\(\frac{\left(13\frac{1}{4}-2\frac{5}{27}-10\frac{5}{6}\right).230\frac{1}{5}+46\frac{3}{4}}{\left(1\frac{3}{10}+\frac{10}{3}\right):\left(12\frac{1}{3}-14\frac{2}{7}\right)}\)
\(A=\frac{\left(13\frac{1}{4}-2\frac{5}{27}-10\frac{5}{6}\right).230\frac{1}{25}+46\frac{3}{4}}{\left(1\frac{3}{10}+\frac{10}{3}\right):\left(12\frac{1}{3}-14\frac{2}{7}\right)}\)
so sánh = cách hợp lí
P1 =\(\left(-\frac{43}{51}\right)\cdot\left(\frac{-19}{80}\right)\)
P2 = \(\left(-\frac{7}{13}\right)\cdot\left(-\frac{4}{65}\right)\cdot\left(-\frac{8}{31}\right)\)
P3= \(-\frac{5}{10}\cdot-\frac{4}{10}\cdot-\frac{3}{10}....\frac{3}{10}\cdot\frac{4}{10}\cdot\frac{5}{10}\)
Tính giá trị của các biểu thức sau một cách hợp lý:
a)A=\(\frac{3^{10}.11+3^{10}.5}{3^9.2^4+2^{10}.13}+\frac{2^{10}.13+2^{10}.65}{2^8.104}\)
b)B=\(\frac{12-\frac{12}{7}-\frac{12}{289}-\frac{12}{85}}{4-\frac{4}{7}-\frac{4}{289}-\frac{4}{85}}:\frac{3+\frac{3}{13}+\frac{3}{169}+\frac{3}{91}}{7+\frac{7}{13}+\frac{7}{169}+\frac{7}{91}}\)
\(\frac{\left(13\frac{1}{4}-2\frac{5}{27}-10\frac{5}{6}\right)\cdot230\frac{1}{5}+46\frac{3}{4}}{\frac{\left(1\frac{3}{7}+\frac{10}{3}\right)}{\left(12\frac{1}{3}-14\frac{2}{7}\right)}}\)
Thực hiện phép tính một cách hợp lý :
A = \(\frac{-10}{3}+\frac{19}{6}.\frac{7}{5}-\frac{19}{3}.\frac{1}{10}+\frac{19}{10}.\frac{4}{3}\)
bài 1 So sánh
a)\(A=\frac{3}{8^3}+\frac{7}{8^4}\) ; \(B=\frac{7}{8^3}+\frac{3}{8^4}\)
b)\(A=\frac{10^{1992}+1}{10^{1991}+1};B=\frac{10^{1993}+1}{10^{1992}+1}\)
c)\(A=\frac{10^7+5}{10^4-8};B=\frac{10^8+6}{10^8-7}\)
d)\(A=\frac{1+5+5^2+...+5^9}{1+5+5^2+...+5^8};B=\frac{1+3+3^2+...+3^9}{1+3+3^2+...+3^8}\)
e)\(A=\frac{2011}{2012}+\frac{2012}{2013};B=\frac{2011+2012}{2012+2013}\)
\(S=\frac{\frac{1}{4}+\frac{1}{6}+\frac{1}{10}}{\frac{5}{4}+\frac{5}{6}+\frac{5}{10}}\)
Tính S
Chứng minh S<\(\frac{3}{10}\)
Bài 3 : a) Tính
\(\frac{\left(13\frac{1}{4}-2\frac{5}{27}-10\frac{5}{6}\right)\cdot230\frac{1}{25}+46\frac{3}{4}}{\left(1\frac{3}{10}+\frac{10}{3}\right):\left(12\frac{1}{3}-14\frac{2}{7}\right)}\)
b) Tính :
\(P=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2012}}{\frac{2011}{1}+\frac{2010}{2}+\frac{2009}{3}+\frac{1}{2011}}\)