Question

问几道6年级的简算题，大家进来看看，可以追加100分！

1：9.6+99.6+999.6+9999.6+99999.6

2：（0.75-0.75乘三分之一）除以四分之三

3：1998除以1998又1999分之1998
4：
2009+20092009+200920092009
---------------------------
2010+20102010+201020102010

5：9999的平方+1999

6：99999乘77778+33333乘66666

7：四分之一+二十八分之一+七十分之一+一百三十分之一+二百零八分之一

8：二分之一+四分之一+八分之一+……+二百五十六分之一

9：3.75乘735-八分之三乘5730+16.2乘62.5

9：
第4题的横线是分数线啊，大家坐坐，做好了100分

Answer 1

1：9.6+99.6+999.6+9999.6+99999.6
=10-0.4+100-0.4+1000-0.4+10000-0.4+100000-0.4
=111110-0.4*5
=111110-2
=111108

2：(0.75-0.75*(1/3))/(3/4)
=(0.75*(1-1/3))/(3/4)
=(0.75*(2/3))/(3/4)
=(1.5/3)/(3/4)
=(1/2)*(4/3)
=2/3

3：1998/(1998又1998/1999)
=1998/((1998*1999+1998)/1999)
=1998*1999/(1998*1999+1998)
=1998*1999/(1998*(1999+1))
=1999/2000

4：(2009+20092009+200920092009)/(2010+20102010+201020102010)
=(20094018+200920092009)/(20104020+201020102010)
=(200940186027)/(201040206030)

5：9999^2+1999
=(10000-1)^2+1999
=10000^2-20000+1+1999
=10000^2
=100000000

6：99999*77778+33333*66666
=99999*77778+33333*3*22222
=99999*77778+99999*22222
=99999*(77778+22222)
=99999*100000
=9999900000

7：1/4+1/28+1/70+1/130+1/208
=7/28+1/28+1/70+1/130+1/208
=8/28+1/70+1/130+1/208
=2/7+1/70+1/130+1/208
=20/70+1/70+1/130+1/208
=21/70+1/130+1/208
=3/10+1/130+1/208
=39/130+1/130+1/208
=40/130+1/208
=20/65+1/208
=320/1040+5/1040
=325/1040
=5/16

8：1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
=2/4+1/4+1/8+1/16+1/32+1/64+1/128+1/256
=3/4+1/8+1/16+1/32+1/64+1/128+1/256
=6/8+1/8+1/16+1/32+1/64+1/128+1/256
=7/8+1/16+1/32+1/64+1/128+1/256
=14/16+1/16+1/32+1/64+1/128+1/256
=15/16+1/32+1/64+1/128+1/256
=30/32+1/32+1/64+1/128+1/256
=31/32+1/64+1/128+1/256
=62/64+1/64+1/128+1/256
=63/64+1/128+1/256
=126/128+1/128+1/256
=127/128+1/256
=254/256+1/256
=255/256

9：3.75*735-(3/8)*5730+16.2*62.5
=3.75*735-(3/4)*2865+16.2*62.5
=375*7.35-(3/4)*2865+16.2*62.5
=375*(7.35-(3/4)*7.64)+16.2*62.5
=375*(7.35-3*1.91)+16.2*62.5
=375*1.62+16.2*62.5
=1.62*(375+62.5)
=1.62*427.5
=708.75