借助乘法的运算律说明式子(a+b+c)÷d=a÷d+b÷d+c÷d的正确性,并计算下列各题:

问题描述:

借助乘法的运算律说明式子(a+b+c)÷d=a÷d+b÷d+c÷d的正确性,并计算下列各题:
① ﹣1/201+13又1/3÷5-(-6又2/3)÷5+(-196又1/7)÷5+76又1/6÷5
②-8-[-7+(1-2/3×0.6)÷(-3)]

证明:(a+b+c)÷d=(a+b+c)×1/d=a×1/d+b×1/d+c×1/d+d×1/d=a÷d+b÷d+c÷d
1原式=(40/3+20/3-196+76-1/7+1/6)÷5﹣1/201=(20-120+1/42)÷5﹣1/201=(-100+1/42)÷5-1/201=(-100)÷5+1/42÷5﹣1/201=(-100)÷5+1/201﹣1/201=-20
2原式8-[-7+1×(-1/3)-(2/3×0.6)×(-1/3)]=8-[-7-1/3+2/15]=8-[-7-1/5]=8+36/5=76/5