五下数学同步上的1/2-1/3+1/4-1/5+1/6-1/7等于多少
3个回答

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