数学题求简便运算详解，做好的给100分

Question

1>19.2*135-144/1000*1920+209*123/125

<2>1/1*3+1/3*5+1/5*7+......+1/97*99

<3>1/8128+1/254+1/508+1/1016+1/2032+1/4046+1/8128`

<4>44/45*37-8/45

<5>3/4*17+0.25*29

<6>12/13/(53.9*2/3)

<7>2.6/[(7/12-5/16)*1.6]

Answer 1

<1>
19.2*135-144/1000*1920+209*123/125
=19.2*135-14.4*19.2+209*(1-2/125)
=19.2*(135-14.4)+209-418/125
=(20-0.8)*120.6+209-418*8/1000
=2412-96.48+209-3.344
=2621-99.824
=2521.176

<2>
1/1*3+1/3*5+1/5*7+......+1/97*99
=[(1-1/3)+(1/3-1/5)+(1/5-1/7)+......+(1/97-1/99)]÷2
=(1-1/99)÷2
=49/99

<3>
1/8128+1/254+1/508+1/1016+1/2032+1/4064+1/8128
=1/8128+1/8128+1/4064+1/2032+1/1016+1/508+1/254
=1/4064+1/4064+1/2032+1/1016+1/508+1/254
=1/2032+1/2032+1/1016+1/508+1/254
=1/1016+1/1016+1/508+1/254
=1/508+1/508+1/254
=1/254+1/254
=1/127

<4>
44/45*37-8/45
=4/45*(11*37-2)
=4/45*(407-2)
=4/45*405
=36

<5>
3/4*17+0.25*29
=1/4*(3*17+29)
=1/4*(51+29)
=1/4*80
=20

<6>
12/13/(53.9*2/3)
=

<7>
2.6/[(7/12-5/16)*1.6]
=2.6/[7*1.6/12-5*1.6/16]
=2.6/[28/30-1/2]
=2.6*30/13
=6

Answer 2

1、原式=19.2*135-14.4*19.2+209*123*8/1000=19.2*120.6+205.656=2521.176；
2、原式=1/2(1-1/3+1/3-1/5+1/5-1/7+...+1/97-1/99)=1/2(1-1/99)=49/99；
3、原式=1/8128+1/8128+1/4064+1/2032+1/1016+1/508+1/254
=1/8128(1+1+2+4+8+16+32)=64/8128=1/127；
4、原式=(44*37-8)/45=36；
5、原式=(3*17)/4+29/4=(51+29)/4=20；
6、原式=(12*3)/(13*53.9*2)=0.0257；
7、原式=2.6/[(7*4-5*3)*1.6/48)]=(2.6*48)/(13*1.6)=6。

Answer 3

19.2*135-144/1000*1920+209*123/125
= (20-0.8)*135-144*(2-0.08)+209*(1-2/125)
=2700-0.8*135-288+144*0.08+209-209*2/125

=2700-288+209-135*0.8+144*0.08-418*0.008

=2700-79-0.008*(135*100-144*10+418)
=2621-0.008*(13500-1440+418)
=2621-0.008*12478

=2521.176

=1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+.....+1/2(1/97-1/99)
=1/2(1-1/3+1/3-1/5+1/5-1/7+...+1/97-1/99)
=1/2(1-1/99)
=1/2*98/99
=49/99

追问

加油写，写好我再加20分！

追答

1/8128+1/254+1/508+1/1016+1/2032+1/4046+1/8128
1/8128+1/254+1/508+1/1016+1/2032+1/4046+1/8128
=1/254+1/508+1/1016+1/2032+1/4064+1/8128*2
=1/254+1/2*1/254+1/4*1/254+1/8*1/254+1/16*1/254+1/32*1/254*2
=1/254(1+1/2+1/4+1/8+1/16+1/32*2)
=1/254(1+15/16+1/16)
=1/254*2
=1/127

44/45*37-8/45
44/45*37-8/45
=(1-1/45)*37-8/45
=37-37/45-8/45
=37-(37/45+8/45)
=37-1
=36

3/4*17+0.25*29
3/4*17+0.25*29
=(1-1/4)*17+1/4*29
=17-1/4*17+1/4*29
=17+1/4(29-17)
=17+1/4*12
=17+3
=20

12/13/(53.9*2/3)
12/13/(53.9*2/3)
=12/13*(1/(53.9*2/3))
=12/13*(1/(107.8/3))
=12/13*(3/107.8)
=12/13*(15/539)
=12*15/(13*539)
=180/7007

2.6/[(7/12-5/16)*1.6]
=2.6/[(4*7/48-5*3/48)*1.6]
=2.6/(13*1.6/48)
=2.6/(13/30)
=2.6*30/13
=0.2*30
=6

Answer 4

你的题表述的有问题吧，我看着就第二个没问题，你把1/1*3拆成1/1-1/3前面再乘以1/2就可以了，后面的也都依次这样拆成两项就可以约去中间相，只剩首尾两项。其他的表述的不清楚！

追问

不一定

追答

什么意思？

追问

对着呢，你仔细想一想！！我急呀！！！！！！！！！