8.计算：
(1) $-2^3 - 3×(-2)^3 - (-1)^4$；
(2) $-1^4 - [(\frac{1}{3} - \frac{1}{2})×6 - 2]$；
(3) $5^2 - 24×(\frac{1}{3} - \frac{1}{2} + \frac{5}{6})$；
(4) $-3^3 - (-3)^2×(-\frac{1}{3}) + (-3)^3÷3$；
(5) $(-1)^3 - (1 - \frac{1}{2})÷3×[2 - (-3)^2]$；
(6) $-1 - [2 - (1 - \frac{1}{3}×0.5)]×[3^2 - (-2)^2]$；

8.(1)15 (2)2 (3)9 (4)-33 (5)$\frac{1}{6}$ (6)$-\frac{41}{6}$

9.如图,小明有5张写着不同数字的卡片,请你按要求抽出卡片,解答下列问题:
从中抽出4张卡片,用学过的运算方法,使结果为24.如何抽?请写出运算式子.(写出三种)

9.解:$[0-(-3)+3]×4=24$;$[0-(-3)-(-5)]×3=24$;$-[(-3)÷3+(-5)]×4=24.$(答案不唯一)

10.先观察,再解题:
$1-\frac{1}{2}=\frac{1}{1×2},\frac{1}{2}-\frac{1}{3}=\frac{1}{2×3},\frac{1}{3}-\frac{1}{4}=\frac{1}{3×4},…$
(1)按照上面的规律,得$\frac{1}{5×6}=$;
(2)计算:$\frac{1}{1×2}+\frac{1}{2×3}+\frac{1}{3×4}+…+\frac{1}{49×50}$;
(3)参照上述解法计算:$\frac{1}{1×3}+\frac{1}{3×5}+\frac{1}{5×7}+…+\frac{1}{49×51}.$

10.(1)$\frac{1}{5}-\frac{1}{6}$
(2)解:原式$=(1-\frac{1}{2})+(\frac{1}{2}-\frac{1}{3})+(\frac{1}{3}-\frac{1}{4})+…+(\frac{1}{49}-\frac{1}{50})=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+…+\frac{1}{49}-\frac{1}{50}=1-\frac{1}{50}=\frac{49}{50}.$
(3)解:原式$=\frac{1}{2}×(1-\frac{1}{3})+\frac{1}{2}×(\frac{1}{3}-\frac{1}{5})+\frac{1}{2}×(\frac{1}{5}-\frac{1}{7})+…+\frac{1}{2}×(\frac{1}{49}-\frac{1}{51})=\frac{1}{2}×(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+…+\frac{1}{49}-\frac{1}{51})=\frac{1}{2}×(1-\frac{1}{51})=\frac{1}{2}×\frac{50}{51}=\frac{25}{51}.$