小学5年级数学题(分数的简便运算):

问题描述:

小学5年级数学题(分数的简便运算):
1:1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90
2:1/5×7 + 1/7×9 + 1/9×11 + 1/ 11×13 + 1/ 13×15
3: 6/1×7 - 6/7×13 - 6/13×19- ...-6/97×103
现在前面的都弄懂了,就是最后一道和大家做的有出入,帮我看看做得对不.
6/1×7 - 6/7×13 - 6/13×19- ...-6/97×103
=(1-1/103)×1/2
=102/103×1/2
=51/103
1个回答 分类:数学 2014-10-22

问题解答:

我来补答
1:1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90
=(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)+(1/9-1/10)
=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
=1/3-1/10
=7/30
2:1/5×7 + 1/7×9 + 1/9×11 + 1/ 11×13 + 1/ 13×15
=1/2×(1/5-1/7)+1/2×(1/7-1/9)+1/2×(1/9-1/11)+1/2×(1/11-1/13)+1/2×(1/13-1/15)
=1/2×(1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15)
=1/2×(1/5-1/15)
=1/2×2/15
=1/15
3: 6/1×7 - 6/7×13 - 6/13×19- ...-6/97×103
=(1-1/7)-(1/7-1/13)-(1/13-1/19)-.-(1/97-1/103)
=1-1/7-1/7-1/13+1/13-1/19-.-1/97+1/103
=1-1/7-1/7+1/103
=5/7+1/103
=522/721
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