《2025年同步学习目标与检测七年级数学上册人教版》

【例 2】计算：
(1)$(-5)-(-5)×\frac{1}{10}÷\frac{1}{10}×(-5)$；
(2)$-1-\{ (-3)^{3}-[3+\frac{2}{3}×(-1\frac{1}{2})]÷(-2)\}$.

答案： 解
(1)$(-5)-(-5)× \frac{1}{10}÷ \frac{1}{10}× (-5)=(-5)-(-5)× \frac{1}{10}× 10× (-5)=(-5)-25=-30$.
(2)$-1-\left\{(-3{)}^{3}-\left[3+\frac{2}{3}× \left(-1\frac{1}{2}\right)\right]÷ (-2)\right\}$
$=-1-\left\{-27-\left[3+\frac{2}{3}× \left(-\frac{3}{2}\right)\right]÷ (-2)\right\}$
$=-1-[-27-2÷ (-2)]$
$=-1-[-27-(-1)]$
$=-1-(-26)=25$.

【对点训练 2】计算：$-9-5×(-6)-(-4)^{2}÷(-\frac{1}{3})$.

答案： 解 $-9-5×(-6)-(-4)^{2}÷(-\frac{1}{3})=-9-(-5×6)-16×(-3)=-9+30+48=69$.

【例 3】计算：(1)$\frac{2}{7}×(-\frac{11}{13})+\frac{3}{7}×(-\frac{11}{13})+\frac{2}{7}×(-\frac{11}{13})$.
(2)$(\frac{1}{3}+\frac{5}{6}-\frac{4}{9})×(-18)$.

答案： 解
(1)$\frac{2}{7}× \left(-\frac{11}{13}\right)+\frac{3}{7}× \left(-\frac{11}{13}\right)+\frac{2}{7}× \left(-\frac{11}{13}\right)=\left(-\frac{11}{13}\right)× \left(\frac{2}{7}+\frac{3}{7}+\frac{2}{7}\right)=\left(-\frac{11}{13}\right)× 1=-\frac{11}{13}$.
(2)$\left(\frac{1}{3}+\frac{5}{6}-\frac{4}{9}\right)× (-18)=-18× \frac{1}{3}-18× \frac{5}{6}+18× \frac{4}{9}=-6-15+8=-21+8=-13$.

【对点训练 3】计算：
(1)$\frac{5}{7}÷(-2\frac{2}{5})-\frac{5}{7}×\frac{5}{12}-\frac{5}{3}÷4$；
(2)$(-36)×(\frac{3}{4}-\frac{7}{6}+\frac{11}{12})$.

答案： 解
(1)$\frac{5}{7}÷ \left(-2\frac{2}{5}\right)-\frac{5}{7}× \frac{5}{12}-\frac{5}{3}÷ 4=\frac{5}{7}÷ \left(-\frac{12}{5}\right)-\frac{5}{7}× \frac{5}{12}-\frac{5}{3}× \frac{1}{4}=\frac{5}{7}× \left(-\frac{5}{12}\right)-\frac{5}{7}× \frac{5}{12}-\frac{5}{12}=-\frac{5}{7}× \frac{5}{12}-\frac{5}{7}× \frac{5}{12}-\frac{5}{12}× 1=\frac{5}{12}× \left(-\frac{5}{7}-\frac{5}{7}-1\right)=\frac{5}{12}× \left(-\frac{17}{7}\right)=-\frac{85}{84}$.
(2)$(-36)× \left(\frac{3}{4}-\frac{7}{6}+\frac{11}{12}\right)=-36× \frac{3}{4}+36× \frac{7}{6}-36× \frac{11}{12}=-27+42-33=15-33=-18$.

【例 4】若$\vert a + 3\vert + (b - 2)^{2} = 0$,则$(a + b)^{2024}$的值是(A)
A.1
B.$-1$
C.$-2024$
D.无法计算

答案： A

【对点训练 4】若$\vert x + 1\vert + (y - \frac{1}{3})^{2} = 0$,则$x^{3} + y^{2}$的值是(C)
A.$\frac{1}{9}$
B.$\frac{8}{9}$
C.$-\frac{8}{9}$
D.$-\frac{1}{9}$

答案： C