作业帮1.1乘1.2乘1.3乘1.4乘1.5=?简便方法
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/05 14:39:35
1.1乘1.2乘1.3乘1.4乘1.5=?简便方法
1.1乘1.2乘1.3乘1.4乘1.5=?简便方法
1.1乘1.2乘1.3乘1.4乘1.5=?简便方法
方法一：
1.1×1.2×1.3×1.4×1.5
设：1.1=a 可知：1.21=a²,1.331=a³,1.4641=(a²)²,1.61051=a×(a²)²
那么：
原式=a(a+0.1)(a+0.2)(a+0.3)(a+0.4)
=a(a²+0.2a+0.1a+0.02)(a²+0.4a+0.3a+0.12)
=a(a²+0.3a+0.02)(a²+0.7a+0.12)
=a[((a²)²+0.7a³+0.12a²)+(0.3a³+0.21a²+0.036a)+(0.02a²+0.014a+0.0024)]
=a[(a²)²+(0.7+0.3)a³+(0.12+0.21+0.02)a²+(0.036+0.014)a+0.0024]
=a[(a²)²+a³+0.35a²+0.05a+0.0024]
=[a×(a²)²]+(a²)²+0.35a³+0.05a²+0.0024a
将1.1=a代入上式,又可知：1.21=a²,1.331=a³,1.4641=(a²)²,1.61051=a×(a²)²
所以：
原式=1.61051+1.4641+(0.35×1.331)+(0.05×1.21)+(0.0024×1.1)
=1.61051+1.4641+0.46585+0.0605+0.00264
=3.6036
方法二：
1.1×1.2×1.3×1.4×1.5
=[(1+0.1)×(1+0.2)]×[(1+0.3)×(1+0.4)×(1+0.5)]
=(1+0.2+0.1+0.02)×[(1+0.4+0.3+0.12)×(1+0.5)]
=(1+0.2+0.1+0.02)×[(1+0.5)+0.4×(1+0.5)+0.3×(1+0.5)+0.12×(1+0.5)]
=(1+0.2+0.1+0.02)×[(1+0.5)+(0.4+0.2)+(0.3+0.15)+(0.12+0.06)]
=(1+0.2+0.1+0.02)×(1.5+0.6+0.45+0.18)
=(1.2+0.12)×(1.95+0.78)
=(1.2×1.95)+(1.2×0.78)+(0.12×1.95)+(0.12×0.78)
=2.34+0.936+0.234+0.0936
=1.17+2.4336
=3.6036
方法三：
1.1×1.2×1.3×1.4×1.5
因为：1.1×1.2×1.3×1.4×1.5=(11×12×13×14×15)÷100000
所以,原式=(11×12×13×14×15)÷100000
因此：
第一步先计算：
11×12×13×14×15
=[(10+1)×(10+2)]×[(10+3)×(10+4)×(10+5)]
=(100+20+10+2)×[(10+3)×(100+50+40+20)]
=(100+20+10+2)×[((10+3)×100)+((10+3)×50)+((10+3)×40)+((10+3)×20)]
=(100+20+10+2)×(1300+650+520+260)
=(120+12)×(1170+1560)
=(120×1170)+(120×1560)+(12×1170)+(12×1560)
=140400+187200+14040+18720
=360360
第二步再计算：
360360÷100000=3.6036