Tính

a, 4\(\times\left(-\dfrac{1}{2}\right)^3-2\times\left(-\dfrac{1}{2}\right)^2+3\times\left(-\dfrac{1}{2}\right)+1\)

b, \(\dfrac{4^6\times9^5+6^9\times120}{-8^4\times3^{12}+6^{11}}\)

c, \(\dfrac{155-\dfrac{10}{7}-\dfrac{5}{11}+\dfrac{5}{23}}{403-\dfrac{26}{7}-\dfrac{13}{11}+\dfrac{12}{23}}+\dfrac{\dfrac{3}{5}+\dfrac{3}{13}-0,9}{\dfrac{7}{91}+0,2-\dfrac{3}{10}}\)

d,\(\dfrac{30\times4^7\times3^{29}-5\times14^5\times2^{12}}{54\times6^{14}\times9^7-12\times8^5\times7^5}\)

Bài 1.( 2 điểm)Tính bằng cách hợp lí:

a) \(\dfrac{1}{2}+\dfrac{9}{10}+\dfrac{5}{6}-\dfrac{11}{14}-\dfrac{1}{3}+\dfrac{-4}{35}\)

b) \(\left(\dfrac{18}{23}+\dfrac{7}{12}\right)+\left(\dfrac{-13}{19}-\dfrac{3}{4}\right)+\left(\dfrac{-6}{19}+\dfrac{5}{23}\right)\)

c) \(\dfrac{4}{3}+\dfrac{-5}{6}+\dfrac{-1}{4}\)

d) \(\dfrac{5}{6}-\dfrac{7}{5}+\dfrac{17}{30}\)

Tính bằng cách hợp lý:

\(a,\dfrac{2}{3}+\left(\dfrac{5}{7}+\dfrac{-2}{3}\right)\) 

\(b,\left(\dfrac{-1}{4}+\dfrac{5}{8}\right)+\dfrac{-3}{8}\)

\(c,\dfrac{7}{5}.\dfrac{8}{19}+\dfrac{7}{5}.\dfrac{12}{19}-\dfrac{7}{5}.\dfrac{1}{19}\)

\(d,6\dfrac{3}{10}-\left(3\dfrac{4}{7}+2\dfrac{3}{10}\right)\)

\(e,\left(31,12-5,97\right)-\left(-68,88+4,03\right)\)

\(h,3,7.\left(-10,56\right)+3,7.110,56\)     

1, Tìm các số hữu tỉ:

a) Có dạng \(\dfrac{12}{b}\) sao cho \(\dfrac{-8}{19}< \dfrac{12}{b}< \dfrac{-2}{5}\)

b) Có dạng \(\dfrac{9}{b}\) sao cho \(\dfrac{8}{11}< \dfrac{9}{b}< \dfrac{12}{13}\)

2, Tính:

M=\(54-\dfrac{1}{2}\left(1+2\right)-\dfrac{1}{3}\left(1+2+3\right)-\dfrac{1}{4}\left(1+2+3+4\right)-...\dfrac{1}{12}\left(1+2+3+...+12\right)\)

3, Rút gọn các biểu thức sau:

a) A= \(\dfrac{9^9+27^7}{9^6+243^3}\)

b) B= \(\dfrac{\left(\dfrac{2}{3}\right)^5.\left(\dfrac{-27}{8}\right)^2.729}{\left(\dfrac{3}{2}\right)^4.216}\)

4, Cho a,b,c là các số nguyên dương sao cho mỗi số nhỏ hơn tổng của hai số kia. Chứng minh rằng \(\dfrac{a}{b+c}+\dfrac{b}{c+a}+\dfrac{c}{a+b}< 2\)

5, Cho A= \(\dfrac{1001}{1000^2+1}+\dfrac{1001}{1000^2+2}+...+\dfrac{1001}{1000^2+1000}\)

Chứng minh rằng 1<A² < 4