五下数学同步上的1/2-1/3+1/4-1/5+1/6-1/7等于多少

题目

五下数学同步上的1/2-1/3+1/4-1/5+1/6-1/7等于多少

答案

1/2-1/3+1/4-1/5+1/6-1/7
=1/2+1/4+1/6-1/3-1/5-1/7
=1/2+1/4+1/6-[1/3+1/5+1/7] --2,4,6最小公倍数是12.3,5,7最小公倍数是105.
=6/12+3/12+2/12 - [35/105+21/105+15/105]
=11/12 -71/105 --12*105 =1260
=1155/1260 - 852/1260
=303/1260
=101/420
简便算法为：
1/2-1/3+1/4-1/5+1/6-1/7
=[3-2] /[2*3] +[5-4]/[5*4]+[7-6]/[7*6]
=1/6 + 1/20+ 1/42
=70/420 +21/420 +10/420
=[70+21+10] /420
=101/420