那么 a=_文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10

15、K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4

16、P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6

17、N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码

18、:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7

19、W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9

20、 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4名师精编优秀教案11*用“”或“”号填空：(1)如果 a0，b0，那么 a-b_0；(2)如果 a0，b0，那么 a-b_0；(

21、3)如果 a0，b0，|a|b|，那么 a-b_0；(4)如果 a0，b0，那么 a-(-b)_012*解下列方程：(1)x+8=5；(2)x-(-7)=-3；(3)x-11=-4；(4)6+x=-1013*把下面加减法混合运算的式子改成只含加法的式子：(1)-30-15+13-(-7)；(2)-7-4+(-9)-(-5)八、板书设计25 有理数的减法（一）知识回顾（三）例题解析（五）课堂小结例 1、例 2、例 3（二）观察发现（四）课堂练习练习设计九、教学后记根据斯托利亚尔的观点，我们把教学作为一个过程，那么在教学一个新的内容时，我们总是把学生视为探索者，将教学过程模拟成一个“科研过程”，引

22、导学生发现矛盾，提出问题，最后用新的理论来解决原先提出问题，解决原先发现的矛盾这种教法，归纳起来就是“三部曲”：提出问题建立理论解决问题这节课的设计正是这一教学方法的具体体现文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编

23、码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q

24、7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F

25、9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10

26、A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U1

27、0K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH

28、4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J

29、6N4名师精编优秀教案文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L

30、1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文

31、档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK

32、2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F

33、6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS

34、10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4文档编码:CK2Q7W6F6F9 HS10A6G2U10K5 ZH4P4L1J6N4

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关键词：: 2022年243有理数的加法 2022 243 有理数加法

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