《2025年通城学典课时作业本七年级数学上册湘教版》

7. 计算$2.64× 7.6388 + 26.4× (-0.31388)-2.64× (-0.5)$的结果为(B)
A.$-13.2$
B.$13.2$
C.$1.32$
D.$-1.32$

答案： B

8. 计算:$\dfrac{5}{3}× (12 - 2\dfrac{2}{5}-0.6)× (-\dfrac{1}{2})= $$-\frac{15}{2}$.

答案： $-\frac{15}{2}$

9. $(-\dfrac{5}{31})× (-\dfrac{9}{2})× (-\dfrac{31}{5})× \dfrac{2}{9}= -(\dfrac{5}{31}× \dfrac{9}{2}× \dfrac{31}{5}× \dfrac{2}{9})…$①$=-[(\dfrac{5}{31}× \dfrac{31}{5})× (\dfrac{9}{2}× \dfrac{2}{9})]…$②$=-1$
其中,步骤①的依据是有理数的乘法法则,步骤②的依据是乘法交换律和乘法结合律.

答案： 有理数的乘法法则 乘法交换律和乘法结合律

10. (新考法·项目式学习)阅读材料,并解答问题:
学习有理数的乘法后,老师让同学们思考这样一道题目:计算$49\dfrac{24}{25}× (-5)$,看谁算得又对又快.有三名同学的解法如下:
小方:原式$=-\dfrac{49× 25 + 24}{25}× 5= -\dfrac{1249}{25}× 5= -\dfrac{1249}{5}= -249\dfrac{4}{5}$；
小军:原式$=(49+\dfrac{24}{25})× (-5)= 49× (-5)+\dfrac{24}{25}× (-5)= -245-\dfrac{24}{5}= -249\dfrac{4}{5}$；
小红:原式$=(50-\dfrac{1}{25})× (-5)= 50× (-5)-\dfrac{1}{25}× (-5)= -250+\dfrac{1}{5}= -249\dfrac{4}{5}$.
根据上面解法对你的启示,请用你认为最合适的方法计算:$19\dfrac{15}{16}× (-8)$.

答案： $19\frac{15}{16}×(-8)=\left(20-\frac{1}{16}\right)×(-8)=20×(-8)-\frac{1}{16}×(-8)=-160+\frac{1}{2}=-159\frac{1}{2}$

11. 先阅读材料,再解答问题:
$(1+\dfrac{1}{2})× (1-\dfrac{1}{3})= \dfrac{3}{2}× \dfrac{2}{3}= 1$；
$(1+\dfrac{1}{2})× (1+\dfrac{1}{4})× (1-\dfrac{1}{3})× (1-\dfrac{1}{5})= \dfrac{3}{2}× \dfrac{5}{4}× \dfrac{2}{3}× \dfrac{4}{5}= (\dfrac{3}{2}× \dfrac{2}{3})× (\dfrac{5}{4}× \dfrac{4}{5})= 1× 1= 1$；
…
根据上述材料计算:$(1+\dfrac{1}{2})× (1+\dfrac{1}{4})× (1+\dfrac{1}{6})× … × (1+\dfrac{1}{2024})× (1-\dfrac{1}{3})× (1-\dfrac{1}{5})× (1-\dfrac{1}{7})× … × (1-\dfrac{1}{2025})$。
原式$=\frac{3}{2}×\frac{5}{4}×\frac{7}{6}×\cdots×\frac{2025}{2024}×\frac{2}{3}×\frac{4}{5}×\frac{6}{7}×\cdots×\frac{2024}{2025}=\left(\frac{3}{2}×\frac{2}{3}\right)×\left(\frac{5}{4}×\frac{4}{5}\right)×\left(\frac{7}{6}×\frac{6}{7}\right)×\cdots×\left(\frac{2025}{2024}×\frac{2024}{2025}\right)=1$

答案： 原式$=\frac{3}{2}×\frac{5}{4}×\frac{6}{7}×\cdots×\frac{2025}{2024}×\frac{2}{3}×\frac{4}{5}×\frac{6}{7}×\cdots×\frac{2024}{2025}=\left(\frac{3}{2}×\frac{2}{3}\right)×\left(\frac{5}{4}×\frac{4}{5}\right)×\left(\frac{7}{6}×\frac{6}{7}\right)×\cdots×\left(\frac{2025}{2024}×\frac{2024}{2025}\right)=1$