Tính giá trị của các biểu thức bằng cách hợp lí
a/\(\frac{-8}{18}\)-\(\frac{15}{27}\)
b/\(\frac{19}{24}\)- ( \(\frac{-1}{2}\)\(+\)\(\frac{7}{24}\))
c/ P=\(\frac{3^{11}\times11+3^{11}\times21}{3^9\times2^5}\)
d/\(\frac{2}{1\times2}\)\(+\)\(\frac{2}{2\times3}\)\(+\)\(\frac{2}{3\times4}\)\(+\)... \(+\)\(\frac{2}{99\times100}\)
a) \(-\frac{8}{18}-\frac{15}{27}=-\frac{4}{9}-\frac{5}{9}=\frac{-9}{9}=-1\)
b) \(\frac{19}{24}-\left(-\frac{1}{2}+\frac{7}{24}\right)\)
\(=\frac{19}{24}+\frac{12}{24}-\frac{7}{24}=\frac{24}{24}=1\)
c) \(P=\frac{3^{11}.11+3^{11}.21}{3^9.2^5}\)
\(P=\frac{3^{11}.\left(11+21\right)}{2^9.2^5}=\frac{3^{11}.32}{2^9.32}=3^2=9\)
d) \(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{99.100}\)
\(=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\right)\)
\(=2\left(1-\frac{1}{100}\right)\)
\(=2.\frac{99}{100}=\frac{99}{50}\)
