《2025年培优课堂七年级数学上册华师大版四川专版》

1. (1)说出下列计算中每一步所依据的运算律或法则：
(-0.4)×(-0.8)×(-1.25)×2.5
=-(0.4×0.8×1.25×2.5) (第一步) =-(0.4×2.5×0.8×1.25) (第二步)
=-[(0.4×2.5)×(0.8×1.25)] (第三步) =-(1×1)= -1.

答案： 第一步:多个有理数相乘的乘法法则；第二步:乘法交换律；第三步:乘法结合律.

(2)用简便方法计算：$ (-\frac{5}{8})×\frac{3}{14}×(-\frac{16}{5})×(-\frac{7}{6}). $

答案： 原式$=-\left(\dfrac{5}{8}× \dfrac{3}{14}× \dfrac{16}{5}× \dfrac{7}{6}\right)$$=-\left(\dfrac{5}{8}× \dfrac{16}{5}× \dfrac{3}{14}× \dfrac{7}{6}\right)$$=-\left[\left(\dfrac{5}{8}× \dfrac{16}{5}\right)× \left(\dfrac{3}{14}× \dfrac{7}{6}\right)\right]$$=-\left(2× \dfrac{1}{4}\right)=-\dfrac{1}{2}$.

$2. $利用运算律进行计算$,$能简便运算的就简便运算$.$　　
$(1) 8×(-\frac{4}{5})×\frac{1}{16} ；$　　
$(2) (-\frac{2}{3})×\frac{2}{7}×(-\frac{3}{4}) ；$　　
$(3) (-2)×(-8)×(-125) ；$　　
$(4) 0.25×(-3.1)×(-8) ；$　　
$(5) (-24)×(\frac{3}{4}-\frac{5}{8}-\frac{5}{12}) ；$　　
$(6) (2\frac{1}{2}-\frac{10}{7}-\frac{5}{12})×(-\frac{4}{5}) ；$　　
$(7) (-2)×(-3)×(-4)×(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}) ；$　　
$(8) -79×\frac{77}{78} ；$　　
$(9) -99\frac{15}{17}×34 ；$　　
$(10) 9\frac{1}{19}×(-19) ；$　　
$(11) (-5.25)×(-4.73)-4.73×(-19.75)+25×(-14.73) ；$　　
$(12) -2×|-5|+(-42)×(-\frac{4}{7})×\frac{11}{12}-(-18) ；$　　
$(13) (-3.85)×(-13)+(-13)×(-6.15)+0.79×\frac{7}{15}+\frac{8}{15}×0.79 ；$　　
$(14) (\frac{7}{9}-\frac{5}{6}+\frac{7}{12}-3\frac{1}{3})×(-36) ；$　　
$(15) 25×\frac{3}{4}+(-25)×\frac{1}{2}+25×(-\frac{1}{4}) .$　　

答案：
(1)解:原式$=-8× \dfrac{4}{5}× \dfrac{1}{16}=-\dfrac{2}{5}$.
(2)解:原式$=\dfrac{2}{3}× \dfrac{2}{7}× \dfrac{3}{4}=\dfrac{1}{7}$.
(3)解:原式$=-2× (8× 125)=-2× 1000=-2000$.
(4)解:原式$=3.1× (0.25× 8)=3.1× 2=6.2$.
(5)解:原式$=-18+15+10=7$.
(6)解:原式$=-2+\dfrac{8}{7}+\dfrac{1}{3}=-\dfrac{11}{21}$.
(7)解:原式$=-12+(-8)+(-6)=-26$.
(8)解:原式$=-78× \dfrac{77}{78}-1× \dfrac{77}{78}=-77\dfrac{77}{78}$.
(9)解:原式$=-3400+4=-3396$.
(10)解:原式$=\left(10-\dfrac{18}{19}\right)× (-19)=10× (-19)-\dfrac{18}{19}× (-19)=-172$.
(11)解:原式$=(-5.25-19.75)× (-4.73)+25× (-14.73)=-25× (-4.73)+25× (-14.73)=25× (4.73-14.73)=25× (-10)=-250$.
(12)解:原式$=-2× 5+24× \dfrac{11}{12}+18=-10+22+18=30$.
(13)解:原式$=(-13)× [(-3.85)+(-6.15)]+0.79× \left(\dfrac{7}{15}+\dfrac{8}{15}\right)=(-13)× (-10)+0.79× 1=130.79$.
(14)解:原式$=\dfrac{7}{9}× (-36)-\dfrac{5}{6}× (-36)+\dfrac{7}{12}× (-36)-\dfrac{10}{3}× (-36)=101$.
(15)解:原式$=25× \left(\dfrac{3}{4}-\dfrac{1}{2}-\dfrac{1}{4}\right)=25× 0=0$.