登录
1. 计算:
(1) $(-81)÷ 2\dfrac{1}{4}× \dfrac{4}{9}÷ (-16)$；
(2) $-2^2+(-2)^2-\left|-\dfrac{1}{4}\right|× (-10)^2$；
(3) $-5^2÷ (-3)^2× (-5)^3÷ [-(-5)^2]$；
(4) $-99\dfrac{71}{72}× 36+1^{100}÷ (-1^2-1^3)$.
(1) $(-81)÷ 2\dfrac{1}{4}× \dfrac{4}{9}÷ (-16)$；
(2) $-2^2+(-2)^2-\left|-\dfrac{1}{4}\right|× (-10)^2$；
(3) $-5^2÷ (-3)^2× (-5)^3÷ [-(-5)^2]$；
(4) $-99\dfrac{71}{72}× 36+1^{100}÷ (-1^2-1^3)$.
答案
1. (1)1 (2)-25 (3)$-\dfrac{125}{9}$ (4)-3 600
2. 计算:
(1) $( \dfrac{1}{2} - \dfrac{1}{6} + \dfrac{1}{9} ) ÷ ( -\dfrac{1}{36} ) + 36 ÷ ( \dfrac{1}{2} - \dfrac{1}{6} + \dfrac{1}{9} )$；
(2) $( -\dfrac{1}{42} ) ÷ [ \dfrac{1}{2} - \dfrac{1}{3} + \dfrac{5}{7} + ( -\dfrac{2}{3} )^2 × (-6) ]$。
(1) $( \dfrac{1}{2} - \dfrac{1}{6} + \dfrac{1}{9} ) ÷ ( -\dfrac{1}{36} ) + 36 ÷ ( \dfrac{1}{2} - \dfrac{1}{6} + \dfrac{1}{9} )$；
(2) $( -\dfrac{1}{42} ) ÷ [ \dfrac{1}{2} - \dfrac{1}{3} + \dfrac{5}{7} + ( -\dfrac{2}{3} )^2 × (-6) ]$。
答案
2. (1)65
(2)根据题意得 $[\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{5}{7}+(-\dfrac{2}{3})^2×(-6)]÷ (-\dfrac{1}{42})= [\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{5}{7}+\dfrac{4}{9}×(-6)]×(-42)= -21+14-30+112=75,则原式=\dfrac{1}{75}.$
【反思总结】本题的解答运用了整体法,虽然除法没有分配律,但是这道题在计算的时候可以先计算$[\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{5}{7}+(-\dfrac{2}{3})^2×(-6)]÷ (-\dfrac{1}{42})$,其结果的倒数就是原题的解,注意在最后不要忘记还原.
(2)根据题意得 $[\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{5}{7}+(-\dfrac{2}{3})^2×(-6)]÷ (-\dfrac{1}{42})= [\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{5}{7}+\dfrac{4}{9}×(-6)]×(-42)= -21+14-30+112=75,则原式=\dfrac{1}{75}.$
【反思总结】本题的解答运用了整体法,虽然除法没有分配律,但是这道题在计算的时候可以先计算$[\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{5}{7}+(-\dfrac{2}{3})^2×(-6)]÷ (-\dfrac{1}{42})$,其结果的倒数就是原题的解,注意在最后不要忘记还原.
