(1/6+1/7+1/8)×(1/7+1/8+1/9)-(1/6+1/7+1/8+1/9)×(1/7+1/8)
- 时间:2020-06-13 17:16:40
- 分类:数学世界
- 阅读:93 次
“神马都是浮云”同学问:(1/6+1/7+1/8)×(1/7+1/8+1/9)-(1/6+1/7+1/8+1/9)×(1/7+1/8)怎么计算?第二种问法,请问一下各位:(6分之1+7分之1+8分之1)*(7分之1+8分之1+9分之1)—(6分之1+7分之1+8分之1+9分之1)*(7分之1+8分之1)这道算式等于多少啊?应该有简便算法吧!有老师能告诉我方法吗?
数学题解答:此题算式较长,其中有些部分为几个分数相加,且多次出现,故可以用换元法来解决。设1/6+1/7+1/8=a,则原式变成:
=(1/7+1/8+1/9)a-(a+1/9)×(1/7+1/8)
=(1/7+1/8+1/9)a-(1/7+1/8)a-(1/7+1/8)×1/9
=1/9a-(1/7+1/8)×1/9
此时再将a换回,变成1/6+1/7+1/8,这样算式又变成了:
=(1/6+1/7+1/8)×1/9-(1/7+1/8)×1/9
=1/6×1/9
=1/54
至此,已算出得数,主要用了换元法和乘法分配律解决了这个问题。
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