Tính hợp lý:
(75%+1/2): |- \(1\frac{1}{2}\)| - \(\frac{5}{27}\).1,8 . 20120
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2) 1\26+1\27+1\28+........+1\50=1+1\2+1\3+......+1\50 -( 1+1\2+1\3+.....+1\25)=1+1\2+1\3+....+1\50-2.(1\2+1\4+1\6+....+1\50)=1-1\2+1\3-1\4+.....+1\49-1\50=vế phải(đpcm)
a)
\(\frac{8}{11}.\frac{14}{23}+\frac{9}{23}:\frac{11}{8}-\frac{8}{11} \)
\(=\frac{8}{11}.\frac{14}{23}+\frac{9}{23}.\frac{8}{11}-\frac{8}{11}\)
\(=\frac{8}{23}.(\frac{14}{23}+\frac{9}{23}-1)\)
\(=\frac{8}{23}.0\)
=0
b)
\(1,8.\frac{-20}{27}\)+(75%\(-\frac{5}{16}):3\frac{1}{2}\)
=\(\frac{9}{5}.\frac{-20}{27}+(\frac{3}{4}-\frac{5}{16}):\frac{7}{2}\)
=\(\frac{-4}{3}+\frac{1}{8}\)
=\(\frac{-29}{24}\)
a . ( -1/3 ) . 9/11 + ( -8/9 ) . 27
= 9/3 . ( -1/11 ) + 27/9 . ( -8 )
= 3 . ( -1/11 ) + 3 . ( -8 )
= 3 . ( -1/11 + ( -8 ) )
= 3 . ( -89/11 )
= -267/11
b . ( 1/2 - 13/14 ) : 5/7 - ( - - 2/21 + 1/7 ) : 5/7
= -3/7 : 5/7 - 5/21 : 5/7
= ( -3/7 - 5/21 ) : 5/7
= -2/3 : 5/7
= -14/15
\(3C=\frac{3}{1.2.3.4}+\frac{3}{2.3.4.5}+...+\frac{3}{27.28.29.30}\)
\(3C=\frac{4-1}{1.2.3.4}+\frac{5-2}{2.3.4.5}+...+\frac{30-27}{27.28.29.30}\)
\(3C=\frac{1}{1.2.3}-\frac{1}{2.3.4}+\frac{1}{2.3.4}-\frac{1}{3.4.5}+...+\frac{1}{27.28.29}+\frac{1}{28.29.30}\)
\(3C=\frac{1}{1.2.3}-\frac{1}{28.29.30}\Rightarrow C=\left(\frac{1}{1.2.3}-\frac{1}{28.29.30}\right):3\)
chán thím ghê -,-
\(25\left(-\frac{1}{5}\right)^3+\frac{1}{5}-2\left(-\frac{1}{2}\right)^2-\frac{1}{2}\)
\(=\)\(\left(25.\frac{\left(-1\right)^3}{5^3}+\frac{1}{5}\right)-\left(2.\frac{\left(-1\right)^2}{2^2}+\frac{1}{2}\right)\)
\(=\)\(\left(25.\frac{-1}{5^3}+\frac{1}{5}\right)-\left(2.\frac{1}{2^2}+\frac{1}{2}\right)\)
\(=\)\(\frac{1}{5}\left(25.\frac{-1}{5^2}+1\right)-\frac{1}{2}\left(2.\frac{1}{2}+1\right)\)
\(=\)\(\frac{1}{5}\left(-1+1\right)-\frac{1}{2}\left(1+1\right)\)
\(=\)\(\frac{1}{5}.0-\frac{1}{2}.2\)
\(=\)\(-1\)
\(\frac{\frac{2}{5}+\frac{2}{7}-\frac{2}{11}}{\frac{3}{5}+\frac{3}{7}-\frac{3}{11}}+\frac{\frac{1}{4}-\frac{1}{5}+\frac{1}{7}}{\frac{3}{4}-\frac{3}{5}+\frac{3}{7}}\)
\(=\frac{2\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{11}\right)}{3\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{11}\right)}+\frac{1\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{7}\right)}{3\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{7}\right)}\)
\(=\frac{2}{3}+\frac{1}{3}\)
\(=1\)
\(\left(75\%+\frac{1}{2}\right)\text{ : }\left|-1\frac{1}{2}\right|-\frac{5}{27}\cdot1,8\cdot2012^0\)
\(=\left(\frac{3}{4}+\frac{1}{2}\right):\left|-\frac{3}{2}\right|-\frac{5}{27}\cdot\frac{9}{5}\)
\(=\frac{5}{4}\text{ : }\frac{3}{2}-\frac{1}{3}\)
\(=\frac{5}{6}-\frac{1}{3}\)
\(=\frac{1}{2}\)
\(\left(75\%+\frac{1}{2}\right)-\left|-1\frac{1}{2}\right|-\frac{5}{27}\cdot1,8\cdot2012^0\)
\(=\left(\frac{75}{100}+\frac{1}{2}\right)-\left|-\frac{3}{2}\right|-\frac{5}{27}\cdot\frac{9}{5}\cdot1\)
\(=\left(\frac{3}{4}+\frac{1}{2}\right)-\frac{3}{2}-\frac{5}{27}\cdot\frac{9}{5}\)
\(=\left(\frac{3}{4}+\frac{2}{4}\right)-\frac{3}{2}\cdot\frac{1}{3}\)
\(=\frac{5}{4}-\frac{1}{2}=\frac{5}{4}-\frac{2}{4}=\frac{3}{4}\)
Ez mà :)))