《2025年学习质量监测七年级数学上册人教版》

3. 计算$3.1416×7.5944 + 3.1416×(-5.5944)$的结果为6.2832.

答案： 6.2832 【提示】逆用分配律,原式$=3.1416×(7.5944-5.5944)=3.1416×2=6.2832.$

4. 5 个数相乘,积为负,则其中正因数的个数为0或2或4.

答案： 0或2或4

5. 计算：
(1)$(-\frac{4}{5})×(-\frac{5}{13})-(-\frac{3}{5})×(+\frac{5}{13})+(-\frac{5}{13})×(-1\frac{2}{5})-\frac{5}{13}$；
(2)$(-47.65)×2\frac{6}{11}+(-37.15)×(-2\frac{6}{11})+10.5×(-7\frac{5}{11})$；
(3)$3\frac{1}{7}×(3\frac{1}{7}-7\frac{1}{3})×\frac{7}{22}×\frac{21}{22}$.

答案： 【解】
(1)原式$=\frac {4}{5}×\frac {5}{13}+\frac {3}{5}×\frac {5}{13}+\frac {5}{13}×\frac {7}{5}-\frac {5}{13}=\frac {5}{13}×(\frac {4}{5}+\frac {3}{5}+\frac {7}{5}-1)=\frac {5}{13}×\frac {9}{5}=\frac {9}{13}.$
(2)原式$=2\frac {6}{11}×(-47.65+37.15)+10.5×(-7\frac {5}{11})=2\frac {6}{11}×(-10.5)+10.5×(-7\frac {5}{11})=-10.5×(2\frac {6}{11}+7\frac {5}{11})=-10.5×10=-105.$
(3)原式$=\frac {22}{7}×\frac {7}{22}×\frac {21}{22}×(\frac {22}{7}-\frac {22}{3})=\frac {21}{22}×(\frac {22}{7}-\frac {22}{3})=3-7=-4.$