小学奥数11

（1+1/2+1/4）*（1/2+1/4+1/6）-（1+1/2+1/4+1/6）*（1/2+1/4）
=(4/4 +2/4 +1/4) *(6/12 +3/12 +2/12)-(12/12 +6/12 +3/12 +2/12)*(6/12 +3/12)
=7/4 *11/12 -23/12 *9/12
=77/48-207/144
=77/48 -207/144
=231/144 -207/144
=(231-207)/144
=24/144
=1/6

[1+(1/2+1/4）]*（1/2+1/4+1/6）-（1+1/2+1/4+1/6）*（1/2+1/4）
=（1/2+1/4+1/6)+(1/2+1/4）*（1/2+1/4+1/6）-（1+1/2+1/4+1/6）*（1/2+1/4）
=1/2+1/4+1/6+（1/2+1/4）*(1/2+1/4+1/6-1+1/2+1/4+1/6)
=1/2+1/4+1/6+（1/2+1/4）*(-1)
=1/2+1/4+1/6-1/2-1/4
=1/6

（1+1/2+1/4）*（1/2+1/4+1/6）-（1+1/2+1/4+1/6）*（1/2+1/4）=？
令：1/2+1/4=a
1/2+1/4+1/6=b
(1+a)*b-(1+b)*a
=b+ab-a-ab
=b-a
=1/2+1/4+1/6-1/2-1/4
=1/6