《2025年新编基础训练七年级数学上册通用版S》

1. 计算：$11.54+(-3.3)+(-11.54)+3.3$.

答案： 11.54+(-3.3)+(-11.54)+3.3=(11.54-11.54)+(-3.3+3.3)=0.

2. 计算：$2.3+(-1.7)+6.2+(-2.2)-1.1$.

答案： 2.3+(-1.7)+6.2+(-2.2)-1.1=2.3+6.2-(1.7+2.2+1.1)=8.5-5=3.5.

3.计算
 (1)$[(+3\frac{2}{5})+(-2\frac{7}{8})]-[(-5\frac{3}{5})+(+\frac{1}{8})]$；
(2)$(-1.75)-(-2\frac{3}{4})+(-3\frac{4}{5})-(-1\frac{4}{5})$.

答案：
(1)原式=$(+3\frac{2}{5})+(-2\frac{7}{8})-(-5\frac{3}{5})-(+\frac{1}{8})$=$(3\frac{2}{5}+5\frac{3}{5})-(2\frac{7}{8}+\frac{1}{8})$=9-3=6.
(2)原式=$[(-1.75)-(-2\frac{3}{4})]+[-3\frac{4}{5}-(-1\frac{4}{5})]$=1+(-2)=-1.

4. 观察下列两组等式：
$\frac{1}{1×2}= 1-\frac{1}{2}$；$\frac{1}{2×3}= \frac{1}{2}-\frac{1}{3}$；$\frac{1}{3×4}= \frac{1}{3}-\frac{1}{4}$；…$$.
$\frac{1}{1×4}= \frac{1}{3}×(1-\frac{1}{4})$；$\frac{1}{4×7}= \frac{1}{3}×(\frac{1}{4}-\frac{1}{7})$；$\frac{1}{7×10}= \frac{1}{3}×(\frac{1}{7}-\frac{1}{10})$；…$$.
根据你的观察,先写出猜想：\n(1)$\frac{1}{n(n+1)}=$$\frac{1}{n}$-$\frac{1}{n+1}$；\n(2)$\frac{1}{n(n+d)}=$$\frac{1}{d}$×$\frac{1}{n}-\frac{1}{n+d}$；\n(3)用简便方法计算：$\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}$.
$\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}$=$\frac{1}{1×3}+\frac{1}{3×5}+\frac{1}{5×7}+\frac{1}{7×9}+\frac{1}{9×11}$=$\frac{1}{2}×(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11})$=$\frac{1}{2}×(1-\frac{1}{11})$=$\frac{5}{11}$.

答案：
(1)$\frac{1}{n}$ $\frac{1}{n+1}$
(2)$\frac{1}{d}$ $\frac{1}{n}-\frac{1}{n+d}$
(3)$\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}$=$\frac{1}{1×3}+\frac{1}{3×5}+\frac{1}{5×7}+\frac{1}{7×9}+\frac{1}{9×11}$=$\frac{1}{2}×(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11})$=$\frac{1}{2}×(1-\frac{1}{11})$=$\frac{5}{11}$.

5.计算
- (1)$0.75×\frac{8}{9}÷\frac{10}{9}$；\n(2)$8×(-\frac{3}{4})×(-4)×(-2)$；\n(3)$25×\frac{3}{4}-(-25)×\frac{1}{2}+25×(-\frac{1}{4})-2$；\n(4)$(-\frac{1}{6}+\frac{3}{4}-\frac{1}{12})÷(-\frac{1}{48})$.

答案：
(1)原式=$\frac{3}{4}×(\frac{8}{9}×\frac{9}{10})=\frac{3}{5}$.
(2)原式=$[8×(-2)]×[(-\frac{3}{4})×(-4)]=(-16)×3=-48$.
(3)原式=$25×\frac{3}{4}+25×\frac{1}{2}-25×\frac{1}{4}-2$=$25×(\frac{3}{4}-\frac{1}{4}+\frac{1}{2})-2$=25-2=23.
(4)原式=$(-\frac{1}{6}+\frac{3}{4}-\frac{1}{12})×(-48)$=$-\frac{1}{6}×(-48)+\frac{3}{4}×(-48)-\frac{1}{12}×(-48)$=8+3×(-12)+4=-24.