19. (12分)计算:
(1)$-40-28-(-19)+(-24)$;
(2)$18-12 ÷(-4) ×\left(-\frac{1}{3}\right)$;
(3)$\left(-\frac{1}{6}+\frac{3}{4}-\frac{1}{12}\right) ×(-48)$;
(4)$(-1)^{4}+(1-0.5) × \frac{1}{3} ×\left[2-(-3)^{2}\right]$.
(1)$-40-28-(-19)+(-24)$;
(2)$18-12 ÷(-4) ×\left(-\frac{1}{3}\right)$;
(3)$\left(-\frac{1}{6}+\frac{3}{4}-\frac{1}{12}\right) ×(-48)$;
(4)$(-1)^{4}+(1-0.5) × \frac{1}{3} ×\left[2-(-3)^{2}\right]$.
答案:(1) -73 (2) 17 (3) -24 (4) -$\frac{1}{6}$
解析:
(1)解:$-40-28-(-19)+(-24)$
$=-40-28+19-24$
$=(-40-28-24)+19$
$=-92+19$
$=-73$
(2)解:$18-12÷(-4)×\left(-\frac{1}{3}\right)$
$=18-(-3)×\left(-\frac{1}{3}\right)$
$=18-1$
$=17$
(3)解:$\left(-\frac{1}{6}+\frac{3}{4}-\frac{1}{12}\right)×(-48)$
$=-\frac{1}{6}×(-48)+\frac{3}{4}×(-48)-\frac{1}{12}×(-48)$
$=8-36+4$
$=-24$
(4)解:$(-1)^4+(1-0.5)×\frac{1}{3}×\left[2-(-3)^2\right]$
$=1+\frac{1}{2}×\frac{1}{3}×(2-9)$
$=1+\frac{1}{6}×(-7)$
$=1-\frac{7}{6}$
$=-\frac{1}{6}$
$=-40-28+19-24$
$=(-40-28-24)+19$
$=-92+19$
$=-73$
(2)解:$18-12÷(-4)×\left(-\frac{1}{3}\right)$
$=18-(-3)×\left(-\frac{1}{3}\right)$
$=18-1$
$=17$
(3)解:$\left(-\frac{1}{6}+\frac{3}{4}-\frac{1}{12}\right)×(-48)$
$=-\frac{1}{6}×(-48)+\frac{3}{4}×(-48)-\frac{1}{12}×(-48)$
$=8-36+4$
$=-24$
(4)解:$(-1)^4+(1-0.5)×\frac{1}{3}×\left[2-(-3)^2\right]$
$=1+\frac{1}{2}×\frac{1}{3}×(2-9)$
$=1+\frac{1}{6}×(-7)$
$=1-\frac{7}{6}$
$=-\frac{1}{6}$
20. (12分)化简:
(1)$8 x-(-3 x-5)$;
(2)$2 m-(m+3)-3(m+1)$;
(3)$2 x^{2} y-\left(3 x y^{2}-2 y x^{2}\right)-3 x y^{2}$;
(4)$\frac{1}{2}[a-4(2 a-3)]-(3 a-5)$.
(1)$8 x-(-3 x-5)$;
(2)$2 m-(m+3)-3(m+1)$;
(3)$2 x^{2} y-\left(3 x y^{2}-2 y x^{2}\right)-3 x y^{2}$;
(4)$\frac{1}{2}[a-4(2 a-3)]-(3 a-5)$.
答案:(1) 11x + 5 (2) -2m - 6 (3) 4x²y - 6xy² (4) -$\frac{13}{2}$a + 11
解析:
(1) 解:原式=8x+3x+5=11x+5
(2) 解:原式=2m-m-3-3m-3=-2m-6
(3) 解:原式=2x²y-3xy²+2x²y-3xy²=4x²y-6xy²
(4) 解:原式=$\frac{1}{2}(a-8a+12)-3a+5$=$\frac{1}{2}(-7a+12)-3a+5$=$-\frac{7}{2}a+6-3a+5$=$-\frac{13}{2}a+11$
(2) 解:原式=2m-m-3-3m-3=-2m-6
(3) 解:原式=2x²y-3xy²+2x²y-3xy²=4x²y-6xy²
(4) 解:原式=$\frac{1}{2}(a-8a+12)-3a+5$=$\frac{1}{2}(-7a+12)-3a+5$=$-\frac{7}{2}a+6-3a+5$=$-\frac{13}{2}a+11$