tính nhanh 

a, \(\frac{-2}{5}\cdot\left(\frac{5}{17}-\frac{9}{15}\right)-\frac{2}{5}\cdot\frac{2}{17}+\frac{-2}{5}\)

b, \(\frac{1}{5}\cdot\left(\frac{4}{13}-\frac{9}{11}\right)+\frac{1}{3}\left(\frac{9}{13}-\frac{4}{22}\right)\)

c, \(\left(\frac{1}{2}+1\right)\cdot\left(\frac{1}{3}+1\right)\cdot\left(\frac{1}{4}+1\right)\cdot...\cdot\left(\frac{1}{99}+1\right)\)

d, \(\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot...\cdot\left(1-\frac{1}{100}\right)\)

Tính nhanh giá trị biểu thức sau:

a) \(-\frac{9}{10}\cdot\frac{5}{14}+\frac{1}{10}\cdot\left(-\frac{9}{2}\right)+\frac{1}{7}\cdot\left(-\frac{9}{10}\right)\)

^{b)\(\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{6}+\frac{1}{11}\right)\cdot132\)}

^{c)\(-\frac{2}{3}\cdot\left(\frac{8}{9}\cdot\frac{8}{13}-\frac{8}{27}\cdot\frac{3}{13}+\frac{4}{3}\cdot\frac{22}{39}\right)\)}

Thực hiện phép tính hợp lí nếu có thể:

a/ \(\frac{6}{7}+\frac{1}{7}\cdot\frac{2}{7}+\frac{1}{7}\cdot\frac{5}{7}\)

b/\(\frac{2}{3}\cdot\frac{5}{7}\cdot\frac{-3}{8}\cdot\frac{11}{5}\)

c/\(11\frac{4}{7}-\left(2\frac{3}{5}+5\frac{4}{7}\right)\)

d/\(\frac{3}{4}-\frac{3}{4}\cdot\left(\frac{2}{3}+1\right)\)

e/\(0.5\cdot1\frac{1}{3}\cdot75\%:\frac{2}{5}+\frac{3}{5}\)

f/\(\frac{6}{7}+\frac{5}{8}:5-\frac{3}{16}\cdot\left(-2\right)^2\)

g/\(1\frac{3}{8}+\left(\frac{-5}{6}+\frac{7}{12}\right):\frac{2}{3}\)

h/\(1\frac{1}{4}\cdot\frac{-3}{2}+50\%\cdot98\)

i/\(\left(2,09:1,1+4,5\right)\cdot\frac{5}{8}+4,32\)

Tính giá trị biểu thức

a,\(A=\frac{24\cdot47-23}{24+47-23}\cdot\frac{3+\frac{3}{7}-\frac{3}{11}+\frac{3}{1001}-\frac{3}{13}}{\frac{9}{1001}-\frac{9}{13}+\frac{9}{7}-\frac{9}{11}+9}\)

b,\(M=\frac{1+2+2^2+2^3+...+2^{2012}}{2^{2014}-2}\)

c,\(A=81\cdot\left[\frac{12-\frac{12}{7}-\frac{12}{289}-\frac{12}{85}}{4-\frac{4}{7}-\frac{4}{289}-\frac{4}{85}}:\frac{5+\frac{5}{13}+\frac{5}{169}+\frac{5}{91}}{6+\frac{6}{13}+\frac{6}{169}+\frac{6}{91}}\right]:\frac{158158158}{711711711}\)

d,\(A=\frac{5\cdot\left(2^2.3^2\right)^9\cdot\left(2^2\right)^6-2\cdot\left(2^2\cdot3\right)^{14}\cdot3^4}{5\cdot2^{28}\cdot3^{18}-7\cdot2^{29}\cdot3^{18}}\)

b3 tính nhanh nếu có thể

a \(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}\)

b \(\frac{1}{2}\cdot\frac{1}{2}+\frac{1}{2}\cdot\frac{1}{3}+\frac{1}{3}\cdot\frac{1}{4}+\frac{1}{4}\cdot\frac{1}{5}+\frac{1}{5}\cdot\frac{1}{6}\)

c\(1\frac{1}{24}\cdot5\frac{2}{5}\cdot2-3\frac{7}{9}\cdot2\frac{2}{17}\)

d\(2\frac{3}{13}\cdot\frac{26}{58}\cdot4\cdot2\frac{15}{24}\cdot\frac{8}{21}\)

e \(\left(1-\frac{6}{11}\right)-\frac{5}{11}\)

f\(\left(\frac{15}{7}-\frac{2}{3}\right)+\frac{2}{3}\)

g\(\left(\frac{5}{8}-\frac{1}{4}\right)+\frac{3}{8}\)

\(h\frac{3}{3\cdot5}+\frac{3}{5\cdot8}+\frac{3}{8\cdot11}+\frac{3}{11\cdot14}+\frac{3}{14\cdot17}+\frac{3}{17\cdot20}\)