三、解答题
1. 直接写出答案:
(1) $\left| -\dfrac{2}{3} \right| ÷ \left| +\dfrac{3}{2} \right| = \_\_\_\_\_\_$;
(2) $(-5)+(+9) = \_\_\_\_\_\_$;
(3) $( \dfrac{1}{3} - \dfrac{1}{2} ) × 36 = \_\_\_\_\_\_$;
(4) $(-1)^{999} - (-1)^{1000} = \_\_\_\_\_\_$。
1. 直接写出答案:
(1) $\left| -\dfrac{2}{3} \right| ÷ \left| +\dfrac{3}{2} \right| = \_\_\_\_\_\_$;
(2) $(-5)+(+9) = \_\_\_\_\_\_$;
(3) $( \dfrac{1}{3} - \dfrac{1}{2} ) × 36 = \_\_\_\_\_\_$;
(4) $(-1)^{999} - (-1)^{1000} = \_\_\_\_\_\_$。
答案
解:
(1) $\dfrac{4}{9}$
(2) $4$
(3) $-6$
(4) $-2$
(1) $\dfrac{4}{9}$
(2) $4$
(3) $-6$
(4) $-2$
2. 计算:
(1) $(-5)+(+9)+(-5)+(+3)$;
(2) $16-(-8)÷(-2)+4×(-3)$;
(3) $(-7)×(-5)-90÷(-15)$;
(4) $-3×2^2-(2×3)^2$;
(5) $4-$
$×(-\frac{1}{2})^3$;
(6) $8×(\frac{1}{4})^2+\frac{1}{8}×(-2)^2$;
(7) $4-(-2)^3-3^2÷(-1)$;
(8) $-2^3÷(\frac{4}{9})^2×(-\frac{1}{3})^3$;
(9) $1-\frac{1}{2}×[3×(-\frac{2}{3})^2-(-1)^4]+\frac{1}{4}÷(-\frac{1}{2})^3$.
(1) $(-5)+(+9)+(-5)+(+3)$;
(2) $16-(-8)÷(-2)+4×(-3)$;
(3) $(-7)×(-5)-90÷(-15)$;
(4) $-3×2^2-(2×3)^2$;
(5) $4-$
(6) $8×(\frac{1}{4})^2+\frac{1}{8}×(-2)^2$;
(7) $4-(-2)^3-3^2÷(-1)$;
(8) $-2^3÷(\frac{4}{9})^2×(-\frac{1}{3})^3$;
(9) $1-\frac{1}{2}×[3×(-\frac{2}{3})^2-(-1)^4]+\frac{1}{4}÷(-\frac{1}{2})^3$.
答案
解:
(1) 原式$=[(-5)+(-5)]+[(+9)+(+3)]$
$=-10+12$
$=2$
(2) 原式$=16-4+(-12)$
$=12-12$
$=0$
(3) 原式$=35-(-6)$
$=35+6$
$=41$
(4) 原式$=-3×4 - 6^2$
$=-12-36$
$=-48$
(5) 原式$=4-6×(-\dfrac{1}{8})$
$=4+\dfrac{3}{4}$
$=\dfrac{19}{4}$
(6) 原式$=8×\dfrac{1}{16}+\dfrac{1}{8}×4$
$=\dfrac{1}{2}+\dfrac{1}{2}$
$=1$
(7) 原式$=4-(-8)-9÷(-1)$
$=4+8+9$
$=21$
(8) 原式$=-8÷\dfrac{16}{81}×(-\dfrac{1}{27})$
$=-8×\dfrac{81}{16}×(-\dfrac{1}{27})$
$=\dfrac{81}{2}×\dfrac{1}{27}$
$=\dfrac{3}{2}$
(9) 原式$=1-\dfrac{1}{2}×[3×\dfrac{4}{9}-1]+\dfrac{1}{4}÷(-\dfrac{1}{8})$
$=1-\dfrac{1}{2}×(\dfrac{4}{3}-1)+\dfrac{1}{4}×(-8)$
$=1-\dfrac{1}{2}×\dfrac{1}{3}-2$
$=1-\dfrac{1}{6}-2$
$=-\dfrac{7}{6}$
(1) 原式$=[(-5)+(-5)]+[(+9)+(+3)]$
$=-10+12$
$=2$
(2) 原式$=16-4+(-12)$
$=12-12$
$=0$
(3) 原式$=35-(-6)$
$=35+6$
$=41$
(4) 原式$=-3×4 - 6^2$
$=-12-36$
$=-48$
(5) 原式$=4-6×(-\dfrac{1}{8})$
$=4+\dfrac{3}{4}$
$=\dfrac{19}{4}$
(6) 原式$=8×\dfrac{1}{16}+\dfrac{1}{8}×4$
$=\dfrac{1}{2}+\dfrac{1}{2}$
$=1$
(7) 原式$=4-(-8)-9÷(-1)$
$=4+8+9$
$=21$
(8) 原式$=-8÷\dfrac{16}{81}×(-\dfrac{1}{27})$
$=-8×\dfrac{81}{16}×(-\dfrac{1}{27})$
$=\dfrac{81}{2}×\dfrac{1}{27}$
$=\dfrac{3}{2}$
(9) 原式$=1-\dfrac{1}{2}×[3×\dfrac{4}{9}-1]+\dfrac{1}{4}÷(-\dfrac{1}{8})$
$=1-\dfrac{1}{2}×(\dfrac{4}{3}-1)+\dfrac{1}{4}×(-8)$
$=1-\dfrac{1}{2}×\dfrac{1}{3}-2$
$=1-\dfrac{1}{6}-2$
$=-\dfrac{7}{6}$
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