1. 计算:
(1)$(-0.25)×(-125)×(-4);$
(2)$(-\dfrac{7}{6})×(-15)×(-\dfrac{6}{7})×\dfrac{1}{5};$
(3)$-\dfrac{5}{31}×(-\dfrac{2}{9})×(-2\dfrac{1}{15})×(-4\dfrac{1}{2});$
(4)$-1\dfrac{5}{7}×\dfrac{5}{6}×\left|-1\dfrac{2}{5}\right|×1.2.$
(1)$(-0.25)×(-125)×(-4);$
(2)$(-\dfrac{7}{6})×(-15)×(-\dfrac{6}{7})×\dfrac{1}{5};$
(3)$-\dfrac{5}{31}×(-\dfrac{2}{9})×(-2\dfrac{1}{15})×(-4\dfrac{1}{2});$
(4)$-1\dfrac{5}{7}×\dfrac{5}{6}×\left|-1\dfrac{2}{5}\right|×1.2.$
答案
(1)解:原式$=-(0.25×4)×125=-1×125=-125.$
(2)解:原式$=-(\dfrac{7}{6}×\dfrac{6}{7})×(15×\dfrac{1}{5})=-1×3=-3.$
(3)解:原式$=\dfrac{5}{31}×\dfrac{2}{9}×\dfrac{31}{15}×\dfrac{9}{2}=(\dfrac{5}{31}×\dfrac{31}{15})×(\dfrac{2}{9}×\dfrac{9}{2})=\dfrac{1}{3}×1=\dfrac{1}{3}.$
(4)解:原式$=-\dfrac{12}{7}×\dfrac{5}{6}×\dfrac{7}{5}×\dfrac{6}{5}=-(\dfrac{12}{7}×\dfrac{7}{5})×(\dfrac{5}{6}×\dfrac{6}{5})=-\dfrac{12}{5}×1=-\dfrac{12}{5}.$
(2)解:原式$=-(\dfrac{7}{6}×\dfrac{6}{7})×(15×\dfrac{1}{5})=-1×3=-3.$
(3)解:原式$=\dfrac{5}{31}×\dfrac{2}{9}×\dfrac{31}{15}×\dfrac{9}{2}=(\dfrac{5}{31}×\dfrac{31}{15})×(\dfrac{2}{9}×\dfrac{9}{2})=\dfrac{1}{3}×1=\dfrac{1}{3}.$
(4)解:原式$=-\dfrac{12}{7}×\dfrac{5}{6}×\dfrac{7}{5}×\dfrac{6}{5}=-(\dfrac{12}{7}×\dfrac{7}{5})×(\dfrac{5}{6}×\dfrac{6}{5})=-\dfrac{12}{5}×1=-\dfrac{12}{5}.$
2.计算:
(1)$(-36)×(-\dfrac{4}{9}+\dfrac{5}{6}-\dfrac{7}{12});$
(2)$99\dfrac{17}{18}×(-9);$
(3)$-105\dfrac{5}{9}×(-\dfrac{3}{5});$
(4)$(\dfrac{3}{4}+\dfrac{5}{6}-\dfrac{11}{15}-\dfrac{7}{12})×(-60).$
(1)$(-36)×(-\dfrac{4}{9}+\dfrac{5}{6}-\dfrac{7}{12});$
(2)$99\dfrac{17}{18}×(-9);$
(3)$-105\dfrac{5}{9}×(-\dfrac{3}{5});$
(4)$(\dfrac{3}{4}+\dfrac{5}{6}-\dfrac{11}{15}-\dfrac{7}{12})×(-60).$
答案
(1)解:原式$=(-36)×(-\dfrac{4}{9})-36×\dfrac{5}{6}-36×(-\dfrac{7}{12})=16-30+21=7.$
(2)解:原式$=(100-\dfrac{1}{18})×(-9)=100×(-9)-\dfrac{1}{18}×(-9)=-900+\dfrac{1}{2}=-899\dfrac{1}{2}.$
(3)解:原式$=(105+\dfrac{5}{9})×\dfrac{3}{5}=105×\dfrac{3}{5}+\dfrac{5}{9}×\dfrac{3}{5}=63+\dfrac{1}{3}=63\dfrac{1}{3}.$
(4)解:原式$=\dfrac{3}{4}×(-60)+\dfrac{5}{6}×(-60)-\dfrac{11}{15}×(-60)-\dfrac{7}{12}×(-60)=-45-50+44+35=-16.$
(2)解:原式$=(100-\dfrac{1}{18})×(-9)=100×(-9)-\dfrac{1}{18}×(-9)=-900+\dfrac{1}{2}=-899\dfrac{1}{2}.$
(3)解:原式$=(105+\dfrac{5}{9})×\dfrac{3}{5}=105×\dfrac{3}{5}+\dfrac{5}{9}×\dfrac{3}{5}=63+\dfrac{1}{3}=63\dfrac{1}{3}.$
(4)解:原式$=\dfrac{3}{4}×(-60)+\dfrac{5}{6}×(-60)-\dfrac{11}{15}×(-60)-\dfrac{7}{12}×(-60)=-45-50+44+35=-16.$
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