Question

a) \(\frac{10}{17}\)_\(\frac{5}{13}\) +\(\frac{7}{17}\) +\(\frac{-8}{13}\) _\(\frac{11}{25}\)

b) 1-2+3-4+5-6+.............+2011-2012

Answer 1

a) \(\frac{10}{17}-\frac{5}{13}+\frac{7}{17}+\frac{-8}{13}-\frac{11}{25}\)

\(=\frac{10}{17}+\frac{-5}{13}+\frac{7}{17}+\frac{-8}{13}+\frac{-11}{25}\)

\(=\left(\frac{10}{17}+\frac{7}{17}\right)+\left(\frac{-5}{13}+\frac{-8}{13}\right)+\frac{-11}{25}\)

\(=1+\left(-1\right)+\frac{-11}{25}\)

\(=0+\frac{-11}{25}\)

\(=\frac{-11}{25}\)

Answer 2

a) \(\frac{10}{17}-\frac{5}{13}+\frac{7}{17}+\frac{-8}{13}-\frac{11}{25}\)

\(=\frac{10}{17}+\frac{-5}{13}+\frac{7}{17}+\frac{-8}{13}+\frac{-11}{15}\)

\(=\left(\frac{10}{17}+\frac{7}{17}\right)+\left(\frac{-5}{13}+\frac{-8}{13}\right)+\frac{-11}{15}\)

\(=1+\left(-1\right)+\frac{-11}{15}\)

\(=0+\frac{-11}{15}\)

\(=\frac{-11}{15}\)

b) 1 - 2 + 3 - 4 + ...... + 2011 - 2012 ( có 2012 số )

= ( 1 - 2 ) + ( 3 - 4 ) + ....... + ( 2011 - 2012 ) ( có 1006 nhóm )

= ( - 1 ) + ( - 1 ) + ........ + ( - 1 ) ( có 1006 số )

= ( - 1 ) . 1006

= - 1006