急~求高人帮忙出25道分数简算（简单一点儿的,如分配律、结合律什么的,要答案~~~~~~~~~~~急

Question

急~求高人帮忙出25道分数简算（简单一点儿的,如分配律、结合律什么的,要答案~~~~~~~~~~~急

Answer 1

1.
3/(1*4)=1/1-1/4
3/(4*7)=1/4-1/7
...
3/(97*100)=1/97-1/100
因此原式=1/1-1/4+1/4-1/7+...+1/97-1/100=1-1/100=99/100
2.
1/2=1-1/2
1/6=1/2-1/3
1/12=1/3-1/4
...
1/90=1/9-1/10
因此原式=1-1/2+1/2-1/3+1/3-1/4+...+1/9-1/10=1-1/10=9/10
1/2+5/6+11/12+...+109/110
=(1-1/2)+(1-1/6)+...+(1-1/110)
=10-(1/2+1/6+1/12+...+1/110)
=10-[1/(1*2)+1/(2*3)+1/(3*4)+...+1/(10*11)]
=10-[(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/10-1/11)]
=10-(1-1/11)
=10-10/11
=100/11
检举 2/1(1+2)+3/(1+2)(1+2+3)+...+10/(1+2+...+9)(1+2+...+10)
=(1-1/(1+2))+(1/(1+2)-1(1+2+3))+...+(1/(1+2+...+9)-1/(1+2+...+10))
=1-1/55
=54/55
1/2+5/6+11/12+19/20+29/30+41/42+55/56
=(1-1/1*2)+(1-1/2*3)+...+(1-1/7*8)
=7-(1/1*2+1/2*3+...+1/7*8)
=7-((1-1/2)+(1/2-1/3)+...+(1/7-1/8))
=7-(1-1/8)
=49/8
127/139*140
＝127/139×(139+1)
＝127/139×139＋127/139×1
＝127＋127/139
＝127又127/139
(1)5/6+5*2/9=5*[(1/6)+(2/9)]=35/18
(2)7/12-8/15*5/16=(7/12)-(1/6)=5/12
(3)150-150*3/10=150*[1-(3/10)]=1050
(4)(3/5+3/5)*3/7=2*(3/5)*(3/7)=12/35
1/42+1/56+1/72+1/90+1/110+1/132
=(1/6-1/7)+(1/7-1/8)+(1/8-1/9)+(1/9-1/10)+(1/10-1/11)+(1/11-1/12)
中间正负抵消
=1/6-1/12
=1/12
39*148/149+148*86/149+48*74/149
=39*2*74/149+74*2*86/149+48*74/149
=（39*2+2*86+48）*74/149
=298*74/149
=2*74*149/149
=2*74
=148
4/3-1/15-1/15-3/15
＝4/3-（1/15+1/15+3/15）
＝4/3-1/3
＝1
3/5-1/4+2/5-3/4
=(3/5+2/5)-(1/4+3/4)
=1-1
=0
7/15-(4/15+2/25)
=(7/15-4/15)-2/25
=1/5-2/25
=5/25-2/25
=3/25
希望能给你帮助!