Question

计算奥数题，题目在下面，帮忙解一下！要详细点！

（0.1＋0.12＋0.123＋0.1234）×（0.12＋0.123＋0.1234＋0.12345）－（0.1＋0.12＋0.123＋0.1234＋0.12345）×（0.12＋0.123＋0.1234）

Answer 1

设（0.1+0.12+0.123+0.1234）=A （0.12+0.123+0.1234）=B
原式=A*（B+0.12345）-（A+0.12345）*B
=AB+0.12345A-（AB+0.12345B）..........................此处是括号，不能没有！
=AB+0.12345A-AB-0.12345B.....................................可直接写，不写上面那一步。
=0.12345*（A-B）.............乘法分配律
=0.012345

Answer 2

原式表示为A×B-C×D
则A - D = 0.1 = C - B,C-A=0.12345
原式=A×B - A×C + A×C - C×D
=A×(B - C)+ C×( A - D)
=(A - D)×(C - A)
=0.1×0.12345
=0.012345