计算:
(1)$(-7)+21+(-27)-5$; (2)$18+(-12)+(-21)-(-12)$;
(3)$0.35+(-0.6)+0.25-(+5.4)$; (4)$-20-(-14)-|-18|-13$;
(5)$1.125-(+3\frac {3}{4})-(+\frac {1}{8})-0.25$; (6)$+5.7+(-8.4)+(-4.2)-(-10)$;
(7)$\frac {2}{3}-(-\frac {7}{9})+1\frac {2}{9}+(-1\frac {2}{3})$; (8)$1\frac {1}{3}-1\frac {1}{5}+\frac {5}{3}-(-0.6)-(-3\frac {3}{5})$;
(9)$\frac {2}{5}-(-1\frac {1}{2})-(+2\frac {1}{4})-(-2.75)$;
(10)$|1-\frac {1}{2}|+|\frac {1}{2}-\frac {1}{3}|+|\frac {1}{3}-\frac {1}{4}|+... +|\frac {1}{99}-\frac {1}{100}|$.
(1)$(-7)+21+(-27)-5$; (2)$18+(-12)+(-21)-(-12)$;
(3)$0.35+(-0.6)+0.25-(+5.4)$; (4)$-20-(-14)-|-18|-13$;
(5)$1.125-(+3\frac {3}{4})-(+\frac {1}{8})-0.25$; (6)$+5.7+(-8.4)+(-4.2)-(-10)$;
(7)$\frac {2}{3}-(-\frac {7}{9})+1\frac {2}{9}+(-1\frac {2}{3})$; (8)$1\frac {1}{3}-1\frac {1}{5}+\frac {5}{3}-(-0.6)-(-3\frac {3}{5})$;
(9)$\frac {2}{5}-(-1\frac {1}{2})-(+2\frac {1}{4})-(-2.75)$;
(10)$|1-\frac {1}{2}|+|\frac {1}{2}-\frac {1}{3}|+|\frac {1}{3}-\frac {1}{4}|+... +|\frac {1}{99}-\frac {1}{100}|$.
答案:(1)-18 (2)-3 (3)-5.4 (4)-37 (5)-3 (6)3.1 (7)1 (8)6 (9)$2\frac{2}{5}$ (10)$\frac{99}{100}$
解析:
(1)解:$(-7)+21+(-27)-5$
$=(-7-27-5)+21$
$=-39+21$
$=-18$
(2)解:$18+(-12)+(-21)-(-12)$
$=18-12-21+12$
$=(18-21)+(-12+12)$
$=-3+0$
$=-3$
(3)解:$0.35+(-0.6)+0.25-(+5.4)$
$=0.35-0.6+0.25-5.4$
$=(0.35+0.25)+(-0.6-5.4)$
$=0.6-6$
$=-5.4$
(4)解:$-20-(-14)-|-18|-13$
$=-20+14-18-13$
$=(-20-18-13)+14$
$=-51+14$
$=-37$
(5)解:$1.125-(+3\frac{3}{4})-(+\frac{1}{8})-0.25$
$=1.125-3.75-0.125-0.25$
$=(1.125-0.125)+(-3.75-0.25)$
$=1-4$
$=-3$
(6)解:$+5.7+(-8.4)+(-4.2)-(-10)$
$=5.7-8.4-4.2+10$
$=(5.7+10)+(-8.4-4.2)$
$=15.7-12.6$
$=3.1$
(7)解:$\frac{2}{3}-(-\frac{7}{9})+1\frac{2}{9}+(-1\frac{2}{3})$
$=\frac{2}{3}+\frac{7}{9}+1\frac{2}{9}-1\frac{2}{3}$
$=(\frac{2}{3}-1\frac{2}{3})+(\frac{7}{9}+1\frac{2}{9})$
$=-1+2$
$=1$
(8)解:$1\frac{1}{3}-1\frac{1}{5}+\frac{5}{3}-(-0.6)-(-3\frac{3}{5})$
$=1\frac{1}{3}-1\frac{1}{5}+\frac{5}{3}+0.6+3\frac{3}{5}$
$=(1\frac{1}{3}+\frac{5}{3})+(-1\frac{1}{5}+3\frac{3}{5}+0.6)$
$=3+3$
$=6$
(9)解:$\frac{2}{5}-(-1\frac{1}{2})-(+2\frac{1}{4})-(-2.75)$
$=0.4+1.5-2.25+2.75$
$=0.4+1.5+( -2.25+2.75)$
$=1.9+0.5$
$=2.4$
$=2\frac{2}{5}$
(10)解:$|1-\frac{1}{2}|+|\frac{1}{2}-\frac{1}{3}|+|\frac{1}{3}-\frac{1}{4}|+\cdots+|\frac{1}{99}-\frac{1}{100}|$
$=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\cdots+\frac{1}{99}-\frac{1}{100}$
$=1-\frac{1}{100}$
$=\frac{99}{100}$
$=(-7-27-5)+21$
$=-39+21$
$=-18$
(2)解:$18+(-12)+(-21)-(-12)$
$=18-12-21+12$
$=(18-21)+(-12+12)$
$=-3+0$
$=-3$
(3)解:$0.35+(-0.6)+0.25-(+5.4)$
$=0.35-0.6+0.25-5.4$
$=(0.35+0.25)+(-0.6-5.4)$
$=0.6-6$
$=-5.4$
(4)解:$-20-(-14)-|-18|-13$
$=-20+14-18-13$
$=(-20-18-13)+14$
$=-51+14$
$=-37$
(5)解:$1.125-(+3\frac{3}{4})-(+\frac{1}{8})-0.25$
$=1.125-3.75-0.125-0.25$
$=(1.125-0.125)+(-3.75-0.25)$
$=1-4$
$=-3$
(6)解:$+5.7+(-8.4)+(-4.2)-(-10)$
$=5.7-8.4-4.2+10$
$=(5.7+10)+(-8.4-4.2)$
$=15.7-12.6$
$=3.1$
(7)解:$\frac{2}{3}-(-\frac{7}{9})+1\frac{2}{9}+(-1\frac{2}{3})$
$=\frac{2}{3}+\frac{7}{9}+1\frac{2}{9}-1\frac{2}{3}$
$=(\frac{2}{3}-1\frac{2}{3})+(\frac{7}{9}+1\frac{2}{9})$
$=-1+2$
$=1$
(8)解:$1\frac{1}{3}-1\frac{1}{5}+\frac{5}{3}-(-0.6)-(-3\frac{3}{5})$
$=1\frac{1}{3}-1\frac{1}{5}+\frac{5}{3}+0.6+3\frac{3}{5}$
$=(1\frac{1}{3}+\frac{5}{3})+(-1\frac{1}{5}+3\frac{3}{5}+0.6)$
$=3+3$
$=6$
(9)解:$\frac{2}{5}-(-1\frac{1}{2})-(+2\frac{1}{4})-(-2.75)$
$=0.4+1.5-2.25+2.75$
$=0.4+1.5+( -2.25+2.75)$
$=1.9+0.5$
$=2.4$
$=2\frac{2}{5}$
(10)解:$|1-\frac{1}{2}|+|\frac{1}{2}-\frac{1}{3}|+|\frac{1}{3}-\frac{1}{4}|+\cdots+|\frac{1}{99}-\frac{1}{100}|$
$=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\cdots+\frac{1}{99}-\frac{1}{100}$
$=1-\frac{1}{100}$
$=\frac{99}{100}$