不用竖式计算,你能判断87.8*6.5与87.9*6.4哪个乘积大吗?请写出比较过程.

Question

不用竖式计算,你能判断87.8*6.5与87.9*6.4哪个乘积大吗?请写出比较过程.

Answer 1

87.8*6.5-87.9*6.4
=（87+0.8）*（6+0.5）-（87+0.9）*（6+0.4）
=87*6+0.8*6+0.5*0.8+87*0.5-87*6-87*0.4-0.9*0.4-0.9*6
=87*（6+0.5-0.4-6）+ 0.8*（6+0.5）-0.9*（0.4+6）
=87*0.1+0.8*6.5-0.9*6.4
=87*0.1+0.8*（6.4+0.1）-0.9*6.4
=87*0.1+0.8*6.4+0.8*0.1-0.9*6.4
=87*0.1+6.4*（0.8-0.9）+0.8*0.1
=87*0.1-6.4*0.1+0.8*0.1 ＞0
∴87.8*6.5＞87.9*6.4