76*(1/23-1/53)+23*(1/53+1/76)+53*(1/23-1/76)的简便算法
问题描述:
76*(1/23-1/53)+23*(1/53+1/76)+53*(1/23-1/76)的简便算法
请说明理由,
答
76*(1/23-1/53)+23*(1/53+1/76)-53*(1/23-1/76)
=76/23-76/53+23/53+23/76-53/23+53/76
=(76/23-53/23)-(76/53-23/53)+(23/76+53/76)
=1-1+1
=1