简便计算8分之7+24分之7+48分之7+80分之7+120分之7
问题描述：
简便计算8分之7+24分之7+48分之7+80分之7+120分之7
答
7/8+7/24+7/48+7/80+7/120
=7×(1/8+1/24+1/48+1/80+1/120)
=7×[1/(2×4)+1/(4×6)+1/(6×8)+1/(8×10)+1/(10×12)]
=7×[1/2(1/2-1/4)+1/2/(1/4-1/6)+1/2(1/6-1/8)+1/2(1/8-1/10)+1/2(1/10-1/12)]
=7×1/2×(1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10+1/10-1/12)
=7/2×(1/2-1/12)
=7/2×5/12
=35/24
答
8分之7+24分之7+48分之7+80分之7+120分之7
=7/8x(1+1/3+1/6+1/10+1/12)
=7/8x(1+20/60+10/60+6/60+5/60)
=7/8x101/60
=707/480