Question

(1/2+1/6+1/12+1/20)÷(1/99+1/63+1/35+1/15)=

解题过程，小学奥数，谢谢

Answer 1

首先结果是6.6
然后先算第一个（1/2+1/6+1/12+1/20）
1/2=1/1*2=1-1/2
1/6=1/2*3=1/2-1/3
1/12=1/3*4=1/3-1/4
1/20=1/4*5=1/4-1/5
所以（1/2+1/6+1/12+1/20）=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5中间相互抵消，结果为1-1/5=4/5
接下来是（1/99+1/66+1/35+1/15）
1/99=1/9*11=（1/9-1/11）/2
1/63=1/7*9=(1/7-1/9)/2
1/35=1/5*7=(1/5-1/7)/2
1-15=1/3*5=(1/3-1/5)/2
所以（1/99+1/66+1/35+1/15）=（1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11）/2=（1/3-1/11）/2=4/33
（4/5）/（4/33）=6.6

Answer 2

裂项法：
(1/2+1/6+1/12+1/20)÷(1/99+1/63+1/35+1/15)
=（1-1/2+1/2-1/3+1/3-1/4+1/4-1/5）÷【1/2×（1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11）】
=（1-1/5）÷【1/2×（1/3-1/11）】
=4/5÷4/33
=6.6

Answer 3

原式=6.6
因为1/2+1/6+1/12+1/20=（1-1/2）+（1/2-1/3）+（1/3-1/4）+（1/4-1/5）=1-1/5=4/5
因为1/99+1/63+1/35+1/15=[（1/9-1/11）+（1/7-1/9）+（1/5-1/7）+（1/3-1/5）]/2=（1/3-1/11）/2=4/33
所以
(1/2+1/6+1/12+1/20)÷(1/99+1/63+1/35+1/15)=（4/5）/（4/33）=33/5=6.6

Answer 4

(1/2+1/6+1/12+1/20)÷(1/99+1/63+1/35+1/15)
＝[（3x4x5+1x4x5+1x2x5+1x2x3）/(1x2x3x4x5)]÷[(7x5x3+11x5x3+11x9x3+11x9x7)/(11x9x7x5x3)]
=[(60+20+10+6)/120 ]÷[(105+165+297+693)/10395]
=(96/120)÷(1260/10395)
=(4/5)x(231/28)
=231/35=33/5=6.6

Answer 5

(1/2+1/6+1/12+1/20)÷(1/99+1/63+1/35+1/15)
=（1-1/2+1/2-1/3+1/3-1/4+1/4-1/5）÷【1/2×（1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11）】
=（1-1/5）÷【1/2×（1/3-1/11）】
=4/5÷4/33
=6.6