题目

计算：①12又8分之7--4又3分之2+3又3分之1--3.875 ②14.15--（7又8分之7--6又20分之17）--2.125
③13又13分之7--（4又4分之1+3又13分之7）--0.75
④1--0.1+2分之1--0.34+3分之1--0.56+5分之1－0.78
⑤1--2分之1--4分之1--8分之1--16分之1--32分之1--64分之1
⑥2分之1+4分之3+8分之7＋16分之15+32分之31+64分之63+128分之127+256分之255

提问时间：2020-07-22

答案

12又7/8-4又2/3+3又1/3-3.875
=12又7/8-4又2/3+3又1/3-3又7/8
=(12又7/8-3又7/8)-(4又2/3-3又1/3)
=9-1又1/3
=7又2/3
14.15-(7又7/8-6又17/20)-2.125
=14又3/20-7又7/8+6又17/20-2又1/8
=(14又3/20+6又17/20)-(7又7/8+2又1/8)
=21-10
=11
13又7/13-(4又1/4+3又7/13)-0.75
=13又7/13-4又1/4-3又7/13-3/4
=(13又7/13-3又7/13)-(4又1/4+3/4)
=10-5
=5
1-0.1+1/2-0.34+1/3-0.56+1/5-0.78
=[1-(0.1+0.34+0.56)]+(1/2+1/3+1/5)-0.78
=(1-1)+(15/30+10/30+6/30)-0.78
=31/30-0.78
=31/30-39/50
=155/150-117/150
=38/150
=19/75
1-1/2-1/4-1/8-1/16-1/32-1/64
=1-(1/2+1/4+1/8+1/16+1/32+1/64)
=1-(1/2+1/4+1/8+1/16+1/32+1/64+1/64)+1/64
=1-(1/2+1/4+1/8+1/16+1/32+1/32)+1/64
=1-(1/2+1/4+1/8+1/16+1/16)+1/64
=1-(1/2+1/4+1/8+1/8)+1/64
=1-(1/2+1/4+1/4)+1/64
=1-(1/2+1/2)+1/64
=1/64
1/2+3/4+7/8+15/16+31/32+63/64+127/128+255/256
=1-1/2+1-1/4+1-1/8+1-1/16+1-1/32+1-1/64+1-1/128+1-1/256
=8-(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256)
=8-(1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/256)+1/256
=8-1+1/256
=7+1/256
=7又1/256