解:(1)149+587+51,
=(149+51)+587,
=200+587,
=787;
(2)75×0.5+15×0.5,
=(75+15)×0.5,
=90×0.5,
=45;
(3)(

-

)×45,
=

×45-

×45,
=15-9,
=6;
(4)8×

×12.5,
=8×12.5×

,
=100×

,
=60.
分析:(1)运用加法交换律与结合律简算;
(2)运用乘法分配律的逆运算简算;
(3)根据数字特点,运用乘法分配律简算;
(4)运用乘法交换律与结合律简算.
点评:此题考查了运算定律与简便计算,对于这类题目,应注意审题,选择合适的方法,进行简算.