《2025年金版学案同步优学智慧作业七年级数学上册人教版》

乘除混合运算往往先将除法转化为乘法,然后确定积的符号,最后求出结果.

答案： 乘法 符号

- 练习 1 计算$(-1)÷ (-5)× \left(-\dfrac {1}{5}\right)$的结果是(A).
A.$-\dfrac {1}{25}$
B.$-1$
C.$1$
D.$\dfrac {1}{25}$

答案： A
【解析】$(-1)÷ (-5)× \left(-\dfrac{1}{5}\right)=\dfrac{1}{5}× \left(-\dfrac{1}{5}\right)=-\dfrac{1}{25}$.

- 练习 2 下列运算正确的是(D).
A.$1÷ \dfrac {1}{9}× (-9)= -1$
B.$-6-4× 3= -30$
C.$3÷ \left(-\dfrac {5}{4}\right)× \dfrac {4}{5}= -3$
D.$12÷ \left(\dfrac {1}{4}-\dfrac {1}{3}\right)= -144$

答案： D
【解析】A. 原式$=1× 9× (-9)=-81$,故本选项计算错误,不符合题意;
B. 原式$=-6-12=-18$,故本选项计算错误,不符合题意;
C. 原式$=3× \left(-\dfrac{4}{5}\right)× \dfrac{4}{5}=-\dfrac{48}{25}$,故本选项计算错误,不符合题意;
D. 原式$=12÷ \left(-\dfrac{1}{12}\right)=12× (-12)=-144$,故本选项计算正确,符合题意.
故选D.

1. 某冷冻厂一个冷库的室温是$-2^{\circ}C$,现有一批食品需要在$-26^{\circ}C$的室温下保存,如果该厂这个冷库每小时能降温$4^{\circ}C$,则降到所需温度需要(D)小时.
A.$9$
B.$8$
C.$7$
D.$6$

答案： D
【解析】根据题意得:$[-2-(-26)]÷4=24÷ 4=6$(小时),则降到所需温度需要6小时.故选D.

2. 以下计算正确的是(C).

A.$3÷ (-6)× \dfrac {1}{6}= 3÷ (-1)= -3$
B.$[(-4)-(+4)]÷ 6= 0$
C.$5\dfrac {5}{12}÷ (-5)= \left(-5\dfrac {5}{12}\right)× \dfrac {1}{5}= (-5)× \dfrac {1}{5}-\dfrac {5}{12}× \dfrac {1}{5}= -1\dfrac {1}{12}$
D.$16÷ (8 - 2)= 16÷ 8 - 16÷ 2= 2 - 8= -6$

答案： C
【解析】$3÷ (-6)× \dfrac{1}{6}=\left(-\dfrac{1}{2}\right)×\dfrac{1}{6}=-\dfrac{1}{12}$,选项A不符合题意;
$[(-4)-(+4)]÷ 6=(-8)÷ 6=-\dfrac{4}{3}$,选项B不符合题意;
$5\dfrac{5}{12}÷ (-5)=\left(-5\dfrac{5}{12}\right)× \dfrac{1}{5}=(-5)×\dfrac{1}{5}-\dfrac{5}{12}× \dfrac{1}{5}=-1\dfrac{1}{12}$,选项C符合题意;
$16÷ (8-2)=16÷ 6=\dfrac{8}{3}$,选项D不符合题意.
故选C.

3. 计算：
(1) $\dfrac {11}{5}× \left(\dfrac {1}{3}-\dfrac {1}{2}\right)× \dfrac {3}{11}÷ \dfrac {5}{4}$；
(2) $\left[2\dfrac {1}{3}× \left(-\dfrac {1}{2}\right)-\dfrac {2}{3}× (-2)÷ \dfrac {1}{5}\right]× (-12)$.

答案：
(1)$-\dfrac{2}{25}$；
(2)$-66$
【解】
(1)原式$=\dfrac{11}{5}× \left(-\dfrac{1}{6}\right)×\dfrac{3}{11}× \dfrac{4}{5}=-\left(\dfrac{11}{5}× \dfrac{1}{6}× \dfrac{3}{11}× \dfrac{4}{5}\right)=-\dfrac{2}{25}$.
(2)原式$=\left[\dfrac{7}{3}× \left(-\dfrac{1}{2}\right)+\dfrac{4}{3}× 5\right]×(-12)=\left(-\dfrac{7}{6}+\dfrac{20}{3}\right)× (-12)=\left(-\dfrac{7}{6}\right)×(-12)+\dfrac{20}{3}× (-12)=14-80=-66$.