31/2-(-21/4)+(-1/3)-1/4-(+1/6)=

31/2-(-21/4)+(-1/3)-1/4-(+1/6)=

=31/2+21/4-1/3-1/4-1/6
=186/12+63/12-4/12-3/12-2/12
=240/12=20

1 / 15 + 1 / 35 + 1 / 63 + 1 / 99 + 1 / 143 + 1 / 195

Split term method
1/15+1/35+1/63+1/99+1/143+1/195
=1/2×（1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13+1/13-1/15）
=1/2×（1/3-1/15）
=1/2×4/15
=2/15

One third multiplied by nine plus five sixths, can we use simple calculation? How to calculate?

If there are no brackets, the original formula = (1 / 3) × 9 + 5 / 6 = 3 + 5 / 6 = 3 and 5 / 6, so there is no need to calculate simply
If there are brackets, the original formula = 1 / 3 × (9 + 5 / 6) = (1 / 3) × 9 + (1 / 3) (5 / 6) = 3 + 5 / 18 = 3 and 5 / 18, it doesn't need any simple calculation

Minus one and a third, minus one and a half

The answer is one in six