Question

小学数学 计算：（1+1/2+1/3+1/4）x（1/2+1/3+1/4+1/5）x（1+1/2+1/3+1/4+1/5）x（1/2+1/3+1/4）

小学数学 计算：（1+1/2+1/3+1/4）x（1/2+1/3+1/4+1/5）x（1+1/2+1/3+1/4+1/5）x（1/2+1/3+1/4）用简便方法

Answer 1

（1+1/2+1/3+1/4）x（1/2+1/3+1/4+1/5）-（1+1/2+1/3+1/4+1/5）x（1/2+1/3+1/4）
中间该是减号.
设1/2+1/3+1/4+1/5=M,1/2+1/3+1/4=N
原式=(1+N)*(M)-(1+M)*N
=M+NM-N-NM
=M-N
=1/5

Answer 2

中间是减号吧
(1+1/2+1/3+1/4)(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)(1/2+1/3+1/4)
=[1+(1/2+1/3+1/4)][(1/2+1/3+1/4)+1/5]-[(1+1/5) + (1/2+1/3+1/4)] * (1/2+1/3+1/4)
令X=1/2+1/3+1/4)
则原式＝(1+x)(x+1/5) - ((1+1/5)+x)*x
= x + 1/5 +x*x +x/5 -[x*x +x +x/5]
= x+1/5+x*x+x/5 -x*x -x -x/5
= 1/5

Answer 3

(1+1/2+1/3+1/4)×(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)×(1/2+1/3+1/4)
=1 x(1/2+1/3+1/4+1/5）+ (1/2+1/3+1/4) x(1/2+1/3+1/4+1/5) -[1 x(1/2+1/3+1/4)+(1/2+1/3+1/4+1/5)x(1/2+1/3+1/4)]
=1 x(1/2+1/3+1/4+1/5）+ (1/2+1/3+1/4) x(1/2+1/3+1/4+1/5) -1 x(1/2+1/3+1/4)-(1/2+1/3+1/4+1/5)x(1/2+1/3+1/4)
=(1/2+1/3+1/4+1/5)-(1/2+1/3+1/4)
=1/5

Answer 4

(1+1/2+1/3+1/4)(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)(1/2+1/3+1/4)
=[1+(1/2+1/3+1/4)][(1/2+1/3+1/4)+1/5]-[(1+1/5) + (1/2+1/3+1/4)] * (1/2+1/3+1/4)
令X=1/2+1/3+1/4)
则原式＝(1+x)(x+1/5) - ((1+1/5)+x)*x
= x + 1/5 +x*x +x/5 -[x*x +x +x/5]
= x+1/5+x*x+x/5 -x*x -x -x/5
= 1/5

Answer 5

1/5