38 67 45
例 4：计算： 1 2 2 3 3 4 4 5 3 1 5 2 7 3 9 4
3 4 5 6 3 4 5 6
模仿练习
计算：（1 5 3 5 9 5 ）（1 1 3 1 9 1 ） 99 33 11 99 33 11
加法交换律：a b b a ；
加法结合律：(a b) c a (b c) ；
乘法交换律： a b b a
乘法结合律： a b c a (b c)
乘法分配律： a (b c) a b a c 减法的性质： a b c a (b c)
思路点拨 以上的每个分数的分母正好是相邻两个自然数的积，而且分子正好是分母
两个因数的差（1），我们可以直接利用裂项公式进行裂项产生加减抵消后化繁
为简。
模仿练习
1 1 4

4
1
7

1 7 10

00
例 2：计算：975×0.25+ 9 3 76 －9.75
4
模仿练习
糖果工作室原创文档
数学
小升初衔接班教程
目录
糖果工作室原创文档
第一讲 第二讲 第三讲 第四讲 第五讲 第六讲 第七讲 第八讲 第九讲 第十讲 第十一讲 第十二讲 第十三讲 第十四讲 第十五讲
计算中的技巧 1 ·········································································· 行程问题 5 ················································································· 工程问题 8 ················································································· 图形的面积 17 ············································································· 有理数 21 ····················································································· 有理数的加减法 24 ······································································ 有理数的乘除法 28 ······································································ 有理数的乘方 科学计数法 30 ·················································· 整式 33 ·························································································· 一元一次方程 35 ··········································································· 实际问题与一元一次方程 39 ························································· 图形的初步认识 43 ········································································ 角 45 ······························································································ 相交线 平行线 51 ········································································· 平行线的性质 命题 定理 54 ·························································
除法的性质： a b c a (b c)
3、灵活运用通分和约分
4、分数、小数化成统一的形式再计算，一般是分数化成小数。
5、凑整法：运用运算定律，使式子中一些数凑成整十、整百或整千的
数再计算。我们通常是利用运算律将一些数凑成整一、整十或整百再计算。
6、分组分解法：利用交换律和结合律对式子进行分组求解，最后再综
合求解。
7、综合方法：计算比较复杂的式子时要多种方法一起用。
重难点
运算法则和运算定律与性质的掌握和应用。
易错点
第 1 页 共 47 页
糖果工作室原创文档
去括号是的变号法则，尤其是括号前是减号。
精典例题 例 1： 1 ＋ 1 ＋ 1 ＋ 1 ＋ 1 ＋ 1 ＋ 1 ＋ 1 ＋ 1
2 6 12 20 30 42 56 72 90
第一讲 计算的技巧
糖果工作室原创文档
知识导航
我们在进行运算时，除了熟练掌握好运算法则外，还要通过观察和分析，
找出题目中数的特点，合理、有效地进行计算。整数、小数与分数四则混合运
算常用的方法、技巧如下：
1、运算法则：先乘除后加减；先算小括号，再算中括号；同级运算从左
到右依次计算。
2、运算定律与性质：
31 25 36 4 11 4.44 4 5
37 111 37 25
8
例 3： 51 2 ÷ 5 + 71 3 ÷ 7 + 91 4 ÷ 9
33 44 55
（2010 年成都育才网络班招生数学试题）
第 2 页 共 47 页
模仿练习
糖果工作室原创文档
计算： 85 1 3 71 1 6 56 1 4 （2013 年成都外国语学校本地生招生考试题）