Thực hiện phép tính:
\(\frac{69}{157}\)- ( 2 +( 3 +(4+5-1 )-1)-1)-1
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\(5+\frac{1}{1+\frac{1}{1+\frac{2}{1+\frac{3}{4}}}}\)\(=5+\frac{15}{7}=\frac{50}{7}\)
69/157 - (2 + (3 + (4 + 5-1)-1)-1)-1
= 69/157 - (2 + 21/68)-1
= 69/157 - (157/68)-1
= 69/157 - 68/157
= 1/157
1-2+3-4+5-6+...+2011-2012
=2012-2011+...+6-5+4-3+2-1
=(2012-2001)+...+(6-5)+(4-3)+(2-1)
=1+1+1+...+1+1(có 1006 số 1)
=1x60
=60
\(6\frac{5}{12}:2\frac{3}{4}+11\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{5}\right)\)
\(=\frac{77}{12}:\frac{11}{4}+\frac{45}{4}.\left(\frac{5}{15}-\frac{3}{15}\right)\)
\(=\frac{77}{12}.\frac{4}{11}+\frac{45}{4}.\frac{2}{15}\)
\(=\frac{7}{3}+\frac{3}{2}\)
\(=\frac{14}{6}+\frac{9}{6}\)
\(=\frac{23}{6}=3\frac{5}{6}\)
\(\frac{69}{157}-\left\{2+\left[3+\left(4+5^{-1}\right)^{-1}\right]^{-1}\right\}^{-1}\)
\(=\frac{69}{157}-\left\{2+\left[3+\left(4+\frac{1}{5}\right)^{-1}\right]^{-1}\right\}^{-1}\)
\(=\frac{69}{157}-\left\{2+\left[3+\left(\frac{21}{5}\right)^{-1}\right]^{-1}\right\}^{-1}\)
\(=\frac{69}{157}-\left[2+\left(3+\frac{5}{21}\right)^{-1}\right]^{-1}\)
\(=\frac{69}{157}-\left[2+\left(\frac{68}{21}\right)^{-1}\right]^{-1}\)
\(=\frac{69}{157}-\left(2+\frac{21}{68}\right)^{-1}\)
\(=\frac{69}{157}-\left(\frac{157}{68}\right)^{-1}\)
\(=\frac{69}{157}-\frac{68}{157}\)
\(=\frac{1}{157}\)