20. (18分)计算:
(1)$1+(-2)-|-2-3|-5$; (2)$-2^{2}×7-(-3)×6+5$;
(3)$(-3)^{2}÷\frac{3}{4}×\left(-\frac{1}{2}\right)-[1+(-2)^{3}]$;
(4)$-3^{2}-\frac{1}{3}×[(-5)^{2}×\left(-\frac{3}{5}\right)-240÷(-4)×\frac{1}{4}]$;
(5)$-2^{2}-(-2)^{2}×0.25÷\frac{1}{2}$; (6)$-0.5^{2}+\frac{1}{4}-|-3^{2}-9|-\left(-1\frac{1}{2}\right)^{3}×\frac{16}{27}$.
(1)$1+(-2)-|-2-3|-5$; (2)$-2^{2}×7-(-3)×6+5$;
(3)$(-3)^{2}÷\frac{3}{4}×\left(-\frac{1}{2}\right)-[1+(-2)^{3}]$;
(4)$-3^{2}-\frac{1}{3}×[(-5)^{2}×\left(-\frac{3}{5}\right)-240÷(-4)×\frac{1}{4}]$;
(5)$-2^{2}-(-2)^{2}×0.25÷\frac{1}{2}$; (6)$-0.5^{2}+\frac{1}{4}-|-3^{2}-9|-\left(-1\frac{1}{2}\right)^{3}×\frac{16}{27}$.
答案：（1）原式 = 1 - 2 - 5 - 5 = -11. （2）原式 = -28 + 18 + 5 = -5. （3）原式 = 9×$\frac{4}{3}$×(-$\frac{1}{2}$) - (-7) = -6 + 7 = 1. （4）原式 = -9 - $\frac{1}{3}$×(-15 + 15) = -9. （5）原式 = -4 - 4×$\frac{1}{4}$×2 = -4 - 2 = -6. （6）原式 = -$\frac{1}{4}$ + $\frac{1}{4}$ - |-18| - (-$\frac{27}{8}$)×$\frac{16}{27}$ = -18 + 2 = -16.
解析：
(1)解：原式=1-2-|-5|-5
=1-2-5-5
=-11
(2)解：原式=-4×7+18+5
=-28+18+5
=-5
(3)解：原式=9÷$\frac{3}{4}$×(-$\frac{1}{2}$)-[1+(-8)]
=9×$\frac{4}{3}$×(-$\frac{1}{2}$)-(-7)
=12×(-$\frac{1}{2}$)+7
=-6+7
=1
(4)解：原式=-9-$\frac{1}{3}$×[25×(-$\frac{3}{5}$)-(-60)×$\frac{1}{4}$]
=-9-$\frac{1}{3}$×[-15+15]
=-9-$\frac{1}{3}$×0
=-9-0
=-9
(5)解：原式=-4-4×0.25×2
=-4-1×2
=-4-2
=-6
(6)解：原式=-0.25+0.25-|-9-9|-(-$\frac{3}{2}$)$^{3}$×$\frac{16}{27}$
=0-|-18|-(-$\frac{27}{8}$)×$\frac{16}{27}$
=-18+2
=-16
=1-2-5-5
=-11
(2)解：原式=-4×7+18+5
=-28+18+5
=-5
(3)解：原式=9÷$\frac{3}{4}$×(-$\frac{1}{2}$)-[1+(-8)]
=9×$\frac{4}{3}$×(-$\frac{1}{2}$)-(-7)
=12×(-$\frac{1}{2}$)+7
=-6+7
=1
(4)解：原式=-9-$\frac{1}{3}$×[25×(-$\frac{3}{5}$)-(-60)×$\frac{1}{4}$]
=-9-$\frac{1}{3}$×[-15+15]
=-9-$\frac{1}{3}$×0
=-9-0
=-9
(5)解：原式=-4-4×0.25×2
=-4-1×2
=-4-2
=-6
(6)解：原式=-0.25+0.25-|-9-9|-(-$\frac{3}{2}$)$^{3}$×$\frac{16}{27}$
=0-|-18|-(-$\frac{27}{8}$)×$\frac{16}{27}$
=-18+2
=-16
21. (10分)用简便方法计算:
(1)$\left(-\frac{1}{6}+\frac{3}{4}-\frac{1}{12}\right)×(-48)$; (2)$99\frac{31}{36}×(-72)$.
(1)$\left(-\frac{1}{6}+\frac{3}{4}-\frac{1}{12}\right)×(-48)$; (2)$99\frac{31}{36}×(-72)$.
答案：（1）原式 = (-$\frac{1}{6}$)×(-48) + $\frac{3}{4}$×(-48) + (-$\frac{1}{12}$)×(-48) = 8 - 36 + 4 = -24. （2）原式 = (100 - $\frac{5}{36}$)×(-72) = 100×(-72) + (-$\frac{5}{36}$)×(-72) = -7200 + 10 = -7190.
解析：
(1)解：原式$=\left(-\frac{1}{6}\right)×(-48)+\frac{3}{4}×(-48)+\left(-\frac{1}{12}\right)×(-48)$
$=8-36+4$
$=-24$
(2)解：原式$=\left(100-\frac{5}{36}\right)×(-72)$
$=100×(-72)+\left(-\frac{5}{36}\right)×(-72)$
$=-7200+10$
$=-7190$
$=8-36+4$
$=-24$
(2)解：原式$=\left(100-\frac{5}{36}\right)×(-72)$
$=100×(-72)+\left(-\frac{5}{36}\right)×(-72)$
$=-7200+10$
$=-7190$
22. (6分)设$[a]$表示不超过a的最大整数,例如,$[3.1]= 3,\left[-3\frac{5}{6}\right]=-4,[4]= 4$.
(1)填空:$\left[2\frac{1}{5}\right]=$
(2)令$\{a\}= a-[a]$,求$\left\{3\frac{4}{5}\right\}-[-2.4]+\left\{-7\frac{4}{5}\right\}$.
(1)填空:$\left[2\frac{1}{5}\right]=$
2
,$[3.6]=$3
;(2)令$\{a\}= a-[a]$,求$\left\{3\frac{4}{5}\right\}-[-2.4]+\left\{-7\frac{4}{5}\right\}$.
解：原式 = 3$\frac{4}{5}$ - [3$\frac{4}{5}$] - (-3) + (-7$\frac{4}{5}$) - [-7$\frac{4}{5}$] = 3$\frac{4}{5}$ - 3 + 3 - 7$\frac{4}{5}$ - (-8) = -4 + 8 = 4.
答案：（1）2 3 （2）解：原式 = 3$\frac{4}{5}$ - [3$\frac{4}{5}$] - (-3) + (-7$\frac{4}{5}$) - [-7$\frac{4}{5}$] = 3$\frac{4}{5}$ - 3 + 3 - 7$\frac{4}{5}$ - (-8) = -4 + 8 = 4.
解析：
(1) 2；3
(2) 解：原式 = $3\frac{4}{5} - \left[3\frac{4}{5}\right] - [-2.4] + \left(-7\frac{4}{5} - \left[-7\frac{4}{5}\right]\right)$
$= 3\frac{4}{5} - 3 - (-3) + \left(-7\frac{4}{5} - (-8)\right)$
$= 3\frac{4}{5} - 3 + 3 - 7\frac{4}{5} + 8$
$= (3\frac{4}{5} - 7\frac{4}{5}) + (-3 + 3 + 8)$
$= -4 + 8$
$= 4$
(2) 解：原式 = $3\frac{4}{5} - \left[3\frac{4}{5}\right] - [-2.4] + \left(-7\frac{4}{5} - \left[-7\frac{4}{5}\right]\right)$
$= 3\frac{4}{5} - 3 - (-3) + \left(-7\frac{4}{5} - (-8)\right)$
$= 3\frac{4}{5} - 3 + 3 - 7\frac{4}{5} + 8$
$= (3\frac{4}{5} - 7\frac{4}{5}) + (-3 + 3 + 8)$
$= -4 + 8$
$= 4$