1) \(\left(-34\right)+24+\left(-7\right)+27\)
\(=-34+24-7+27\)
\(=-\left(34-24\right)-7+27\)
\(=-10-7+27\)
\(=-\left(10+7\right)+27\)
\(=-17+27\)
\(=27-17\)
\(=10\)
2) \(99+\left(-100\right)+101\)
\(=99-100+101\)
\(=-100+99+101\)
\(=-\left(100-99\right)+101\)
\(=-1+101\)
\(=101-1\)
\(=100\)
3) \(\left(-75\right)+69+\left(-25\right)+131\)
\(=-75+69-25+131\)
\(=-\left(75-69\right)-25+131\)
\(=-6-25+131\)
\(=-\left(6+25\right)+131\)
\(=-31+131\)
\(=131-31\)
\(=100\)