方法一：
原式=(29/6-29/7)+(37/7-37/8)+(41/8-41/9)+(42.5/9-42.5/11)+(53.5/11-53.5/13)+(177/13-177/14)
=(4又5/6-4又1/7)+(4又9/7-4又5/8)+(4又9/8-4又5/9)+(3又15.5/9-3又9.5/11)+
(4又9.5/11-4又1.5/13)+(12又21/13-12又9/14)
=5/6-1/7+9/7-5/8+9/8-5/9+15.5/9-9.5/11+9.5/11-1.5/13+21/13-9/14
=5/6+8/7+1/2+10.5/9+19.5/13-9/14
=5/6+16/14-9/14+1/2+7/6+3/2
=2+1/2+1/2+3/2
=4.5
方法二：
原式=(42-6-7)/42 + (21+16)/56 + (9+32)/72 +（22+63）/99+ (52+55)/143+(112+65)/182
=1- 1/7 - 1/6 + 3/8 + 2/7 +1/8 +4/9 +2/9+7/11+4/11+ 5/13+ 8/13+ 5/14
=1+(- 1/7+ 2/7+ 5/14)+(1/8+ 3/8+5/13+ 8/13)+4/9+4/11+2/9+7/11 -1/6
=4.5