Question

30分之2+42分之2+56分之2+70二分之一+9十分之一等于多少？

Answer 1

裂项，错位相消，

Answer 2

1/15 + 1/21 + 1/28 +1/70 + 1/90
15、21、28、72、90 的最小公倍数：
15 = 3 × 5
21 = 3 × 7
28 = 2² × 7
72 = 2³ × 3²
90 = 2 × 3² × 5
每个因数各取次数最大那个一次，
2³ × 3² × 5 × 7 = 2520
2520 ÷ 15 = 168

2520 ÷ 21 = 120
2520 ÷ 28 = 90
2520 ÷ 72 = 35
2520 ÷ 90 = 28
（168 + 120 + 90 + 35 + 28）/2520
= 441/2520（公因数 63）
= 7/40

Answer 3

2/30+2/42+2/56+1/72+1/90
=6/90+1/90+（1/21+1/28）+1/72
=7/90+（4/84+3/84）+1/72
=7/90+1/72+7/84
=56/720+10/720+1/12
=66/720+1/12
=11/360+30/360
=41/360

Answer 4

2/30+2/42+2/56+1/72+1/90
=1/15+1/21+1/28+1/72+1/90
= 7/40

追答

2/30+2/42+2/56+1/72+1/90
=1/15+1/21+1/28+1/72+1/90
= 7/40

Answer 5

2/30+2/42+2/56+1/70+1/90
=2×(1/5-1/6+1/6-1/7+1/7-1/8)+1/70+1/90
=2×(1/5-1/8)+1/70+1/90
=2×(8/40-5/40)+1/70+1/90
=2×3/40+1/70+1/90
=3/20+1/70+1/90
=189/1260+18/1260+14/1260
=221/1260