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1. $(-56)×(\dfrac{4}{7}-\dfrac{3}{8}+\dfrac{1}{14})$.
2. $(-\dfrac{7}{18}-\dfrac{5}{12}+\dfrac{1}{6}+\dfrac{2}{9})×(-6)^2$.
2. $(-\dfrac{7}{18}-\dfrac{5}{12}+\dfrac{1}{6}+\dfrac{2}{9})×(-6)^2$.
答案
1. 原式$=(-56)×\frac{4}{7}-(-56)×\frac{3}{8}+(-56)×\frac{1}{14}=-32+21-4=-15$.
2. 原式$=(-\frac{7}{18}-\frac{5}{12}+\frac{1}{6}+\frac{2}{9})×36=-\frac{7}{18}×36-\frac{5}{12}×36+\frac{1}{6}×36+\frac{2}{9}×36=-14-15+6+8=-15$.
2. 原式$=(-\frac{7}{18}-\frac{5}{12}+\frac{1}{6}+\frac{2}{9})×36=-\frac{7}{18}×36-\frac{5}{12}×36+\frac{1}{6}×36+\frac{2}{9}×36=-14-15+6+8=-15$.
/类型二/ 逆向运用分配律
3. $25×0.5 - (-25)×0.75 + 25×(-0.25)$.
4. $(-3)×(-2\dfrac{1}{6}) + (-5)×2\dfrac{1}{6} - 4×\dfrac{13}{6}$.
3. $25×0.5 - (-25)×0.75 + 25×(-0.25)$.
4. $(-3)×(-2\dfrac{1}{6}) + (-5)×2\dfrac{1}{6} - 4×\dfrac{13}{6}$.
答案
3. 原式$=25×(0.5+0.75-0.25)=25×1=25$.
4. 原式$=3×\frac{13}{6}-5×\frac{13}{6}-4×\frac{13}{6}=\frac{13}{6}×(3-5-4)=\frac{13}{6}×(-6)=-13$.
4. 原式$=3×\frac{13}{6}-5×\frac{13}{6}-4×\frac{13}{6}=\frac{13}{6}×(3-5-4)=\frac{13}{6}×(-6)=-13$.
5. $99\dfrac{17}{18}×(-18)$.
6. $48\dfrac{24}{25}÷(-48)$.
6. $48\dfrac{24}{25}÷(-48)$.
答案
5. 原式$=(100-\frac{1}{18})×(-18)=100×(-18)-\frac{1}{18}×(-18)=-1\ 800+1=-1\ 799$.
6. 原式$=(48+\frac{24}{25})×(-\frac{1}{48})=48×(-\frac{1}{48})+\frac{24}{25}×(-\frac{1}{48})=-1-\frac{1}{50}=-1\ \frac{1}{50}$.
6. 原式$=(48+\frac{24}{25})×(-\frac{1}{48})=48×(-\frac{1}{48})+\frac{24}{25}×(-\frac{1}{48})=-1-\frac{1}{50}=-1\ \frac{1}{50}$.
目/类型四/ 倒数法
7. $(-\dfrac{1}{30})÷(\dfrac{2}{3}-\dfrac{1}{10}+\dfrac{1}{6}-\dfrac{2}{5}).$
8. $-\dfrac{1}{126}÷(\dfrac{5}{14}+\dfrac{1}{18}-\dfrac{1}{3}).$
7. $(-\dfrac{1}{30})÷(\dfrac{2}{3}-\dfrac{1}{10}+\dfrac{1}{6}-\dfrac{2}{5}).$
8. $-\dfrac{1}{126}÷(\dfrac{5}{14}+\dfrac{1}{18}-\dfrac{1}{3}).$
答案
7. 原式的倒数为$(\frac{2}{3}-\frac{1}{10}+\frac{1}{6}-\frac{2}{5})÷(-\frac{1}{30})$.因为$(\frac{2}{3}-\frac{1}{10}+\frac{1}{6}-\frac{2}{5})÷(-\frac{1}{30})=(\frac{2}{3}-\frac{1}{10}+\frac{1}{6}-\frac{2}{5})×(-30)=\frac{2}{3}×(-30)-\frac{1}{10}×(-30)+\frac{1}{6}×(-30)-\frac{2}{5}×(-30)=-20+3-5+12=-10$,所以原式$=-\frac{1}{10}$.
8. 原式的倒数为$(\frac{5}{14}+\frac{1}{18}-\frac{1}{3})÷(-\frac{1}{126})$.因为$(\frac{5}{14}+\frac{1}{18}-\frac{1}{3})÷(-\frac{1}{126})=(\frac{5}{14}+\frac{1}{18}-\frac{1}{3})×(-126)=\frac{5}{14}×(-126)+\frac{1}{18}×(-126)-\frac{1}{3}×(-126)=-45-7+42=-10$,所以原式$=-\frac{1}{10}$.
8. 原式的倒数为$(\frac{5}{14}+\frac{1}{18}-\frac{1}{3})÷(-\frac{1}{126})$.因为$(\frac{5}{14}+\frac{1}{18}-\frac{1}{3})÷(-\frac{1}{126})=(\frac{5}{14}+\frac{1}{18}-\frac{1}{3})×(-126)=\frac{5}{14}×(-126)+\frac{1}{18}×(-126)-\frac{1}{3}×(-126)=-45-7+42=-10$,所以原式$=-\frac{1}{10}$.
